chunk_uid stringlengths 40 40 | chunk_type stringclasses 2
values | chunk_index int64 0 6.71k | total_chunks int64 1 6.71k | section_title stringlengths 1 157 | embed_text stringlengths 1 83.3k | spans dict | paper_doi stringlengths 0 63 | paper_id_arxiv stringlengths 9 16 | title stringlengths 7 245 | authors listlengths 1 768 | categories listlengths 1 7 | year int64 2k 2.02k | language stringclasses 2
values | discipline stringclasses 8
values | dense_vector listlengths 1.02k 1.02k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1d2e432cebd769b7c3263d95a633829db27bbc51 | subsection | 17 | 39 | A simulation study | We simulate an observational study where individuals may experience a terminating event D, so that the hazard for D depends additively on the treatment A and a covariate process L. A and L are counting processes that jump from 0 to 1 for an individual at the instant treatment is initiated or the covariate changes, resp... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.0220495592802763,
0.0177006833255291,
-0.039033059030771255,
-0.005932018160820007,
0.0005984471645206213,
-0.027436058968305588,
0.019516529515385628,
0.05880899727344513,
0.008224714547395706,
0.012955069541931152,
-0.026993542909622192,
-0.00017226218187715858,
0.00320061924867332,
-... | |
83901bd23f98eda9627da5957e4f507d95bc8b3a | subsection | 18 | 39 | Weight calculation using additive hazard models | We assume that the longitudinal data is organised such that each individual has multiple time-ordered rows; one row for each time either A, L or D changes.Our goal is to convert the data to a format suitable for weighted additive hazard regression. Heuristically, the additive hazard estimates are cumulative sums of lea... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.021459702402353287,
0.0008776193717494607,
-0.03995839133858681,
-0.0027702245861291885,
-0.006452410481870174,
0.01347718108445406,
0.024298610165715218,
0.038096312433481216,
-0.0012277131900191307,
0.001968919998034835,
-0.03715001046657562,
0.038279466331005096,
-0.0077421292662620544... | |
531c60fb5776ffc176ce1b2408b5422b2211f8bc | subsection | 19 | 39 | A marginal structural model | We now suppose the intervention that imposes a marginal treatment initiation rate is causally valid. This implies that the intensity for the event D has the same form under the randomised scenario \tilde{P}, i.e. that the hazard for D under \tilde{P} for the filtration \mathcal {F}_t^{A \cup D \cup L}, generated by A,D... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.044642943888902664,
0.02026173286139965,
-0.017088208347558975,
-0.008139784447848797,
0.007163315545767546,
-0.018339309841394424,
0.01948360912501812,
0.04433779790997505,
0.04787749797105789,
0.0531260184943676,
-0.05611645430326462,
0.010397869162261486,
-0.007289188914000988,
0.045... | |
c8b24fef0cf1f80518f734d9b07b6ce3659ab853 | subsection | 20 | 39 | Simulation details and results | We simulate subjects, none of which are treated at baseline. Initially, all the patients start with L = 0, and the hazards for transitioning from one state to another is constant. As described in Section REF , we fit additive hazard models for the time to treatment initiation, one for the observed treatment scenario, i... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1097/00001648-200009000-00011",
"end": 1337,
"openalex_id": "https://openalex.org/W2009187570",
"raw": "James M Robins, Miguel Angel Hernan, and Babette Brumback. Marginal structural models and causal inference in epidemiology, 2000.",
... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.050504352897405624,
-0.011023986153304577,
-0.013823850080370903,
-0.02674747072160244,
-0.00905568990856409,
0.02563362941145897,
0.023909462615847588,
0.040617093443870544,
0.023863688111305237,
0.022551489993929863,
-0.03939644619822502,
0.05251842364668846,
-0.03509365767240524,
0.0... | |
0620e88f9069bc48c7538e90ca282228e75f3daa | subsection | 21 | 39 | Performance | In Figure REF we plot mean weight estimates based on aggregated simulations of the set-up in Section . The plot suggests that the discrete weights gradually approximate the continuous likelihood ratio as the time discretisation is refined. However, the continuous-time weights (REF ) are closer to the expected value of ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1093/biostatistics/kxy036",
"end": 1888,
"openalex_id": "https://openalex.org/W2886657410",
"raw": "Pål Christie Ryalen, Mats Julius Stensrud, Sophie Fosså, and Kjetil Røysland. Causal inference in continuous time: an example on prostate... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.03949648141860962,
0.009828336536884308,
-0.04746292904019356,
-0.011186599731445312,
-0.003956515807658434,
-0.03156055882573128,
0.04059530049562454,
0.044074900448322296,
0.0255780927836895,
0.03635263442993164,
-0.03296460583806038,
0.027027923613786697,
-0.03281199187040329,
0.0429... | |
58c05fbaf16d4e94b66fc2c8186078dfeebbbb0f | subsection | 22 | 39 | Performance | Utilising the fact that the true likelihood ratio R^i has a constant mean equal to 1, we can find precise estimates of the bias and variance of the additive hazard weight estimator (REF ) at time t_0.We plot the bias and variance of the weight estimator as a function of n under the strategies \kappa _n^1, \kappa _n^2, ... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.018323786556720734,
0.0038848412223160267,
-0.02444188855588436,
-0.0077963825315237045,
-0.0031029144302010536,
-0.02657788246870041,
0.014150967821478844,
0.06185231730341911,
0.018155958503484726,
0.030163303017616272,
-0.046991895884275436,
0.0016306034522131085,
-0.04052288085222244,... | |
9e28ef6e09780928aaeb833bc0d8869cb835d77e | subsection | 23 | 39 | Censoring weights | Most standard martingale-based estimators in survival
analysis are consistent when we have independent censoring, see .
We have assumed independent censoring when
conditioning on \mathcal {V}_0.
A likely situation where this is violated is when we have independent censoring when conditioned on \mathcal {L} \cup \mathca... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/1534625",
"end": 119,
"openalex_id": "https://openalex.org/W2319384619",
"raw": "Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical models based on counting processes. Springer Series in Statistics. S... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.04009459167718887,
0.010183842852711678,
-0.009123503230512142,
-0.00547333899885416,
0.031169425696134567,
-0.057578761130571365,
0.022183232009410858,
0.043451063334941864,
0.013814936392009258,
0.044366464018821716,
-0.009657487273216248,
-0.03969791904091835,
-0.016522999852895737,
... | |
47c96b7211672165b4f174591d522db2b80b336d | subsection | 24 | 39 | Censoring weights | If the model is causal with respect to this intervention, the corresponding
likelihood ratio process is given byR_t^{i,c} = \prod _{s \le t}
\Big ( \frac{\tilde{\lambda }_s^{i,c}}{\lambda _s^{i,c} }\Big )^{\Delta N_s^{i,c} }
\exp \big ( -\int _0^t \tilde{\lambda }_s^{i,c} -
\lambda _s^{i,c} ds \big ).However, as we onl... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.04357462748885155,
0.015325880609452724,
-0.009192476980388165,
0.01393747329711914,
-0.004416965879499912,
-0.0007919452618807554,
0.0035930760204792023,
0.030850104987621307,
0.028408950194716454,
0.034328751266002655,
-0.04674813151359558,
-0.023496123030781746,
-0.007327281404286623,
... | |
f293a325babc27448077d4c97c495fa538b29777 | subsection | 25 | 39 | Discussion | Marginal structural modeling is an appealing concept for causal survival analysis. Here we have developed theory for continuous-time MSMs that may motivate the approach for practical research. Indeed, we show that the continuous-time MSMs yield consistent effect estimates, even if the treatment weights are estimated fr... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1169,
"openalex_id": "",
"raw": "Fred W. Huffer and Ian W. McKeague. Weighted least squares estimation for aalen's additive risk model. Journal of the American Statistical Association, 86(413):114–129, 1991.",
"source_ref_id... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.034243300557136536,
-0.008927064016461372,
-0.0209061149507761,
0.00031878965091891587,
0.004280412569642067,
-0.0256824754178524,
0.035464096814394,
0.029451679438352585,
0.019792139530181885,
0.04309406504034996,
-0.029527978971600533,
0.020661955699324608,
-0.026277612894773483,
0.03... | |
0ba08bce3f61178bea5c5e17b916e0933f134d04 | subsection | 26 | 39 | Funding | The authors were all supported by the research grant NFR239956/F20 - Analyzing clinical health registries: Improved software and mathematics of identifiability. | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.03296167775988579,
0.008415909484028816,
-0.04800807312130928,
-0.008919491432607174,
-0.027803786098957062,
-0.03699032589793205,
0.05002239719033241,
-0.02459917776286602,
0.0769105851650238,
0.008621920831501484,
-0.051762040704488754,
-0.006596150808036327,
-0.04031701385974884,
0.0... | |
260f4d83fe7c19f933d7bcea9696407806dd2bd8 | subsection | 27 | 39 | Appendix: proofs | We need some lemmas to prove Theorem REF .Lemma 1
Suppose that \lbrace V^i\rbrace _i are processes
on [0, T]
such that
\sup _ i E\big [ \sup _{s} | V^i_s | \big ]
< \infty ,
then\lim _{a \rightarrow \infty } \sup _n P \bigg ( \sup _s
\big | \frac{1}{n} \sum _{i=1}^n
V^{i}_{s} \big | \ge a
\bigg ) = 0.By Markov's inequ... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.0385708250105381,
0.026532700285315514,
-0.03054540790617466,
-0.00433692941442132,
-0.009177354164421558,
0.002267637988552451,
-0.011725347489118576,
0.011687204241752625,
-0.014464059844613075,
0.03133879601955414,
-0.05453011393547058,
-0.0017403025412932038,
-0.00836870912462473,
0... | |
13ca8f11ccf9c4968fc672aaa91452ead016a0d8 | subsection | 28 | 39 | Appendix: proofs | Finally, the weak law
of large numbers and the triangle inequality yields& \lim \limits _{n\longrightarrow \infty } E\bigg [ \bigg | \frac{1}{n} \sum _{i = 1} ^n
S_{{(i,n)}} V_{{i}} -E_{ P} [S_{{1}} V_{{1}}] \bigg | \bigg ]
\\\le & \lim \limits _{n\longrightarrow \infty }
E \bigg [\bigg | \frac{1}{n} \sum _{i = 1}^n S_... | {
"cite_spans": []
} | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.0346614271402359,
0.0199089627712965,
-0.05479922890663147,
-0.001962291542440653,
-0.029184555634856224,
0.0018678954802453518,
0.005492127500474453,
0.026118118315935135,
-0.030359260737895966,
0.01987845078110695,
-0.055134858936071396,
0.013806598260998726,
-0.0025973187293857336,
-... | |
a6a7bf6d66b6dffbb0662d218ebd3c270114c6a2 | subsection | 29 | 39 | Appendix: proofs | If the assumptions of Theorem REF are satisfied, then\lim \limits _{n\longrightarrow \infty } P \bigg ( \sup _t \bigg |
\int _0^t \Gamma ^{(n)-1}
\frac{1}{n} \sum _{i=1}^n
R^{(i,n)}_{s-}X_{s-}^{i \intercal } ( \lambda ^{i,D}_s - \gamma ^i_s
)
ds \bigg | \ge \delta \bigg )= 0for every \delta > 0.Assumption \ref {eq:boun... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/1534625",
"end": 1267,
"openalex_id": "https://openalex.org/W2319384619",
"raw": "Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical models based on counting processes. Springer Series in Statistics. ... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.05006800964474678,
0.020350618287920952,
-0.009549840353429317,
-0.02042689360678196,
-0.013600131496787071,
-0.0032589209731668234,
0.022272789850831032,
0.01026684045791626,
-0.008092955686151981,
0.03188364952802658,
-0.03972489386796951,
0.016536783427000046,
-0.02277621626853943,
-... | |
539fb0cb1904585db50f8f53fd431fa6f1ce3065 | subsection | 30 | 39 | Appendix: proofs | Then\Xi ^{(n)}_t := \frac{1}{n} \int _0^t \Gamma ^{(n)-1}_s
X_{s-}^{(n)\intercal } Y^{(n),D}_{s} d
M_s^{(n)}defines a square integrable local martingale with respect to the filtration
\mathcal {F}_{s}^{1,\mathcal {V}_0 \cup \mathcal {L}} \otimes \dots \otimes \mathcal {F}_{s}^{n,\mathcal {V}_0 \cup \mathcal {L}} and\li... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/1534625",
"end": 2144,
"openalex_id": "https://openalex.org/W2319384619",
"raw": "Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical models based on counting processes. Springer Series in Statistics. ... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.0432564839720726,
0.039776429533958435,
-0.007551569025963545,
-0.022528784349560738,
0.015515249222517014,
-0.009463310241699219,
0.030160484835505486,
-0.008081971667706966,
0.0236430112272501,
0.05439877137541771,
-0.013477585278451443,
0.019888214766979218,
-0.01185966469347477,
0.0... | |
476870fb295ec30fedd460169d6e73990373ddec | subsection | 31 | 39 | Appendix: proofs | Moreover, Lemma REF
implies that
\int _0^\cdot \Gamma ^{(n)-1} \frac{1}{n} \sum _{i=1}^n
R^{(i,n)}_{s-}X_{s-}^{i \intercal } ( \lambda ^{i,D}_s - \gamma ^i_s
)
ds
converges in same sense to 0, which proves the consistency.To see that B^{(n)} is P-UT, note that it coincides
with the sum of B_t,
\Xi ^{(n)} and \int _0^... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1093/biomet/asy035",
"end": 540,
"openalex_id": "https://openalex.org/W2962811541",
"raw": "Pål C Ryalen, Mats J Stensrud, and Kjetil Røysland. Transforming cumulative hazard estimates. Biometrika, page asy035, 2018.",
"source_ref_... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.01777329295873642,
0.006910988129675388,
-0.052968986332416534,
-0.01017578225582838,
-0.0022578947246074677,
-0.014394078403711319,
0.03325817734003067,
0.021083854138851166,
-0.01910056732594967,
0.03890291228890419,
-0.04991777986288071,
0.03365483507514,
0.014294913969933987,
-0.010... | |
012e1bbce77c9bea22b6f82c0e3a6f4163996238 | subsection | 32 | 39 | Proof of Theorem | Lemma 6
Suppose that REF . and REF . from Theorem REF are satisfied, and that\lim _{a \rightarrow \infty }
\sup _n P \bigg ( \sup _t \big | \theta ^{(i,n)}_t \big | \ge a
\bigg ) = 0,
\theta _{t-}^{(i,n)}
converges to \theta ^i_t in probability for each i and t.Then we have that K^{(i,n)} is predictably uniformly t... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/2290171",
"end": 1833,
"openalex_id": "https://openalex.org/W2081877251",
"raw": "Jean Jacod and Albert N. Shiryaev. Limit theorems for stochastic processes, volume 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental P... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.020766127854585648,
0.04961899295449257,
-0.009589647874236107,
-0.007598480209708214,
-0.022475022822618484,
0.007529819384217262,
-0.0057522631250321865,
-0.009345520287752151,
0.028196770697832108,
0.042386703193187714,
-0.021956251934170723,
0.024778978899121284,
0.010589046403765678,... | |
495e679b48656dcc642cdc77d0b748b218e8ebc7 | subsection | 33 | 39 | Proof of Theorem | The latter property holds due to \ref {item:tightthetan}), \ref {item:thetaconvergence}) and
.Since \lbrace \int _0^t Y_s^i Z_{s-}^{i\intercal } dW^{(n)}_s \rbrace _n converges in the skorokhod topology, we have that \lbrace \sup _{t \le T}|\int _0^t Y_s^i Z_{s-}^{i\intercal } dW^{(n)}_s | \rbrace _n is tight . Therefo... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/1534625",
"end": 94,
"openalex_id": "https://openalex.org/W2319384619",
"raw": "Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical models based on counting processes. Springer Series in Statistics. Sp... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.007182079367339611,
0.01589745469391346,
0.010801725089550018,
0.009321827441453934,
-0.014440441504120827,
-0.01206802949309349,
0.0201082956045866,
-0.03594472259283066,
0.0010593852493911982,
0.029033450409770012,
-0.037104230374097824,
0.021954353898763657,
-0.025615954771637917,
0.... | |
be32b6c7fc2cc6df45b2da7d7a9e63ef6e0936d1 | subsection | 34 | 39 | Proof of Theorem | For the same reason we also have\lim \limits _{n\longrightarrow \infty } P\bigg ( \sup _{t \le T} | n ^{-1/2} \int _0^t Y_s^i \tilde{Z}_{s-}^{i \intercal } d\tilde{W}^{(n)}_s |\ge \epsilon \bigg ) = 0.By combining (REF ),(REF ) and (REF ),
we obtain that\lim \limits _{n\longrightarrow \infty } P\bigg ( \sup _{t \le T} ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1093/biomet/asy035",
"end": 963,
"openalex_id": "https://openalex.org/W2962811541",
"raw": "Pål C Ryalen, Mats J Stensrud, and Kjetil Røysland. Transforming cumulative hazard estimates. Biometrika, page asy035, 2018.",
"source_ref_... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
0.0027299884241074324,
0.026632171124219894,
-0.024632850661873817,
0.00600559264421463,
-0.02183990739285946,
-0.022709840908646584,
0.009981340728700161,
-0.005524840205907822,
0.011019156314432621,
0.04319142922759056,
-0.04258095100522041,
0.013995244167745113,
-0.01927589252591133,
0.... | |
a17448641d3c59b975dcf41e7791a71bc290298b | subsection | 35 | 39 | Proof of Theorem | This means that K^{(i,n)} is a sum of three processes that are
P-UT, and must therefore be P-UT itself.Lemma 7
Suppose that\lbrace \kappa _n\rbrace _n increasing sequence of positive numbers such that
\lim \limits _{n\longrightarrow \infty } \kappa _n = \infty \text{ and }
\sup _n \frac{\kappa _n }{\sqrt{n}} < \infty ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/1534625",
"end": 1591,
"openalex_id": "https://openalex.org/W2319384619",
"raw": "Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, and Niels Keiding. Statistical models based on counting processes. Springer Series in Statistics. ... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
0.0014850900042802095,
0.014368269592523575,
-0.01936626061797142,
-0.004460039082914591,
-0.021472284570336342,
-0.02347148023545742,
-0.023257825523614883,
-0.0023883527610450983,
-0.03329959139227867,
0.049018461257219315,
-0.029026499018073082,
0.004940761718899012,
-0.008920078165829182... | |
c0d05ccfaf5c68fa2377c7f552ead5087ee0339b | subsection | 36 | 39 | Proof of Theorem | Therefore
implies that
\int _0 ^\cdot Y_s^{i,A} Z_{s-}^{i\intercal } d
W^{(n)}_s
converges in law to a continuous process, so it is C-tight.
Moreover, from we have that\lim _{n \longrightarrow \infty } P \bigg ( \sup _{1/\kappa _n \le t \le T}
\Big |
\int _0 ^t Y_s^{i,A} Z_{s-}^{i\intercal } d
W^{(n)}_s -
\int _0 ^{... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/2290171",
"end": 143,
"openalex_id": "https://openalex.org/W2081877251",
"raw": "Jean Jacod and Albert N. Shiryaev. Limit theorems for stochastic processes, volume 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental Pr... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.016994589939713478,
0.0378030464053154,
-0.015880940482020378,
0.01879473403096199,
-0.014355394057929516,
-0.014645247720181942,
-0.035636771470308304,
0.010045724920928478,
-0.019710062071681023,
0.030404144898056984,
-0.0032551351469010115,
-0.0013262721477076411,
0.006613244768232107,... | |
58ebc934e80e48650b8ca91e09e41bb62e3230c0 | subsection | 37 | 39 | Proof of Theorem | Combining (REF ) and (REF ) yields the claim.[Proof of Theorem REF ]Combining (REF ) and the decomposition in the proof of Lemma
REF , we see that\lim \limits _{n\longrightarrow \infty } P \bigg ( \sup _{ 1/ \kappa _n \le t \le T} \bigg |
\kappa _n \int _{t- 1/\kappa _n} ^t Y_s^{i,A}
\tilde{Z}_{s-}^{i\intercal } d
\til... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/2290171",
"end": 1604,
"openalex_id": "https://openalex.org/W2081877251",
"raw": "Jean Jacod and Albert N. Shiryaev. Limit theorems for stochastic processes, volume 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental P... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
-0.013698267750442028,
0.02582535333931446,
-0.008214384317398071,
-0.004233039449900389,
-0.005064392928034067,
-0.011921154335141182,
-0.028891446068882942,
0.009510991163551807,
-0.00549151049926877,
0.028891446068882942,
-0.039935484528541565,
0.001817156095057726,
0.0013824114575982094,... | |
2c4d746d1595e62d14d472251a83da5e3cf042df | subsection | 38 | 39 | Proof of Theorem | Since K^{(i,n)} is P-UT,R_t^{(i,n)} = 1 + \int _0^t R_{s-}^{(i,n)} dK_{s}^{(i,n)}andR_t^{i} = 1 + \int _0^t R_{s-}^{i} dK_{s}^{i}
implies that R^{(i,n)} converges to
R^{i} in probability. | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.2307/2290171",
"end": 187,
"openalex_id": "https://openalex.org/W2081877251",
"raw": "Jean Jacod and Albert N. Shiryaev. Limit theorems for stochastic processes, volume 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental Pr... | 1802.01946 | The additive hazard estimator is consistent for continuous-time marginal
structural models | [
"Pål Christie Ryalen",
"Mats Julius Stensrud",
"Kjetil Røysland"
] | [
"stat.ME"
] | 2,018 | en | Statistics | [
0.002458593575283885,
0.048920098692178726,
-0.03430205211043358,
0.01721206121146679,
-0.054657451808452606,
0.01390087604522705,
-0.02536032535135746,
-0.03442412242293358,
-0.0013122671516612172,
0.020370658487081528,
-0.020523248240351677,
0.008102486841380596,
-0.0003275899507571012,
... | |
907ce9527fc5fff25884030cd445e04604f5edfc | abstract | 0 | 10 | Abstract | We propose a flow-insensitive analysis that prunes out portions of code which
are irrelevant to a specified set of data-flow paths. Our approach is fast and
scalable, in addition to being able to generate a certificate as an audit for
the computed result. We have implemented our technique in a tool called DSlicer
and a... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.08992162346839905,
0.015345585532486439,
-0.03769626468420029,
-0.007291251327842474,
-0.032812539488077164,
-0.0478300005197525,
-0.004750187508761883,
-0.011415711604058743,
0.01066789124161005,
0.0737442746758461,
-0.015421893447637558,
-0.0026917727664113045,
0.0027852505445480347,
... | |
5c18d8d3f50e809ca15674afc9c7eeb75c0e179b | subsection | 1 | 10 | Introduction | Applying static analysis naively may result in exploring parts of code which are irrelevant to a property of interest.
We propose a lightweight approach for slicing programs that can be invoked by other tools as a preprocessing phase. As slicing criterion, our technique accepts a set of data-flow paths and returns, as ... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.046350155025720596,
0.011892675422132015,
-0.044671908020973206,
0.013410726562142372,
0.009237991645932198,
-0.03515166416764259,
0.03243595361709595,
-0.001206240733154118,
-0.0067702047526836395,
0.05812840536236763,
-0.02207658812403679,
-0.013799775391817093,
0.012365635484457016,
... | |
92c9c9f26e792e04a924f95d991ffd26b0d8a3d4 | subsection | 2 | 10 | Body | To illustrate our approach, let us consider the simple Java example in Figure REF (a). In the function main, an instance of the class C, defined in Figure REF (b), is created and its methods m1, m3, m4 and m5 are consecutively invoked. The function source returns some private (integer) information, it could be for exam... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.054783981293439865,
0.0034697791561484337,
-0.06390956044197083,
0.021410007029771805,
0.02044861577451229,
-0.031893737614154816,
0.03723479434847832,
-0.0025827824138104916,
0.006748806685209274,
0.0057607111521065235,
0.010911015793681145,
0.0021135322749614716,
-0.034640565514564514,
... | |
842db8d3a640724636cbef1ee8bd2bea7954e1b0 | subsection | 3 | 10 | Body | They appear (are used) in the methods m3, m4 and m5, hence they are the relevant methods. Methods m1 and m2 can then be safely discarded. In the next section, we cover the translation from a program to an assignment graph in more details.A key question that may arise is: how can we trust the result (soundness) of the a... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1682,
"openalex_id": "",
"raw": "S. Arzt, S. Rasthofer, C. Fritz, E. Bodden, A. Bartel, J. Klein, Y. L. Traon, D. Octeau, and P. McDaniel. Flowdroid: precise context, flow, field, object-sensitive and lifecycle-aware taint analysi... | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.0465579628944397,
-0.018855059519410133,
-0.06596220284700394,
0.012913275510072708,
0.03307262808084488,
-0.012714961543679237,
-0.02262302115559578,
-0.03098270855844021,
0.013508216477930546,
0.03658125549554825,
-0.01586509868502617,
0.029884355142712593,
-0.01646004058420658,
0.012... | |
52d5021c69e980c84bb7933a8d401d4a33784bb5 | subsection | 4 | 10 | Assignment Graph: a Compact Representation | Our analysis is applied to object oriented programs, therefore we need to account for the main features distinguishing them from simple imperative programs. We use a Jimple-like intermediary representation which allows to encode most of the language constructs using a minimal set of three-address-based instructions. It... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/3-540-46423-9_2",
"end": 318,
"openalex_id": "https://openalex.org/W1536265389",
"raw": "R. Vallée-Rai, E. Gagnon, L. J. Hendren, P. Lam, P. Pominville, and V. Sundaresan. Optimizing java bytecode using the soot framework: Is it fea... | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.05987695977091789,
-0.00896475836634636,
-0.05426158756017685,
0.025116583332419395,
0.00031448181835003197,
-0.031952690333127975,
0.03769013285636902,
-0.015388866886496544,
0.00878927856683731,
0.018417811021208763,
-0.026169465854763985,
-0.021942676976323128,
0.008667205460369587,
... | |
803ebb3e6ea7d3d98285e18b303e7339c367816e | subsection | 5 | 10 | Slice Computation | In this section we describe our approach for computing a slice with respect to a set of sources SR and sinks SK. The slicing criterion is all data-flow paths r \leadsto k such that r \in SR and k \in SK.This is achieved via algorithm ComputeSlice (Algorithm ) which takes as parameters an assignment graph G, a set of so... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.03671387583017349,
-0.004757086746394634,
-0.041657887399196625,
0.06402801722288132,
0.016220634803175926,
-0.003158675041049719,
0.033662013709545135,
-0.013008552603423595,
-0.00984224770218134,
0.038148246705532074,
0.032319195568561554,
0.005382718052715063,
0.003732806071639061,
0... | |
b7f66794abbf6454a166e9d8d90d6ae3642eb225 | subsection | 6 | 10 | Slice Computation | \mathsf {marked}(id^{\prime },G,+) \wedge \lnot \mathsf {marked}(id^{\prime },G,-)
\mathsf {mark}(id^{\prime },G,-)
L := L \cup \lbrace id^{\prime }\rbraceids := \lbrace id \;|\; id \in \mathsf {nodes}(G) \wedge \mathsf {marked}(id,G,+) \wedge \mathsf {marked}(id,G,-)\rbracevia\_locals := \lbrace m \;|\; \exists c \;\... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.02191716991364956,
0.011614879593253136,
-0.030494781211018562,
-0.02017722837626934,
0.006513337604701519,
-0.007883160375058651,
-0.0009777637897059321,
0.04584901034832001,
0.0043078837916255,
-0.013774544931948185,
-0.03843136131763458,
-0.011935395188629627,
-0.009859674610197544,
... | |
f1d02e1d4e5cb15ce4d5320263cefc87f772d742 | subsection | 7 | 10 | DSlicer: Implementation and Experiments | We implemented our approach in a tool called DSlicer, which is written in Python and uses Androguardhttps://github.com/androguard as front-end for parsing and decompiling Android applications. It takes as input an Android application in bytecode format (APK) and a configuration file containing the sources and sinks to ... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.049730557948350906,
-0.019236266613006592,
-0.030372250825166702,
-0.001125992857851088,
-0.015445456840097904,
-0.049547500908374786,
0.009358802810311317,
-0.027367061004042625,
-0.02529241144657135,
0.048693232238292694,
-0.007635013200342655,
-0.02841963991522789,
-0.01899219118058681... | |
e2785b31020498cc2f085f9fb4e65eaacd6d7851 | subsection | 8 | 10 | Related work | Our work is at the intersection of several topics: program slicing, data-flow analysis, and program certification.Program slicing was originally proposed by Weiser . While the initial proposal defined a slice as a set of statements that might influence a program point of interest (criterion), a dynamic variant was exam... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1109/tse.1984.5010248",
"end": 165,
"openalex_id": "https://openalex.org/W2293624369",
"raw": "M. Weiser. Program slicing. In Proceedings of the 5th International Conference on Software Engineering, San Diego, California, USA, March 9-12... | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.07784128934144974,
-0.01616351492702961,
-0.0456974133849144,
0.047559499740600586,
-0.004056141711771488,
-0.008715171366930008,
0.032296501100063324,
-0.008799117989838123,
0.019200850278139114,
0.05384785681962967,
0.007723076734691858,
-0.027885496616363525,
-0.01137093361467123,
0.... | |
bd7b10b6c873e4c3a60e431541763c1efc14054f | subsection | 9 | 10 | Conclusion and Further Work | We presented a lightweight slicing approach for object oriented programs that can detect and discard parts of code that are irrelevant to a specified set of data-flow paths. A distinguishing feature of our approach lies in the compact representation it uses, allowing it to efficiently encode programs without sacrificin... | {
"cite_spans": []
} | 1808.01232 | Data-Flow Guided Slicing | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.SE"
] | 2,018 | en | Computer Science | [
-0.03760089352726936,
0.016664031893014908,
-0.031679973006248474,
0.01800692081451416,
-0.006348202470690012,
-0.010277679190039635,
0.018357902765274048,
-0.010903343558311462,
0.011590047739446163,
0.05750006437301636,
-0.01127721555531025,
-0.006958606652915478,
-0.0006661988445557654,
... | |
987dcba2258758f7c71ed1cd3cb530433dd06995 | abstract | 0 | 22 | Abstract | Proof-carrying-code was proposed as a solution to ensure a trust relationship
between two parties: a (heavyweight) analyzer and a (lightweight) checker. The
analyzer verifies the conformance of a given application to a specified
property and generates a certificate attesting the validity of the analysis
result. It suff... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.04596477001905441,
-0.018450003117322922,
-0.06769578903913498,
0.011826924979686737,
-0.012292372062802315,
-0.02859826758503914,
-0.0419665090739727,
0.032901741564273834,
0.010445845313370228,
0.02881191484630108,
-0.017198637127876282,
-0.00861457921564579,
-0.0036987753119319677,
0... | |
84564422ee6de20ae50a1c2bbd8735058c034f4d | subsection | 1 | 22 | Introduction | Static data-flow analysis has proven its effectiveness in assessing the security of Android applications by identifying data leaks , , , , , , . Once we want to install an application on a mobile device, how can we trust the outcome of these tools? The analysis might be broken, or a (malicious) tool can provide a false... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 144,
"openalex_id": "",
"raw": "A. P. Fuchs, A. Chaudhuri, and J. S. Foster. SCanDroid: Automated Security Certification of Android Applications. Technical Report CS-TR-4991, Department of Computer Science, University of Maryland,... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.05821521580219269,
-0.005819995887577534,
-0.06083916872739792,
0.008146468549966812,
-0.002684978535398841,
-0.027765117585659027,
-0.020152593031525612,
0.02976359613239765,
0.0021434060763567686,
0.03520983085036278,
-0.011983241885900497,
-0.007707871496677399,
-0.014035114087164402,
... | |
17e5925f07326386107013bf3b8fd2ccd9ee3f3d | subsection | 2 | 22 | Example | We start by illustrating our idea through an example. Consider the simple code in Figure REF as part of an Android application. To ease the presentation, we omit irrelevant details. We have the root procedure foo which makes call to function bar which, in turn, calls procedures getId, Send and getNumber. Function getId... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.061779238283634186,
0.005559063516557217,
-0.053812649101018906,
-0.04447250813245773,
0.0211679358035326,
-0.06013097986578941,
-0.008958600461483002,
0.000920469465199858,
-0.049051009118556976,
0.03272102028131485,
-0.023518232628703117,
0.0011780101340264082,
-0.04935624077916145,
0... | |
7db04ff71b192dfd6fc0cc1c688792b9bf6fb8da | subsection | 3 | 22 | Body | Our analysis attempts to find all data leaks, i.e., paths leading from sources to sinks. In addition, it outputs a certificate corroborating its outcome.Let us use id and num to respectively refer to the sources getDeviceId and getLine1Number. We also write sms to refer to the sink sendTextMessage. Our analysis compute... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.08581866323947906,
0.013252757489681244,
-0.05276688188314438,
-0.02436920441687107,
0.03738544136285782,
-0.04779232665896416,
0.022156596183776855,
0.017014190554618835,
-0.03027457743883133,
0.03387578949332237,
-0.0036450806073844433,
0.030396653339266777,
0.0035859504714608192,
0.0... | |
90af14e566f3b02346c91f2e9b613db16c304b51 | subsection | 4 | 22 | Body | For example, assuming the summary for \mathsf {bar} is \lbrace \mathsf {(sms, id)}, \mathsf {(ret, num)}\rbrace , the summary for \mathsf {foo} must be \lbrace \mathsf {(sms, id)}, \mathsf {(ret, num)}\rbrace , which is the case. This is performed by the checker, which takes as input a certificate (computed map) and an... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1145/24039.24041",
"end": 1454,
"openalex_id": "https://openalex.org/W2144344516",
"raw": "J. Ferrante, K. J. Ottenstein, and J. D. Warren. The program dependence graph and its use in optimization. ACM Trans. Program. Lang. Syst., 9(3):3... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.05618641898036003,
0.005936044733971357,
-0.03735588118433952,
-0.007523059379309416,
0.014008454978466034,
-0.041903287172317505,
0.03366301953792572,
-0.002857389161363244,
0.0035612452775239944,
0.05618641898036003,
-0.03525003418326378,
0.006920299027115107,
-0.0031206198036670685,
... | |
96f8fca6cad7b4adaef8f3277136809b2bfd8cec | subsection | 5 | 22 | Preliminaries | In this section we provide some ingredients required for the presentation. We start by introducing a language that we consider along our study. | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
0.016452325507998466,
0.02484636940062046,
-0.008409305475652218,
0.029424937441945076,
-0.022206060588359833,
-0.012675005942583084,
0.011507471092045307,
0.031073223799467087,
0.02829555794596672,
0.009508161805570126,
0.010042328387498856,
-0.0026689243968576193,
-0.026021534577012062,
... | |
51daee1ce8593b7fee52b26705def03bbd660e98 | subsection | 6 | 22 | Intermediary Representation | Without loss of generality, we consider an object oriented language, accounting for the features distinguishing it from simple imperative languages. We use a Jimple-like intermediary representation which allows us to encode most of the language constructs using a minimal set of instructions. It has been shown that the ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/3-540-46423-9_2",
"end": 293,
"openalex_id": "https://openalex.org/W1536265389",
"raw": "R. Vallée-Rai, E. Gagnon, L. J. Hendren, P. Lam, P. Pominville, and V. Sundaresan. Optimizing java bytecode using the soot framework: Is it fea... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.036623191088438034,
0.009117648005485535,
-0.017899584025144577,
0.0011473358608782291,
-0.01861678808927536,
-0.050112731754779816,
0.049654942005872726,
-0.008842973969876766,
-0.020600544288754463,
-0.00497083505615592,
-0.007774797733873129,
-0.0168619267642498,
-0.008301256224513054,... | |
043b2c44be30755ee21443ffcb393994ef6942e3 | subsection | 7 | 22 | Term Representative | A key challenge faced when designing any program analysis is aliasing. As we want our analysis to scale to large applications, we need a light but sound solution for the aliasing problem. Therefore, we use the approach proposed by Vallée et al . Their idea is based on the observation that only objects of compatible typ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1145/353171.353189",
"end": 245,
"openalex_id": "https://openalex.org/W1974608873",
"raw": "V. Sundaresan, L. J. Hendren, C. Razafimahefa, R. Vallée-Rai, P. Lam, E. Gagnon, and C. Godin. Practical virtual method call resolution for java.... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.030288541689515114,
0.02807602845132351,
-0.017608553171157837,
0.07342491298913956,
0.0018234159797430038,
-0.003374082501977682,
0.03781108558177948,
0.011199893429875374,
0.010810796171426773,
0.017196567729115486,
0.011344851925969124,
-0.008155780844390392,
0.02767930179834366,
0.0... | |
0da841e5cafe4169b297661cde70ea7aa8f61326 | subsection | 8 | 22 | Field Access | Two terms o_1.f and o_2.f are aliases if o_1 and o_2 points to the same object. Hence, all potential field access that are aliases must map to the same representative. Observe that in type safe languages, like Java, o_1.f and o_2.f can be aliases only if o1 and o2 belong to the same type hierarchy.Given an object o who... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.03500175476074219,
0.03948759660124779,
-0.03341492637991905,
0.03820592537522316,
0.013388858176767826,
-0.017622942104935646,
0.020689791068434715,
0.010589023120701313,
0.018324807286262512,
0.014945169910788536,
-0.01247338019311428,
-0.022902194410562515,
0.009940559975802898,
-0.0... | |
0c4e580757ffbf10397717e8d826ce9e358fa537 | subsection | 9 | 22 | Array Access | An l-value representing an array access also leads to aliasing. Here the aliasing is due to two causes: reference and index. Two terms a[i] and a[j] refer to the same memory location if i = j. In another scenario, terms a[i] and b[i] also refer to the same memory location if a and b points to the same array, i.e, store... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.019426139071583748,
0.027529263868927956,
-0.02577435038983822,
0.039157480001449585,
-0.02653735689818859,
-0.02134891413152218,
0.021974578499794006,
0.02182197757065296,
0.003301909426227212,
0.02073850855231285,
0.012009717524051666,
0.013467059470713139,
-0.002248960779979825,
0.02... | |
1432f7536788a9b1f44ead6ae7ead60470644354 | subsection | 10 | 22 | Control Flow Graph and Call Graph | Our analysis proceeds at the control flow graph level. Each function is associated with a corresponding control flow graph \mathit {CFG}. A \mathit {CFG} is a directed graph (N,E) where N is the set of pairs (\ell ,st), such that st is a program basic statement and \ell is the corresponding program location. The relati... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1145/353171.353189",
"end": 1600,
"openalex_id": "https://openalex.org/W1974608873",
"raw": "V. Sundaresan, L. J. Hendren, C. Razafimahefa, R. Vallée-Rai, P. Lam, E. Gagnon, and C. Godin. Practical virtual method call resolution for java... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.04608328267931938,
-0.024186095222830772,
-0.06329584866762161,
-0.0007939638453535736,
0.004635032266378403,
-0.047670260071754456,
-0.04815855994820595,
-0.012939942069351673,
-0.013710539788007736,
0.037477001547813416,
0.00034643529215827584,
0.004638846963644028,
0.010826519690454006... | |
fddd1a71057317cf137bbd8142b4ce3be8bbe39e | subsection | 11 | 22 | Data-Flow Certification | As seen in section , our approach has two main components: an analyzer and a checker. The analyzer takes as input an application and produces a certificate. The checker takes as input an application and a certificate, and answers whether the certificate is valid with respect to the input application. As we are in the c... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.030121346935629845,
0.006946678273379803,
-0.04733354598283768,
0.0435187853872776,
0.022552862763404846,
0.0014515162911266088,
-0.006767384707927704,
0.013565286993980408,
0.008415360935032368,
0.04211495444178581,
-0.01383994985371828,
-0.019653644412755966,
-0.0028229225426912308,
0... | |
24ff9a98bdb15a7217acebc4dfdfe41e57fa33a7 | subsection | 12 | 22 | Abstract Domain | A natural way for encoding inter-variable flows is through an abstract domain D representing the powerset of pairs of l-value representatives (section ). Hence, aliases are taken into account in D. We also need to include symbols associated with sources and sinks. Let SR be the set of method identifiers representing so... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.03329204022884369,
0.016676533967256546,
-0.053615134209394455,
0.03146113082766533,
-0.004539129789918661,
-0.015616132877767086,
0.011565245687961578,
-0.001049912185408175,
0.01176359411329031,
0.051509588956832886,
0.02377130836248398,
0.01389965508133173,
0.027280552312731743,
0.00... | |
1f31073d6ca64ba48cc812e6cdb788cde164c784 | subsection | 13 | 22 | Transfer Function | To capture variable dependency relations induced by the program, we model the effect of program basic statements, belonging to our language L, on elements of the abstract domain D. This is achieved through function F that we define below.Let L_b denotes the set of basic statements in L. Given a set of facts d \in D and... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.02430909313261509,
0.01021653413772583,
-0.05133445933461189,
0.02038728818297386,
0.009934225119650364,
-0.035982951521873474,
0.036837510764598846,
0.0287955179810524,
0.005859819240868092,
0.013398232869803905,
-0.023713955655694008,
-0.004524574149399996,
-0.012383446097373962,
0.05... | |
8a2985edbe7c835f69f22b9d931398bb99813237 | subsection | 14 | 22 | Transfer Function | Note that summaries for functions are computed iteratively, on-the-fly, during the analysis as we will see later.Finally, a conditional cond does not have any effect on the input facts, making the transfer function F behave as an identity function.
[Table: Definition of functions \mathsf {flow}and \mathsf {kill} for th... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.01347281876951456,
0.01441881526261568,
-0.045957110822200775,
0.019667567685246468,
0.014586652629077435,
-0.013274464756250381,
0.038022950291633606,
0.026976153254508972,
0.01602090522646904,
0.014960474334657192,
-0.027571214362978935,
-0.021895237267017365,
-0.006255782209336758,
-... | |
869d5454bf87bb8f843e01494d98c7edc7d4b050 | subsection | 15 | 22 | The analyser | In what follows, we describe the algorithm that performs the data-flow analysis. A key feature of our algorithm is that it produces a certificate.To compute all possible flows from sources to sinks, we propose a bottom-up inter-procedural data-flow analysis that computes method summaries that are context-independent. A... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.0332595631480217,
-0.019848942756652832,
-0.05797538906335831,
0.0020386739633977413,
0.019070850685238838,
-0.0064764609560370445,
-0.0033965185284614563,
0.028301144018769264,
-0.0015342499827966094,
0.042840760201215744,
-0.014188713394105434,
0.005728883668780327,
0.002761459210887551... | |
52a2fbb21e4562d3d2a2a675e426bac884d7fb39 | subsection | 16 | 22 | The analyser | When the set of facts associated with a location is updated, all successor locations need to be considered (lines 17-18). Once a fix-point is reached, the algorithm returns the set of facts accumulated at the final location (line 19).In the next section we describe the algorithm implementing the checker.
[h!]
method M
... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
0.0077952551655471325,
-0.03064683824777603,
-0.047130197286605835,
-0.004685547668486834,
-0.003124970244243741,
-0.033180393278598785,
-0.02561025694012642,
0.017521200701594353,
-0.004014003090560436,
0.02437400445342064,
-0.012889071367681026,
0.006127841304987669,
-0.007451851852238178,... | |
d8ae26702ac046a1ae20b0ea2fdec0ca937be5f5 | subsection | 17 | 22 | The checker | The checker component takes as input a program and certificate, and answers whether the certificate is valid with respect to the input program. This is implemented via procedure Checker (Algorithm REF ).
First, it extracts all methods in the program (line 2). For each method it checks its presence in the certificate, w... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.012809800915420055,
-0.018173284828662872,
-0.01947028748691082,
-0.02000434696674347,
0.011589093133807182,
-0.011802717112004757,
0.034851204603910446,
0.01899726316332817,
-0.00259400368668139,
0.022735679522156715,
-0.00930789578706026,
-0.016952577978372574,
-0.02648935653269291,
0... | |
feab6de1fcc61afe2f5738e0415f1bcf3e5d9708 | subsection | 18 | 22 | Discussion | We discuss some aspects related to our analysis without deep diving into detail.s | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.025891633704304695,
0.007727821357548237,
-0.07317399978637695,
0.0322539284825325,
-0.028042912483215332,
-0.029919560998678207,
0.03609876707196236,
0.0046229613944888115,
-0.0024850324261933565,
0.03518332913517952,
0.023008005693554878,
0.0019081158097833395,
-0.00943663902580738,
0... | |
e00d01c914f066d05e5fe14686be4ca18bfe7b81 | subsection | 19 | 22 | Implementation and Experiments | We have implemented our approach in a tool called DCert, which is written in Python and uses Androguardhttps://github.com/androguard as front-end for parsing and decompiling Android applications. It accepts Android applications in bytecode format (APK), so no source code is required. One can simply download an app from... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.015271843411028385,
-0.017575588077306747,
-0.06017197668552399,
-0.023373089730739594,
-0.020108181983232498,
-0.03142856806516647,
-0.03426629304885864,
-0.025066571310162544,
-0.028392506763339043,
0.023251038044691086,
0.007773230783641338,
-0.008940359577536583,
-0.02819417230784893,... | |
b2a5fc9c5fc82cd95525f4c68e4f8401899fb5b9 | subsection | 20 | 22 | Related Work | Our work is related to many topics: certification, taint analysis and Android security. Along these axes we report on related work.The idea of associating proofs with code was initially proposed by Necula under the moniker Proof-Carrying Code (PCC) , . It was then used to support resource policies for mobile code , . F... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1145/238721.238781",
"end": 252,
"openalex_id": "https://openalex.org/W2150769115",
"raw": "G. C. Necula and P. Lee. Safe kernel extensions without run-time checking. In OSDI, pages 229–243, 1996.",
"source_ref_id": "a564dc33329c51... | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.05904192849993706,
-0.008551162667572498,
-0.04830148443579674,
0.020168844610452652,
-0.016919249668717384,
-0.05141377076506615,
0.007223863620311022,
0.02848353423178196,
-0.012250818312168121,
0.06962981075048447,
-0.0028986993711441755,
-0.020245125517249107,
-0.03402157500386238,
... | |
fe57ab34afd1d8e9a49ada193b4514a5e979b9d0 | subsection | 21 | 22 | Conclusion and Further Work | We have presented a data-flow certification approach inspired by the proof-carrying-code idea. It consists of splitting the verification process between a heavyweight analyzer and a lightweight checker and using a certificate to ensure trust between the two elements. We implemented our technique in a tool called DCert ... | {
"cite_spans": []
} | 1808.01246 | Certificate Enhanced Data-Flow Analysis | [
"Mohamed Nassim Seghir"
] | [
"cs.PL",
"cs.CR"
] | 2,018 | en | Computer Science | [
-0.022033216431736946,
-0.010322348214685917,
-0.06451276689767838,
0.01792868971824646,
-0.029586153104901314,
-0.023025015369057655,
-0.025496887043118477,
0.03774942830204964,
0.008094612509012222,
0.029769254848361015,
-0.014480278827250004,
-0.005908838473260403,
0.0029753996059298515,
... | |
45ec73ff827620946d2e17c6ee9c9df1c51b6fe6 | abstract | 0 | 12 | Abstract | The inherent stochasticity in many nano-scale devices makes them prospective
candidates for low-power computations. Such devices have been demonstrated to
exhibit probabilistic switching between two stable states to achieve stochastic
behavior. Recently, superparamagnetic nanomagnets (having low energy barrier EB
$\sim... | {
"cite_spans": []
} | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.01565740816295147,
-0.001465020701289177,
-0.0521303191781044,
0.006336977239698172,
-0.013658265583217144,
-0.018007544800639153,
0.04477469250559807,
0.043614886701107025,
0.0011092572240158916,
0.054877232760190964,
-0.038426272571086884,
-0.008210220374166965,
0.022936729714274406,
... |
23f1269dce337c8d2dd0e3e2b9c189fdf4ec282e | subsection | 1 | 12 | Introduction | Magnetization dynamics of nanomagnets is a function of temperature. In memory applications, reasonably high current is applied to devices based on nanomagnets to achieve deterministic switching across a range of temperature. Recently, however, the stochasticity introduced by the temperature dependence of nanomagnetic d... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.7567/apex.7.083001",
"end": 553,
"openalex_id": "https://openalex.org/W1999802284",
"raw": "A. Fukushima, T. Seki, K. Yakushiji, H. Kubota, H. Imamura, S. Yuasa, and K. Ando, “Spin dice: A scalable truly random number generator based on ... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
0.029025066643953323,
-0.021517004817724228,
-0.07453124225139618,
0.05829429626464844,
-0.022524183616042137,
-0.021135497838258743,
0.05109144002199173,
0.035617511719465256,
-0.004791730083525181,
0.05966772139072418,
-0.053685691207647324,
-0.02217319793999195,
0.02340928092598915,
0.0... |
b9ff2d1c5f5aa07e22c5ca6858acb632b91322ff | subsection | 2 | 12 | Lifetime of a Magnetic State | The energy profile of a nanomagnet shown in Fig. REF (b) gives us insight on its stability. The two low-energy states are separated by an energy barrier (E_B) which is essential for the nanomagnet to retain its alignment along the easy axis (x-axis). On receiving an input stimulus, \vec{m} proceeds towards the opposite... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1147/rd.491.0079",
"end": 812,
"openalex_id": "https://openalex.org/W1973893439",
"raw": "L. Sun, Y. Hao, C.-L. Chien, and P. C. Searson, “Tuning the properties of magnetic nanowires,” ChemInform, vol. 37, no. 18, may 2006. [Online]. Ava... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
0.011261634528636932,
-0.0031473063863813877,
-0.049075089395046234,
0.019639190286397934,
0.010903031565248966,
-0.025468382984399796,
0.03073296882212162,
0.01133793219923973,
0.005352328065782785,
0.02864239364862442,
0.0005808210698887706,
-0.01637362316250801,
-0.00023402129590976983,
... |
0c8d90a6ef09bd3e4e73850bbd563f0815930d2f | subsection | 3 | 12 | A Voltage Controlled Stochastic Device | Ferromagnets are traditionally switched using the current induced spin transfer torque (STT) phenomenon . However, the STT phenomenon leads to sub optimal device performance due to various demerits, such as high write current requirement, switching asymmetry and shared read-write paths . Some of these issues are mitiga... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1016/0304-8853(96)00062-5",
"end": 105,
"openalex_id": "https://openalex.org/W1964504828",
"raw": "J. Slonczewski, “Current-driven excitation of magnetic multilayers,” Journal of Magnetism and Magnetic Materials, vol. 159, no. 1-2, pp. L... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.008720451965928078,
-0.006702464539557695,
-0.06829876452684402,
0.03186054900288582,
0.028946101665496826,
-0.014694305136799812,
-0.007556962314993143,
0.045318882912397385,
-0.0009269771981053054,
0.0376589260995388,
-0.05069001019001007,
-0.017028914764523506,
-0.0005927122547291219,
... |
6ef7d29305fc356ca765c1cf6de8948a9419e39d | subsection | 4 | 12 | Device Modeling | The device described in the previous section is modeled using the Landau-Lifshitz-Gilbert (LLG) equation for magnetization dynamics, which in its implicit form is expressed as :\vspace{-2.84526pt}
\frac{\partial \hat{m}}{\partial t}=-|\gamma | \hat{m}\times H_{eff}+\alpha \hat{m}\times \frac{\partial \hat{m}}{\partial ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1109/tmag.2004.836740",
"end": 489,
"openalex_id": "https://openalex.org/W2107971449",
"raw": "T. Gilbert, “Classics in magnetics a phenomenological theory of damping in ferromagnetic materials,” IEEE Transactions on Magnetics, vol. 40, ... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.031104441732168198,
-0.012400568462908268,
-0.036690421402454376,
-0.034553706645965576,
0.01291948463767767,
-0.045908812433481216,
0.01747526414692402,
0.01034779753535986,
0.023107029497623444,
0.02603737823665142,
-0.026556294411420822,
0.010095970705151558,
0.0036858306266367435,
0... |
6c2045d83b7e472ca39aca2b2942485f32b56788 | subsection | 5 | 12 | Device Modeling | Our aim here is to demonstrate the ADC operation, by sampling the telegraphic switching of the low-barrier magnet over a long duration. A non-linear \alpha _{ME} would only affect the switching characteristics of the magnet, and not the stochastic switching behavior averaged over a long duration. Thus, a linear approxi... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.48550/arxiv.1512.05428",
"end": 476,
"openalex_id": "https://openalex.org/W2329766060",
"raw": "S. Manipatruni, D. E. Nikonov, and I. A. Young, “Spin-orbit logic with magnetoelectric nodes: A scalable charge mediated nonvolatile spintron... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.016955867409706116,
0.0002108037006109953,
-0.07093687355518341,
-0.003796374425292015,
0.0015462117735296488,
0.008378732018172741,
-0.0029588828328996897,
0.02191595360636711,
0.013880613259971142,
0.02892112359404564,
-0.03806294500827789,
-0.005635422188788652,
0.003239318495616317,
... |
f24c43d2eb7cec8410bb5f581645507b41c5eb14 | subsection | 6 | 12 | Influence of | The role of thermal noise and external stimulus on the switching behavior fundamentally depends on E_B. For high E_B devices, the main driving force is the magnetoelectric interaction and thermal noise acts as an instigator of stochasticity. The variation of magnetization switching dynamics for different runs, confirms... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1109/ted.2016.2568762",
"end": 2290,
"openalex_id": "https://openalex.org/W2404427863",
"raw": "A. Sengupta, M. Parsa, B. Han, and K. Roy, “Probabilistic deep spiking neural systems enabled by magnetic tunnel junction,” IEEE Transactions... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.00897310022264719,
-0.03421375900506973,
-0.07331083714962006,
0.02357727847993374,
-0.004448398947715759,
-0.001995293889194727,
0.004852799233049154,
-0.0007267753244377673,
0.0062109725549817085,
0.023409415036439896,
-0.02493545226752758,
-0.019655361771583557,
-0.00782857183367014,
... |
dde2eb4398c8033ed3bbad41cf8709e2188d034c | subsection | 7 | 12 | Influence of | Analog input is fed at the ME oxide terminal of the MTJ and digital output is obtained at the counter output.] | {
"cite_spans": []
} | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.023945463821291924,
-0.009889521636068821,
-0.06593015044927597,
0.0003045167832169682,
-0.000006021181434334721,
0.004998176824301481,
-0.020893141627311707,
0.01835971511900425,
0.018909132108092308,
0.046883661299943924,
0.0012886520707979798,
-0.0262347050011158,
0.011064666323363781,... |
2aeb71439dcd9e15cc2f574ae6995804af7d6f60 | subsection | 8 | 12 | Device Readout | The sensing circuit, shown in Fig. REF , consists of a reference MTJ (R_{Ref}) forms a voltage divider with the resistance of the MTJ (R_{MTJ}). The resistance in the P state (R_P) is lower than the resistance in the AP state (R_{AP}).
Considering the magnetization of PL (m_{x,p}) pinned along x-axis, R_{MTJ} = R_{AP} ... | {
"cite_spans": []
} | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.050938233733177185,
-0.006115487311035395,
-0.034365758299827576,
0.04095812514424324,
0.01035398244857788,
-0.0006886122864671052,
-0.0031874547712504864,
0.050114188343286514,
0.024889232590794563,
0.030260790139436722,
-0.042270492762327194,
-0.011689241044223309,
0.01403166726231575,
... |
8867f059d6a8f5504e763e14d057b723f0082c42 | subsection | 9 | 12 | ADC Implementation | The influence of an analog voltage on the stochastic switching of the spintronic device, described earlier, was used to implement a low-voltage 8-bit ADC. An increase in the input voltage decreases \langle m_x \rangle , thus increasing the probability of the magnet being in AP state. When R_{MTJ} = R_{AP} (R_P) or m_x ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1109/vlsit.2015.7223662",
"end": 756,
"openalex_id": "https://openalex.org/W1515011322",
"raw": "W. H. Choi, Y. Lv, H. Kim, J.-P. Wang, and C. H. Kim, “An 8-bit analog-to-digital converter based on the voltage-dependent switching probabi... | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.01171735767275095,
-0.03652520105242729,
-0.06645938754081726,
0.003716980805620551,
-0.014013532549142838,
0.00979497842490673,
0.01611136645078659,
0.025311322882771492,
-0.004649563226848841,
0.04570990055799484,
-0.046991486102342606,
-0.01081719622015953,
0.007994655519723892,
0.02... |
22b893c5ade87402526ad81f71592ea4be1b8ea9 | subsection | 10 | 12 | ADC Implementation | Moreover, since E_B = K_{u2}V, low E_B magnets are area-eficient. As a result, circuits that utilize low E_B devices promise to achieve lower power and compact area. | {
"cite_spans": []
} | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.027207758277654648,
0.0392475351691246,
-0.068851038813591,
-0.005752846598625183,
-0.0029756100848317146,
-0.06262514740228653,
0.011665917932987213,
0.023331835865974426,
0.016953349113464355,
0.04278774932026863,
-0.007351282984018326,
0.015915699303150177,
0.012993497774004936,
0.00... |
72a4375a7686673cb3846ba27059e7ef0aa53015 | subsection | 11 | 12 | Conclusion | We explore a voltage controlled stochastic spintronic device based on superparamagnetic nanomagnets as a possible candidate to perform approximate low voltage Analog-to-Digital conversions. The simulated device achieves voltage controllable telegraphic switching at a ns scale which enables digital encoding of analog in... | {
"cite_spans": []
} | 10.1109/LMAG.2018.2839097 | 1803.01431 | Design of a Low Voltage Analog-to-Digital Converter using Voltage
Controlled Stochastic Switching of Low Barrier Nanomagnets | [
"Indranil Chakraborty",
"Amogh Agrawal",
"Kaushik Roy"
] | [
"cs.ET"
] | 2,018 | en | Computer Science | [
-0.01701376400887966,
0.0382695272564888,
-0.03073158860206604,
0.01721213199198246,
-0.017975080758333206,
-0.0004260593850631267,
0.04919495806097984,
0.014084040187299252,
0.031555574387311935,
0.058411382138729095,
-0.022552775219082832,
0.010620251297950745,
0.016205038875341415,
-0.0... |
9f23b589ed8ef5e774639805242e16d480b8caa4 | abstract | 0 | 31 | Abstract | Education in the practical applications of logic and proving such as the
formal specification and verification of computer programs is substantially
hampered by the fact that most time and effort that is invested in proving is
actually wasted in vain: because of errors in the specifications respectively
algorithms that... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.02781195566058159,
-0.001625733100809157,
0.021923081949353218,
-0.026454158127307892,
-0.003884596284478903,
0.007940824143588543,
0.03868958726525307,
0.020733103156089783,
-0.006071946118026972,
0.029596924781799316,
-0.020778872072696686,
-0.020214393734931946,
0.0036633822601288557,
... |
0c351df6681abcb89008f29f3c473bbc69289003 | subsection | 1 | 31 | Introduction | From a student's perspective, education in the practical applications of logic
and proving (such as the formal specification of a computational problem, the
development of an algorithm that is supposed to solve this problem, and the
formal verification that the algorithm indeed implements the specification) is
often a ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/s00165-008-0069-4",
"end": 3338,
"openalex_id": "https://openalex.org/W2007452988",
"raw": "Wolfgang Schreiner (2009): The RISC ProofNavigator: A Proving Assistant for Program Verification in the Classroom. Formal Aspects of Computi... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.0434817373752594,
-0.005309348925948143,
0.022579990327358246,
-0.009779577143490314,
0.01260970439761877,
-0.003358392044901848,
0.030315162613987923,
0.013471710495650768,
-0.014471028000116348,
0.04421406239271164,
-0.005946318618953228,
-0.02154253050684929,
0.01832335628569126,
0.0... |
37c359530575212d73124369889a78cefed172b2 | subsection | 2 | 31 | Introduction | RISCAL has been designed in such a way thatevery type has (arbitrarily many but) only finitely many values, and thus
every language construct is executable, and thus
every constant, function, predicate, theorem, procedure can be evaluated.While every RISCAL type such as \mathbb {N}[n] is finite, it may depend on a
co... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 2505,
"openalex_id": "",
"raw": "Jon Barwise Dave Barker-Plummer, John Etchemendy & Albert Liu (2008): Tarski's World: Revised and Expanded. CSLI Publications, Stanford, CA, USA.",
"source_ref_id": "f010cd13b5ebdd524994bd953... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.028903981670737267,
0.02518034353852272,
0.024035781621932983,
0.02026636153459549,
-0.013948383741080761,
0.03857933729887009,
0.06324081122875214,
0.0013677504612132907,
-0.02884293906390667,
0.04599609225988388,
-0.008034818805754185,
-0.004566798452287912,
0.018389280885457993,
0.01... |
6ab2aa6bb5d7f95e9525e7057374c21535232590 | subsection | 3 | 31 | Introduction | As for real programming languages with
support for formal specification, the programming language WhyML of the
verification environment Why3 and Microsoft's programming
language Dafny provide a rich variety of built-in specification
constructs; however, both WhyML and Dafny do not support model checking. Also
for ind... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 307,
"openalex_id": "",
"raw": "Jean-Christophe Filliâtre & Andrei Paskevich (2013): Why3 — Where Programs Meet Provers. In M. Felleisen & P. Gardner, editors: ESOP 2013, Rome, Italy, March 16-24, 2013, Lecture Notes in Computer S... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.026255512610077858,
0.008894226513803005,
0.005015397910028696,
-0.015446661971509457,
-0.021465139463543892,
0.006895695347338915,
0.04271669685840607,
0.01437874510884285,
-0.021022716537117958,
0.03701096773147583,
-0.00712834857404232,
-0.015278846956789494,
0.0011251273099333048,
0... |
920f8c7169a0d9ba3c0422e780a62abfedfb1cb0 | subsection | 4 | 31 | The RISCAL Language and System | In this section, we give a short account of the RISCAL language and
software system; for more details, see the tutorial
and reference manual . | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 142,
"openalex_id": "",
"raw": "Wolfgang Schreiner (2017): The RISC Algorithm Language (RISCAL) — Tutorial and Reference Manual (Version 1.0). Technical Report, RISC, Johannes Kepler University, Linz, Austria. Download from .",
... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.031097164377570152,
0.034331999719142914,
-0.009002613835036755,
0.006122540216892958,
-0.019546352326869965,
-0.0048446268774569035,
0.04952963441610336,
0.04513513669371605,
-0.01829514279961586,
0.03659028559923172,
-0.004169430583715439,
0.009773176163434982,
0.006286570802330971,
0... |
6e62419f3c425e16aa3c520726f40e4d4ef12b5c | subsection | 5 | 31 | System | The user interface of the RISCAL software system is depicted in
Figure REF ; it contains an editor frame for RISCAL specifications
on the left and the control widgets and output frame of the checker on the
right. The RISCAL specification language is based on a statically typed variant
of first order predicate logic. On... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.04494532197713852,
-0.00015745068958494812,
-0.02509675920009613,
-0.008513065055012703,
0.017514333128929138,
0.026195218786597252,
0.026988551020622253,
0.035486359149217606,
0.019818048924207687,
0.025890091434121132,
-0.012441584840416908,
0.03203841671347618,
0.017148179933428764,
... |
d62f3760d4ed021b201e3199ce68f20c8cc1aab2 | subsection | 6 | 31 | Language | RISCAL specifications consist of declarations of
the following kinds of entities:Types
type I = T introduces a named type I defined by the
type expression T; types include booleans, integers, sets, tuples, records,
arrays, and maps (partial functions). All types are finite, e.g., for
integer constants N and M with N\le... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.019795702770352364,
-0.008516578003764153,
-0.016086870804429054,
0.03473787382245064,
0.004281183239072561,
-0.029655396938323975,
0.021566174924373627,
0.04053769260644913,
-0.005673903506249189,
0.039133526384830475,
-0.038278814405202866,
-0.007417665328830481,
0.005559433251619339,
... |
83498cf09a8e806d619992294c2cde708a53d210 | subsection | 7 | 31 | Language | These entities may be also defined recursively; by an annotation
decreases E a termination measure E is stated, i.e., an expression
E that evaluates to a natural number which is decreased in every recursive
invocation.The algorithmic language RISCAL also supports non-deterministic
expression evaluations respectively co... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.052236977964639664,
0.005877422634512186,
0.028422163799405098,
0.0457683801651001,
-0.01048858743160963,
-0.0458294041454792,
0.05775969475507736,
0.0360959954559803,
-0.020321160554885864,
0.03981849178671837,
-0.03707238659262657,
-0.04076436907052994,
-0.017575057223439217,
-0.00891... |
37d561b6c18a2766e34ada37748a6ede88761fe8 | subsection | 8 | 31 | Example | The specification listed in Figure REF introduces the mathematical
theory of the greatest common divisor and its computation by the Euclidean
algorithm; this theory is restricted to the domain of all natural numbers less
than equal N:The theory first introduces the undefined constant N which is
then used as the domain ... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.05192924290895462,
-0.014134090393781662,
-0.03963342308998108,
-0.0019050129922106862,
0.014805326238274574,
0.032799024134874344,
-0.04146406799554825,
0.001604673103429377,
0.024301787838339806,
0.02457638457417488,
-0.026346005499362946,
-0.0033809689339250326,
-0.023874636739492416,
... |
693552c43e6054ddfd4147eb187b234ce334a498 | subsection | 9 | 31 | Example | Its contract specified by the clauses requires
and ensures states that the procedure behaves exactly as the implicitly
defined function; the loop annotations invariant and decreases
describe essential knowledge for proving the total correctness of the procedure
(here the automatically introduced constants old_a and old... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.06141882389783859,
0.018825342878699303,
-0.03963390365242958,
0.019969508051872253,
0.011189942248165607,
0.0014597648987546563,
0.04158661514520645,
-0.03572848439216614,
-0.011289102956652641,
0.04744474217295647,
-0.009084676392376423,
-0.05064840987324715,
-0.009122815914452076,
0.... |
1cc219fd05d6cf076940e73747bb6674d810220c | subsection | 10 | 31 | Evaluation, Execution, and Checking | Whenever the user saves a specification, it is automatically syntactically and
semantically processed, i.e., parsed, type-checked, and translated into an
executable internal representation (see below for more details on the
implementation). Errors are reported by graphical markers in the editor frame
and by textual mes... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.018219750374555588,
0.006050361320376396,
-0.02731436677277088,
0.031068185344338417,
-0.0014944697031751275,
-0.033570729196071625,
0.01971517503261566,
0.025483235716819763,
0.03265516459941864,
0.04718213528394699,
-0.005310279317200184,
-0.008438460528850555,
0.0581078827381134,
0.0... |
492af45fe1515e07f7358a8305e6e4df0c78192a | subsection | 11 | 31 | Implementation | RISCAL has been implemented in Java (using the Eclipse Standard Widget Toolkit
SWT for its graphical user interface). The executable internal representation of
a specification is essentially a Java version of a denotational semantics of the
specification, implemented on top of the lambda expressions introduced in Java
... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.0458969883620739,
0.007152331527322531,
-0.013541747815907001,
0.026564711704850197,
-0.00013792079698760062,
-0.0019759507849812508,
0.022612810134887695,
0.028777167201042175,
-0.002134255599230528,
0.035734955221414566,
-0.004390577785670757,
0.03158469498157501,
0.01995786651968956,
... |
b1aaa99fb3da1772efbba3515faa3d0f001d5bd5 | subsection | 12 | 31 | Implementation | The multi-threaded
version can be selected by the check box Multi-Threaded where by the
input box Threads the number of worker threads can be selected. These
threads run on the local computer and iteratively request from the main thread
new inputs to which the chosen operation is to be applied; thus the domain of
input... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 969,
"openalex_id": "",
"raw": "Wolfgang Schreiner (2017): The RISC Algorithm Language (RISCAL) — Tutorial and Reference Manual (Version 1.0). Technical Report, RISC, Johannes Kepler University, Linz, Austria. Download from .",
... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.002094152383506298,
0.013678744435310364,
0.006183280609548092,
0.05270092934370041,
-0.0304548516869545,
0.05279247835278511,
0.028227191418409348,
0.0072589656338095665,
0.004020467400550842,
0.027143876999616623,
-0.02697603963315487,
0.019057169556617737,
-0.00958961620926857,
0.015... |
ae8f4e4149ab67cd320187a3bb807526f134b742 | subsection | 13 | 31 | Proof-Based Verification | Since RISCAL is based on checking rather than deriving and proving verification
conditions, there is not any direct connection of RISCAL to a verification
calculus like Hoare's axiomatic system or Dijkstra's predicate transformers.
However, as will be sketched in the following section, we plan as future work to
integra... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.02277529239654541,
0.025002481415867805,
-0.010663047432899475,
0.030738255009055138,
-0.04466581344604492,
0.01760394312441349,
0.026100821793079376,
0.051591455936431885,
-0.018275151029229164,
0.023477010428905487,
-0.019937915727496147,
0.001341461669653654,
0.0027382217813283205,
0... |
974eed9e321b2b09705350a8e8c0d2dadbf32ad5 | subsection | 14 | 31 | Using RISCAL in Education | RISCAL shall support the education in formal logic with emphasis on the formal
specification and verification of programs respectively algorithms (abstract
programs). The particular goal of RISCAL is to give students immediate
feedback about the interpretation and adequacy of formal definitions and
specifications befor... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.020571492612361908,
0.013162397779524326,
0.008645215071737766,
-0.007973742671310902,
-0.001762616797350347,
0.002928156638517976,
0.05240542069077492,
0.01412382535636425,
-0.028674950823187828,
0.049627963453531265,
-0.01735147461295128,
-0.03238331526517868,
-0.006131006870418787,
0... |
a100389e66eaef8c0e0f344a2d126a933ccb5287 | subsection | 15 | 31 | Using RISCAL in Education | If none
of these theorems hold, the specification is trivial: a proof of correctness of
an algorithm with respect to the specification typically quickly succeeds but is
pointless (indeed small logical errors may lead to the definitions of
postconditions that are equivalent to true).
Check the validity of \forall x. P(... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.01586891897022724,
0.021880798041820526,
-0.010589451529085636,
0.026504147797822952,
-0.0037135560996830463,
0.0011672810651361942,
0.02918965555727482,
0.027206040918827057,
-0.01576210930943489,
0.05059744045138359,
-0.0262600090354681,
-0.023193035274744034,
0.04159487783908844,
0.0... |
4a70fe64afc32ec77042215de8f7f7b88264c3a1 | subsection | 16 | 31 | Using RISCAL in Education | The corresponding RISCAL
specification is based on the following domains:val N:ℕ; val M:ℕ;type index = ℤ[-N,N]; type elem = ℤ[-M,M]; type array = Array[N,elem];Rather than basing our specifications on a single integer type, we use two
constants N and M to bound the types index of array
indices/lengths and the type ele... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.012783979997038841,
-0.020625228062272072,
-0.02155580371618271,
0.028817350044846535,
-0.009252367541193962,
0.0035945409908890724,
-0.002620105864480138,
0.021830400452017784,
-0.008893867023289204,
0.043508246541023254,
-0.0193132683634758,
0.02694094181060791,
0.03813836723566055,
-... |
f1916d80ff82536d477ca836c000f7869e6d7439 | subsection | 17 | 31 | Using RISCAL in Education | Theorems postNotValid (the
postcondition is not generally valid), postSat (the postcondition is
satisfiable), and resultUnique (the postcondition determines the result
uniquely) are individually verified by corresponding calls of the checker
(in non-deterministic mode with silent execution):Executing postNotValid(Array... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.00032442781957797706,
-0.0002353949093958363,
-0.02347894385457039,
0.019192015752196312,
-0.03298341482877731,
0.006899514235556126,
-0.02128208428621292,
-0.006975794211030006,
-0.019268294796347618,
0.02325010485947132,
0.008222970180213451,
-0.018474984914064407,
0.01810884103178978,
... |
2ae08f4b07f7ad67348a417be8f73d7f7e0c4efe | subsection | 18 | 31 | Using RISCAL in Education | 0 ≤ k ∧ k < i ⇒ m ≥ a[k]);fun Termination(a:array, n:index, m:elem, i:index):index = n-i;By checking the procedure (activity 3a), we verify its correctness with respect
to the specification, and (partially) validate the adequacy of invariant and
termination term:Executing maxProc(Array[ℤ],ℤ) with all 875 inputs.Executi... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/s00165-008-0069-4",
"end": 1968,
"openalex_id": "https://openalex.org/W2007452988",
"raw": "Wolfgang Schreiner (2009): The RISC ProofNavigator: A Proving Assistant for Program Verification in the Classroom. Formal Aspects of Computi... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
0.003848779946565628,
0.006766834296286106,
-0.0083994185552001,
-0.005252497736364603,
-0.02656382881104946,
0.004375174175947905,
-0.014678003266453743,
0.011481494642794132,
0.009086019359529018,
0.038327593356370926,
-0.009513238444924355,
-0.005729303695261478,
0.026975790038704872,
0... |
d301d6ef393d55fe100b6963dbeb0e7515283818 | subsection | 19 | 31 | Sample Specifications | Since the release of the first version of RISCAL in March 2017, we have started
to develop first prototypes of formally checked specifications. They are
intended to serve as the nucleus of a future comprehensive library and
accompanying lecture materials to be used in the class room and for
self-instructed learning in ... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.006235974375158548,
0.017834505066275597,
0.0024162016343325377,
-0.001245287829078734,
0.004058151040226221,
0.0013444531941786408,
0.03386877849698067,
-0.007917971350252628,
-0.001998563064262271,
0.04549400880932808,
0.01876513473689556,
0.010252171196043491,
-0.020977284759283066,
... |
5557e1ea6e77dbd325eb1e5496a08347e0c0655c | subsection | 20 | 31 | Number Theory | In , we describe the application of RISCAL to number-theoretic
algorithms that arise in, e.g., cryptography. In such algorithms, prime
numbers play an important role; thus as our first example we pick the problem
of generating, for a given bound n\in \mathbb {N}, all prime numbers less than
equal n: formally, we wish t... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 108,
"openalex_id": "",
"raw": "Christoph Fürst & Wolfgang Schreiner (2017): Formalization of Two Algorithms Arising in Number Theory. Technical Report, RISC, Johannes Kepler University, Linz, Austria. To appear.",
"source_r... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
0.008378772996366024,
-0.006879292894154787,
0.008775581605732441,
0.014674298465251923,
-0.009408949874341488,
0.010042318142950535,
0.039253558963537216,
0.04081026837229729,
-0.010110996663570404,
0.049662161618471146,
-0.055766914039850235,
-0.006097121629863977,
-0.04960111528635025,
... |
5ccb624197a02c773d8f36ed0b3e515a6d2b5f72 | subsection | 21 | 31 | Number Theory | But then
o<m is also a divisor of n, i.e., m is not the least divisor, which
contradicts our assumption.While this argument can be easily understood by students, we can give
the theorem further credibility by formulating it in RISCAL:theorem leastProperDivisor(n:nat,m:nat) ⇔n ≥ 2 ∧ m > 1 ∧ divides(m,n) ∧ (∀m0:nat. m0 >... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.015792686492204666,
0.013900616206228733,
0.017257515341043472,
0.022475969046354294,
-0.003812751267105341,
0.020095622166991234,
0.013236865401268005,
0.03102080337703228,
-0.012069580145180225,
0.04305986687541008,
-0.05721987783908844,
0.0062064495868980885,
-0.0486140102148056,
-0.... |
895202ade11be4fb66f3fb75352970e3a23728b5 | subsection | 22 | 31 | Sieve of Eratosthenes (Set-Based) | The following algorithm computes for given n\in \mathbb {N} the set P
of all values p\le n with \mathit {isPrime}(p,n):[H]
[1]
P = \lbrace p\ |\ p\in \mathbb {N} \wedge p\le n \wedge \mathit {isPrime}(p) \rbrace
P \leftarrow \emptyset
C \leftarrow \lbrace 2,\ldots ,n\rbrace
C \ne \emptyset
p \leftarrow \min (C)
P\l... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.001122337649576366,
0.005133955739438534,
-0.01608080044388771,
0.03033076971769333,
0.011137556284666061,
-0.03905773162841797,
0.06487245112657547,
0.0277981199324131,
0.000056021526688709855,
0.03606737405061722,
-0.015447637997567654,
-0.0052369399927556515,
0.00005572353984462097,
... |
c979578150cde58e7b5c71e3346bc6bd92729b3d | subsection | 23 | 31 | Sieve of Eratosthenes (Array-Based) | The following algorithm computes for given n\in \mathbb {N} the Boolean
array P of length n such that P[p] has value true if and only if
the property \mathit {isPrime}(p) holds:[H]
[1]
\forall p\in \mathbb {N}.\ p\le n \Rightarrow (P[p] = \textrm {T}
\Leftrightarrow \mathit {isPrime}(p))
P \leftarrow ({\rm T},{\rm T},\... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.022541260346770287,
0.005318638868629932,
-0.013781149871647358,
0.028829006478190422,
-0.012590751983225346,
0.0027737808413803577,
0.04590664431452751,
0.03211023285984993,
0.0040595633909106255,
0.028096452355384827,
-0.04786011949181557,
-0.002205289201810956,
0.0045670089311897755,
... |
5da3c224848e8ecec0f62ba17253f3acea029f37 | subsection | 24 | 31 | Sieve of Eratosthenes (Array-Based) | Checking also this algorithm with N=30Executing SieveOfEratosthenesArray(ℤ) with all 31 inputs.Execution completed for ALL inputs (171 ms, 31 checked, 0 inadmissible).again validates both that the algorithm satisfies its contract and that the
loop annotations are correct (if they should not be sufficient for a proof,
t... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
0.018756819888949394,
0.019107842817902565,
0.014010382816195488,
0.028875429183244705,
0.012240007519721985,
-0.024739466607570648,
0.018741557374596596,
0.010027038864791393,
-0.021488690748810768,
0.0385819673538208,
0.03687264025211334,
-0.018008988350629807,
0.012980207800865173,
0.01... |
15abde23f2314ec2c7acb43f565d98a1a966852a | subsection | 25 | 31 | Discrete Mathematics | In , chosen theories from discrete mathematics have been
formalized in RISCAL. This includes the development of the mathematical
theories, the specification of algorithms and their annotation with
meta-information. The concepts have been validated on small finite domains which
should work as a ground layer for further ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 78,
"openalex_id": "",
"raw": "Alexander Brunhuemer (2017): Validating the Formalization of Theories and Algorithms of Discrete Mathematics by the Computer-Supported Checking of Finite Models. Bachelor thesis, Research Institute f... | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.05640742927789688,
0.000909981841687113,
0.005711710080504417,
0.032385434955358505,
0.009408868849277496,
0.041756149381399155,
0.03272119164466858,
0.015643293038010597,
-0.025914451107382774,
0.03281276300549507,
-0.043984364718198776,
-0.013781360350549221,
0.0010816765716299415,
0.... |
5bfe3dd7b32f0ba2746f4d8673f43b924448f67f | subsection | 26 | 31 | Problem Specification and Implicit Definition | Our problem is to compute the transitive closure of a given binary relation
based on the following definition.Definition 3 (Transitive Closure) S is the
transitive closure of relation R, if S is the smallest
transitive relation S that contains R, i.e., S is a subset of every
transitive relation that contains R.The corr... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.041785452514886856,
0.03244553133845329,
-0.0009738619555719197,
0.03516204655170441,
-0.005463547073304653,
0.03114832192659378,
0.00023607330513186753,
-0.002750850049778819,
-0.014154859818518162,
0.018985062837600708,
-0.0235329307615757,
0.0025886986404657364,
0.006886663381010294,
... |
d7a564bc12f36f1d0d31f25441bddb845ae092ee | subsection | 27 | 31 | Explicit (Recursive) Definition | A natural approach to compute the transitive closure of a relation r
as a recursive function is based on the following fundamental steps:If r is transitive, then we are finished and r is our result.
Otherwise r contains some pairs \langle x,z \rangle and
\langle z,y \rangle that violate the transitivity of r in the se... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.05672949180006981,
0.029875295236706734,
0.008903082460165024,
0.0256793275475502,
0.002910476177930832,
0.040586456656455994,
0.02409248799085617,
-0.0048139202408492565,
-0.028456294909119606,
0.016570260748267174,
-0.016585519537329674,
-0.01629561558365822,
-0.028349488973617554,
0.... |
8d565a4f2b614f12e931e446e79281aa77f15222 | subsection | 28 | 31 | Procedural Definition | Another algorithm which may be easiest expressed as a procedure is based on the
following main steps:We initialize the result variable \mathit {res} with the empty set and
an auxiliary variable \mathit {new} with r.
We choose some pair x\in \mathit {new} and check for every
pair y\in \mathit {res}, if the combination ... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.03632010892033577,
0.00024214200675487518,
-0.0043339962139725685,
0.03277966007590294,
0.007473854348063469,
0.024874696508049965,
0.013261417858302593,
0.04428611695766449,
-0.023409683257341385,
0.03931117802858353,
-0.04321787878870964,
-0.005222923122346401,
0.0021250315476208925,
... |
fda5bffdeec275cf5c57e228bbb3152b32bc5b5b | subsection | 29 | 31 | Procedural Definition | Since the loop terminates when
\mathit {new} is the empty set, the third invariant implies that then
\mathit {res} is transitive and thus itself the transitive closure.The correctness of the invariant of the outer proof has to be verified
with the help of the invariant of the inner loop:invariant new = old_new∪ { ⟨y0.1... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.04772045835852623,
0.019512297585606575,
0.013097191229462624,
0.04155707359313965,
-0.0035832298453897238,
0.00019784996402449906,
0.019100388512015343,
0.01273867767304182,
-0.035119082778692245,
0.03810923919081688,
-0.03887203708291054,
0.014691432937979698,
0.006190082058310509,
0.... |
747f909a0ba12c577b30015ab436ce8e1573d554 | subsection | 30 | 31 | Conclusions and Further Work | RISCAL is still in its infancy with first contents
having been developed and first classroom experience having been gained;
subsequent experience with the use of RISCAL will shape the further
development of language and system. This will proceed along several
possible strands:We will automatize the generation of formul... | {
"cite_spans": []
} | 10.4204/EPTCS.267.8 | 1803.01472 | Teaching the Formalization of Mathematical Theories and Algorithms via
the Automatic Checking of Finite Models | [
"Wolfgang Schreiner",
"Alexander Brunhuemer",
"Christoph Fürst"
] | [
"cs.LO"
] | 2,018 | en | Computer Science | [
-0.04099433869123459,
0.030417615547776222,
0.015620888210833073,
0.013476545922458172,
-0.00234084390103817,
0.030478665605187416,
0.018146786838769913,
0.013674953952431679,
-0.005482954438775778,
0.042642660439014435,
-0.020832939073443413,
-0.002144342754036188,
-0.031119678169488907,
... |
285d60ace1fa3c274fe31d40a3ead7afb7cdb9fb | abstract | 0 | 224 | Abstract | A fundamental tool in noncommutative geometry is Connes' character formula.
This formula is used in an essential way in the applications of noncommutative
geometry to index theory and to the spectral characterisation of manifolds.
A non-compact space is modelled in noncommutative geometry by a non-unital
spectral trip... | {
"cite_spans": []
} | 1803.01551 | The Connes character formula for locally compact spectral triples | [
"Fedor Sukochev",
"Dmitriy Zanin"
] | [
"math.OA"
] | 2,018 | en | Mathematics | [
-0.04414185881614685,
0.0373648926615715,
-0.04011231288313866,
0.01973562501370907,
-0.01813296414911747,
-0.03651013970375061,
0.048232462257146835,
0.004880484193563461,
0.04105864465236664,
0.022223563864827156,
-0.014744480140507221,
0.01145520992577076,
0.013599722646176815,
-0.02245... | |
26dd9f931966c4032eb550ac18e77b14bc224cc7 | subsection | 1 | 224 | Introduction | One of the fundamental tools in noncommutative geometry
is the Chern character. The Connes Character Formula (also known as the Hochschild character theorem) provides an expression for the
class of the Chern character in Hochschild cohomology, and it is an important
tool in the computation of the Chern character. The f... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/978-3-0348-9102-8_4",
"end": 526,
"openalex_id": "https://openalex.org/W2112440022",
"raw": "Connes A., Moscovici H., The local index formula in noncommutative geometry. Geom. Funct. Anal. 5 (1995), no. 2, 174–243.",
"source_r... | 1803.01551 | The Connes character formula for locally compact spectral triples | [
"Fedor Sukochev",
"Dmitriy Zanin"
] | [
"math.OA"
] | 2,018 | en | Mathematics | [
-0.05712588131427765,
0.0013970589498057961,
-0.029859870672225952,
-0.009032725356519222,
0.009559125639498234,
-0.008742823265492916,
0.036832768470048904,
-0.011832565069198608,
0.03756514936685562,
0.004401927813887596,
-0.0182943195104599,
0.015479221940040588,
-0.008300341665744781,
... | |
8b0bdef553ee9e4c579dbbbca9496323310dde99 | subsection | 2 | 224 | Introduction | The conventional definition
of a non-compact spectral triple is to replace the condition that (1+D^2)^{-1/2} be compact with the assumption that for all a \in \mathcal {A} the operator a(1+D^2)^{-1/2} is compact.This raises an important question: is the Connes Character Formula true for locally compact spectral triples... | {
"cite_spans": []
} | 1803.01551 | The Connes character formula for locally compact spectral triples | [
"Fedor Sukochev",
"Dmitriy Zanin"
] | [
"math.OA"
] | 2,018 | en | Mathematics | [
-0.04775355011224747,
0.022625721991062164,
-0.03182552754878998,
-0.002894963603466749,
-0.014348949305713177,
-0.05477164313197136,
0.04274934157729149,
0.0006879829452373087,
0.023510612547397614,
0.0214967243373394,
-0.0007308924687094986,
0.023480098694562912,
0.005908166524022818,
-0... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.