text stringlengths 2 132k | source dict |
|---|---|
process . We consider that the system is com-posed of N uniquely identified processes, denoted by p1, p 2, . . . , p N . Some-times we also denote the processes by p, q, r. The set of system processes is denoted by Π. Unless explicitly stated otherwise, it is assumed that this set is static (does not change) and proces... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
global clock: *DRAFT* 24 (22/11/2004) CHAPTER 2. BASICS 2.1. COMPUTATION one step per clock tick. Even if two steps are executed at the same physical instant, we view them as if they were executed at two different times of our global clock. A correct process executes an infinite number of steps, i.e., every process has... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
talking about messages exchanged between modules of the same process. The process is the unit of communication, just like it is the unit of failures as we will discuss shortly below. In short, a communica-tion step of the algorithm occurs when a process sends a message to another process, and the latter receives this m... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
violated at some time t and never be satisfied again after that time. Roughly speaking, safety properties state that the algorithm should not do anything wrong. To illustrate this, consider a property of perfect links (which we will discuss in more details later in this chapter) that roughly stipulates that no process ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
liveness property is a property of a distributed system execution such that, for any time t, there is some hope that the property can be satisfied at some time t′ ≥ t. It is a property for which, quoting Cicero: “While there is life there is hope”. In general, the challenge is to guarantee both liveness and safety. (Th... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
from the algorithm assigned to it. The arbitrary fault behavior is the most general one. In fact, it makes no assumptions on the behavior of faulty processes, which are allowed any kind of output and in particular can send any kind of messages. These kinds of failures are sometimes called Byzantine (see the historical ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
after some time t, the process also stops executing any local computation after t, we talk here about a crash failure (Figure 2.2), and a crash stop process abstraction. The process is said to crash at time t. With this abstraction, a process is said to be faulty if it crashes. It is said to be cor-rect if it does neve... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
never per-form any computation. Obviously, in practice, processes that crash can in general be rebooted and hence do usually recover. It is important to notice that, in practice, the crash-stop process abstraction does not preclude the possibility of recovery, nor does it mean that recovery should be prevented for a gi... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
of interest) up and operating. A process that crashes and recovers a finite number of times is correct in this model (i.e., according to this abstraction of a process). *DRAFT* 29 (22/11/2004) 2.2. PROCESSES CHAPTER 2. BASICS According to the crash-recovery abstraction, a process can indeed crash, in this case the proc... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
before proceeding to the 〈 Recovery 〉 one. In some sense, a crash-recovery kind of failure matches an omission one if we consider that every process stores every update to any of its variables in stable storage. This is not very practical because access to stable storage is usually expensive (as there is a significant ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
a given execution of the algorithm. • At first glance, one might believe that the crash-stop abstraction can also capture situations where processes crash and recover, by simply having the processes change their identities upon recovery. That is, a process that recovers after a crash, would behave, with respect to the ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
of some specific distributed abstraction, delivers some message or decision to the upper layer (say the application) and subsequently the process hosting the module crashes. Upon recovery, the module cannot determine if the upper layer (i.e., the application) has processed the message or decision before crashing or not... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
Title: Fair Exchange URL Source: Markdown Content: # Chapter 5 Fair Exchange # Mohammad Torabi Dashti and Sjouke Mauw # 5.1 What Is Fairness? Fairness is a broad concept, covering a range of qualifications such as impartiality, courtesy, equity, sportsmanship, etc. Here, we focus on fairness in exchanging (electronic)... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
half to Bob, once Bob takes her to her destination. Do these scenarios describe fair interactions? We will analyze them more carefully in the following. In the cut-and-choose scenario, indeed there is an assumption that neither Alice nor Bob would take the whole cake and simply run away. Under this assumption, cut and ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
that fairness is indeed a subtle issue. In the following, we abstract away various non-technical aspects of fairness, and focus on fairness in electronic exchanges. # 5.2 Fairness in Electronic Exchanges At a high level of abstraction, an action, such as signing a contract, may be considered as a single event even thou... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
Most vendors on Internet, for instance, offer little beyond browsing their catalogues, while contract signing and payment often go via a credit card company. The trust in these sites is largely built upon the trust users have in the credit card companies, which keep records and provide compensation in case of fraud. Fa... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
in the literature, e.g., fair contract signing (CS), fair payment (FP), fair certified email (CEM), and fair exchange of secrets (ES). Below, we introduce these FE variants via examples: • Fair contract signing (CS): Alice and Bob have agreed on a contract and would like to sign it electronically. 2 Alice gives her sig... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
secret unilaterally. Note that this exchange is meaningful only if Alice and Bob can recognize the expected secrets. That is, they can verify that received data are indeed the other party’s secret. Otherwise, any protocol that distributes random bits would be acceptable, since Alice would think that the junk is actuall... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
are conceptually very similar. The challenge in NR protocols is to exchange the evidences in a fair way, otherwise, non-repudiation of the evidences can be achieved using standard digital signatures; cf. [ZG97b]. We remark that in fair contract signing, termination is a challenging problem in practice. For instance con... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
to the ones proposed by [Aso98]. Below, we informally describe these goals for two parties, named A and B: • Fairness states that if A terminates the protocol in a state where A has B’s item, then when B terminates the protocol, B has A’s item, and vice versa. This property is often referred to as strong fairness ; cf.... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
→ B : m, when participant A submits message m to the communication network, with the intention that it should be delivered to participant B. A synchronous channel guarantees to deliver messages in a timely manner, with a pre-known time bound, while asynchronous channels deliver messages eventually, but no time bounds a... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
which has control over the entire communication network. 6 It intercepts all messages that have been transmitted and can store them in its knowledge set. It can also remove or delay messages in favor of others being communicated. “[It] is a legitimate user of the network, and thus in particular can initiate a conversat... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
1 com-munications. We conclude that [Bob] transmits the nth communication, and therefore the first time [Bob] has sufficient information is after n′ communications, where n′ = n. This contradicts [the definition of agreement].” Rabin considers the similar problem of simultaneous exchange of secrets between two non-tr... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
that, in a fully connected network of synchronous channels, n-party SMPC, and thus FE, is achievable if there are at most t Byzantine participants, with t < n/ 3. They also prove that there exist SMPC problems which, with t ≥ n/ 3 Byzantine participants, are unsolvable for n parties. The results of [EY80, Rab81] clearl... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
effects of participant failures, as opposed to channel failures, on solving the FE problem. Below, we consider the case of lossy channels, while assuming that participants are all honest (i.e., they faithfully follow their protocol). In distributed computing, the limitations on reaching agreement in the presence of los... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
other end. # 5.4 Fair Exchange in the Dolev-Yao Model Fair exchange cannot be achieved in the presence of the DY attacker if there is no trust in the system (see Section 5.3). Many fair exchange protocols thus assume the presence of a trusted third party (TTP). The TTP is further assumed to be connected to protocol par... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
be active during each exchange. However, a slight difference is that, intuitively, the TTPs in the latter protocols need not “be aware” of being involved in such exchanges. For instance, the TTP in Rabin’s protocol acts as a beacon, broadcasting signals which can be used by others to perform fair exchange. The third gr... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
the other general would do so. Similarly, a participant may consider the exchange terminated only if she knows the other participant would also do so. In the DY model, however, the communication media are assumed to be under complete control of the intruder. The DY intruder can in particular destroy transmitted message... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
a fair lossy medium and can destroy all the messages that are transmitted through it. Therefore, no reliable channel may be constructed between A and B in the DY model. Nevertheless, the assumption that DY controls all communication media between A and B is often impractical. For instance, in wireless networks, given t... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
The items subject to exchange, and commitments are respectively denoted by iA, i B and cA(iA), c B (iB ). In Figure 5.2 we have m1 = cA(iA), m2 = cB (iB ), m3 = iA,and m4 = iB . If no failures occur, the participants exchange their items successfully using the main sub-protocol. Figure 5.2: Generic four-message protoco... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
the TTP. Naturally, if no message has been exchanged, the participant quits the protocol, e.g., B in Figure 5.2 quits the exchange if he does not receive the first message in time. A ‘none’ option ( −) indicates that the participant has no alternatives but following the optimistic protocol. It turns out that ‘none’ opt... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
cA(iA), and iB from cB (iB ), and that R contains iA and iB . In case the TTP cannot do so, usually an affidavit from the TTP is deemed adequate; cf. weak fairness [PVG03]. The resilient channels guarantee that, in case of failures, protocol participants can ultimately consult the TTP. Participant A can run the recover... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
by A nevertheless does not contain cB (iB ). Therefore, once the TTP computes R for an exchange, it stores R in its secure storage, for possible future uses. In Figure 5.3, a and r stand for valid abort and recovery requests, while A and R stand for the corresponding abort and recovery tokens, respectively. Remark that... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
certain digital items generatable. For instance, see [ASW98b, Ate04, Che98, DJH07, DR03, PCS03] for techniques to enable the TTP to generate participants’ signatures from their commitments; see also [RR00]. In contrast, there are not many digital items that can be revoked by the TTP (see below). The above-mentioned imp... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
that these protocols enforce the structure of the exchanged items, hence being called invasive [ASW98a]. Non-invasive protocols are more favorable, but come at high computation costs, as they rely on heavy cryptographic tools, as in, e.g., the signature exchange protocols of [ASW98b]. A partial remedy to invasiveness i... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
the minimum number of messages in exchange sub-protocols, given that the TTP is allowed to participate in the dispute resolution phase, while this number is four if the TTP is not allowed to do so. Requiring the TTP’s intervention in the evidence verification phase can be a drawback for these protocols because evidence... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
the optimistic sub-protocol, [VPG01] for exchanging time-sensitive items, and [TMH06] for optimistic exchange of non-revocable, non-generatable items; recall that optimistic FE requires that at least one of the items be either revocable or generatable [SW02]. 11 See also [AGGV05, AV04, ES05, FFD +06, GR06] on using tru... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
that the TTP needs to be stateful , i.e., to keep states of disputed exchanges, to guarantee fairness in asynchronous optimistic protocols. From a practical point of view, this result is of great relevance. Optimistic FE not only requires TTPs for recovering from unfair transient states, it needs TTPs which maintain pe... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
the TTP’s burden, and in [RRN05, SXL05] secret sharing schemes are used so that, to subvert the protocol, an attacker needs to com-promise several TTPs. Note that distributed TTPs in general need to run some atomic commit protocol to ensure the consistency of their (distributed) state. We recall that (1) attaining fair... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
into the properties of exchange protocols, when assuming that their participants are rational agents, rather than categorizing them as malicious and honest parties, who blindly act regardless of their interests. For more on this approach see [ADGH06, BHC04, CMSS05, IIK02, IZS05, San97, SW02, TW07]. Concurrent signature... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
of the prudent advice [AN96] and attack scenarios known for authentication and key distribution protocols [Car94, CJ97] are pertinent to FE protocols as well. Papers specifically focusing on FE are unfortunately scarce. We note that compilations of FE protocols are almost non-existent, [KMZ02] being a notable exception... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
indeed Alice would benefit from not giving the other half to Bob. To avoid such situations, Bob must ensure that Alice rips a bill into two halves afresh. > 2Fair and private contract negotiation protocols are discussed in, e.g., [FA05]. > 3Fairness, as defined in this article, is a safety property, while timeliness is... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
susceptible to a replay attack (we skip describing the attack, as it would require a detailed description of the protocol, and the attack is also rather obvious). The ideas behind these protocols can however be salvaged with some changes. > 12 The notion of compromisable trustee may seem to be paradoxical. We note that... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
21(4):181– 185, 1985. [Aso98] N. Asokan. Fairness in electronic commerce . Ph.D. thesis, University of Waterloo, Canada, 1998. [ASW97] N. Asokan, M. Schunter, and M. Waidner. Optimistic protocols for fair ex-change. In CCS ’97 , pages 8–17. ACM Press, 1997. REFERENCES 125 [ASW98a] N. Asokan, V. Shoup, and M. Waidner. A... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
[BP06] G. Bella and L. Paulson. Accountability protocols: Formalized and verified. ACM Trans. Inf. Syst. Secur. , 9(2):138–161, 2006. [BPW07] S. Brams, K. Pruhs, and G. Woeginger, editors. Fair Division . Num-ber 07261 in Dagstuhl Seminar Proceedings. Internationales Begegnungs-und Forschungszentrum f¨ ur Informatik (I... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
, pages 287– 305. Springer, 2004. [CKS04] R. Chadha, S. Kremer, and A. Scedrov. Formal analysis of multi-party con-tract signing. In CSFW ’04 , pages 266–265. IEEE CS, 2004. [Cle90] R. Cleve. Controlled gradual disclosure schemes for random bits and their applications. In CRYPTO ’89 , volume 435 of Lecture Notes in Com... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
P. Ezhilchelvan and S. Shrivastava. A family of trusted third party based fair-exchange protocols. IEEE Trans. Dependable Secur. Comput. , 2(4):273–286, 2005. [Eve83] S. Even. A protocol for signing contracts. SIGACT News , 15(1):34–39, 1983. [EY80] S. Even and Y. Yacobi. Relations among public key signature systems. T... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
of Lecture Notes in Computer Science , pages 210–219. Springer, 2002. [FPH04] J. Ferrer-Gomila, M. Payeras-Capell` a, and L. Huguet-i-Rotger. Optimality in asynchronous contract signing protocols. In TrustBus ’04 , volume 3184 of Lecture Notes in Computer Science , pages 200–208. Springer, 2004. [FR97] M. Franklin and ... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
, volume 4307 of Lecture Notes in Computer Science , pages 30–49. Springer, 2006. [Gra78] J. Gray. Notes on data base operating systems. In Operating Systems, An Advanced Course , volume 60 of Lecture Notes in Computer Science , pages 393–481. Springer, 1978. [GRV05] S. G¨ urgens, C. Rudolph, and H. Vogt. On the securi... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
Computer Communications , 25(17):1606–1621, 2002. [Kre03] S. Kremer. Formal Analysis of Optimistic Fair Exchange Protocols . Ph.D. thesis, Universit´ e Libre de Bruxelles, 2003. [LNJ01] P. Liu, P. Ning, and S. Jajodia. Avoiding loss of fairness owing to failures in fair data exchange systems. Decision Support Systems ,... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
S. Saeednia. Optimistic fair-exchange with transparent signature recovery. In FC ’01 , volume 2339 of Lecture Notes in Computer Science , pages 339–350. Springer, 2002. 130 NOTES [MW87] S. Moran and Y. Wolfstahl. Extended impossibility results for asynchronous complete networks. Inf. Process. Lett. , 26(3):145–151, 198... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
I. Ray and I. Ray. An optimistic fair exchange e-commerce protocol with automated dispute resolution. In EC-WEB ’00 , volume 1875 of Lecture Notes in Computer Science , pages 84–93. Springer, 2000. [RRN05] I. Ray, I. Ray, and N. Natarajan. An anonymous and failure resilient fair-exchange e-commerce protocol. Decision S... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
electronic payment protocols. In ICDCS ’96 , pages 261–269. IEEE CS, 1996. [TIHF04] M. Terada, M. Iguchi, M. Hanadate, and K. Fujimura. An optimistic fair exchange protocol for trading electronic rights. In CARDIS ’04 , pages 255– 270. Kluwer, 2004. [TKJ08] M. Torabi Dashti, S. Krishnan Nair, and H. Jonker. Nuovo DRM P... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
’04 , volume 3348 of Lecture Notes in Computer Science , pages 48–60. Springer, 2004. [WBZ06] G. Wang, F. Bao, and J. Zhou. The fairness of perfect concurrent signatures. In ICICS ’06 , volume 4307 of Lecture Notes in Computer Science , pages 435– 451. Springer, 2006. [WH07] K. Wei and J. Heather. A theorem-proving app... | {
"page_id": null,
"source": 7326,
"title": "from dpo"
} |
Title: Prove that root 2 is an irrational number.[Solved] URL Source: Markdown Content: Prove that root 2 is an irrational number.[Solved] =============== ![Image 1: cuemath_logo2 ⇒ 2q 2 = 4x 2 ⇒ q 2 = 2x 2 ⇒ q 2 is an even number. Therefore, q is also even. Since p and q both are even numbers, they have 2 as a [commo... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
of p/q with "p and q both co-prime numbers" and q ≠ 0. ### Thus, √2 is an irrational number by the contradiction method. **☛ Also Check:**Prove that Root 2 is Irrational Number]( [FAQs]( MATHS WORKSHEETS [Kindergarten Maths Worksheets]( [Maths Worksheet for Grade 1]( [Maths Worksheet for Grade 2]( [Maths Worksheet for ... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
Maths Worksheet for Grade 8]( [FAQs]( CURRICULUM [1st Grade Maths]( [2nd Grade Maths]( [3rd Grade Maths]( [4th Grade Maths]( [5th Grade Maths]( [6th Grade Maths]( [7th Grade Maths]( [8th Grade Maths]( []( [Terms and Conditions]( Policy]( | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
Title: A proof that the square root of 2 is irrational number URL Source: Markdown Content: A proof that the square root of 2 is irrational number =============== [![Image 1: Home - HomeschoolMath.net]( Free worksheets * By Grades * [1st grade]( * [2nd grade]( * [3rd grade]( * [4th grade]( * [5th grade]( * [6th grade]... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
* [Decimals]( * [Percent]( * [Integers]( * [Exponents]( * [Statistics & Graphs]( * [Probability]( * [Geometry topics]( * [Algebra]( * [Calculus]( * [Trigonometry]( * [Logic and proof]( * For all levels * [Favorite math puzzles]( * [Favorite challenging puzzles]( * [Math in real world]( * [Problem solving & projects]( *... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
terms, since that can obviously be done with any fraction. Notice that in order for _a/b_ to be in simplest terms, both of _a_ and _b_ cannot be even. One or both must be odd. Otherwise, we could simplify _a/b_ further. From the equality √2 = _a/b_ it follows that 2 = _a_ 2/_b_ 2, or _a_ 2 = 2 · _b_ 2. So the square of... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
Teaching tens and ones]( * Comparing 2-digit numbers) Grade 1 * Missing addend concept (0-10)]( * Add a 2-digit number and a single-digit number mentally) Grade 3 * Multiplication concept as repeated addition) Grade 3 * Division as making groups]( * [Divisibility]( Grade 4 * [How to teach long division]( * [Long divisi... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
& long division]( * Two-digit divisor) * Understanding fractions) * Lines, rays, and angles * Review: Area of Polygons * Surface Area * Decimals Lessons) * Decimals videos]( * Decimal place value (1 decimal digit)]( * Decimal place value (2 decimal digits)]( * Add & subtract (1 decimal digit)]( * [Add and subtract deci... | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
Multiply and divide decimals by 10, 100, and 1000) * How to teach proportions) * Four habits of highly effective math teaching]( * Keeping math skills sharp in the summer;) Powered By 00:00/00:53 10 Sec 1.2M 12 Welcome to home school math Next Stay ![Image 3]( 4]( 5]( 6]( | {
"page_id": null,
"source": 7329,
"title": "from dpo"
} |
Title: URL Source: Markdown Content: # Distributed Algorithms Fall 2020 ## Consensus 6th exercise session, 26/10/2020 Matteo Monti Jovan Komatovic 1FloodSet Algorithm (1/2) The agreement problem for crash failures has a very simple algorithm, called FloodSet. Processes just propagate all the values in the input set V ... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
construction we have that at the end of round r, W i (r) is the union of all W j (r-1) , ∀j ∈ I. Proof of lemma 2 : We use induction on the number of rounds. Base case is the assumption on the lemma. For the induction step, you just need to note that all processes are broadcasting the same set, and therefore do not mak... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
for W.Exercise 3 What is the communication complexity of the FloodSet algorithm in: ● number of messages, ● bits, given that b is the number of bits required to represent the elements of V? Is the decision rule (last bullet of the algorithm) so critical? In other words, is there any alternative decision rule we can hav... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
a protocol to reach consensus. Optimize your protocol according to speed. b) How many rounds does your protocol require? c) Assume there are w+h faulty processes. In the worst-case scenario, how many rounds does the protocol require now? > 12 ## Exercise 4 (Solution 1/2) a) The goal if the protocol is for every process... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
Title: Parameterized verification of leader/follower systems via first-order temporal logic URL Source: Markdown Content: 1 Introduction -------------- Parameterized verification is becoming increasingly important nowadays, with technologies like the Internet of Things (IoT), sensor networks, robot swarms, and satelli... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
in Computer Science, pp. 352–359. IEEE Computer Society Press")]. The model checking approach has been applied to several scenarios verifying safety properties and some liveness properties, but is in general incomplete. Constraint-based approaches do provide complete procedures for checking safety properties, but these... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
Konev B, Lisitsa A (2008) Practical first-order temporal reasoning. In: International Symposium on Temporal Representation and Reasoning, pp. 156–163. IEEE"), 16 Practical Infinite-State Verification with Temporal Reasoning. In: Verification of Infinite State Systems and Security, NATO Security through Science Series: ... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
of protocols, such as cache coherence, atomic commit, consensus, and synchronization protocols. Sect.5 orchestrates the operation of arbitrarily many, identical finite-state machines (referred to as _followers_). As an example of such a setting, consider a simple consensus protocol in which the leader asks the follower... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
any information to the leader, apart from the _possibility_ of a consensus _in the future_ (assuming the leader has not received any “no” messages). To be able to make a decision about the consensus in the future, the leader has to maintain a persistent record of individual messages together with an identifier for thei... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
pp. 156–163. IEEE"), 16 Practical Infinite-State Verification with Temporal Reasoning. In: Verification of Infinite State Systems and Security, NATO Security through Science Series: Information and Communication, vol. 1, pp. 91–100. IOS Press")] since follower broadcasts can be emulated using the leader as a network re... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
(false); the usual Boolean connectives (\(\lnot , \vee , \wedge , \rightarrow , \leftrightarrow \)); the quantifiers \(\forall \) (for all) and \(\exists \) (exists); and the temporal operators \(\Box \) (always in the future), \(\Diamond \) (sometime in the future), !Image 2, !Image 3, and !Image 4. The syntax of \(\t... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
propositional constants \(\top \) or \(\bot \)), and to each constant symbol _c_ an element \(c^{{\mathfrak {A}}_n}\) of _A_. We require that the interpretation of constants be _rigid_, i.e.\(I_n(c) = I_m(c)\), for all \(n, m \in {\mathbb {N}}\). An _assignment_\({\mathfrak {a}}\) in _A_ is a function from the set of v... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
fragment of first-order logic, decidable [22 Decidable fragments of first-order temporal logics. Annals Pure Appl Logic 106(1–3):85–134")]. Of particular interest to us are the monadic fragment and the two-variable fragment of \(\textsf {MFOTL}\), both decidable and EXPSPACE-complete [21 On the computational complexity... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
simple foraging robotic behaviours. Int J Intell Comput Cybern 2(4):604–643"),4 Abstract accountability language: translation, compliance and application. In: Asia-Pacific Software Engineering Conference, pp. 214–221. IEEE"),5 Checking accountability with a prover. In: Computer Software and Applications Conference, vol... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
of Liverpool")] report on characterizing finite domains using \(\textsf {MFOTL}\). In particular, [17 Temporal verification of fault-tolerant protocols. In: Methods, Models and Tools for Fault Tolerance, pp. 44–56. Springer")] reports that each of the following three axioms enforces finite domains (and is derivable fro... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
1} x \, P(x)\) in place of \(\exists x P(x)\) sometimes for emphasis.) Due to the aforementioned limitation, \(\exists ^{=1} x \, P(x)\) and \(\exists ^{> 1} x \, P(x)\) cannot be input to TeMP or TSPASS. To address this issue, one option is attempting to specify equality axiomatically. In a non-temporal setting, equal... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
to check the validity of a monodic formula \(\chi \) containing equality: one uses TeMP or TSPASS to check whether \(\textsf {EqAx} \rightarrow [\chi ]_E\) is valid; if the prover concludes that it is, then one knows that \(\chi \) is valid; if the prover concludes that \(\textsf {EqAx} \rightarrow [\chi ]_E\) is not v... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
appropriate inbox. Every follower has an inbox of messages and, upon delivery, each message to a follower is added to the follower’s inbox. The leader’s transitions correspond to three types of actions: (a)reacting to one of its inboxes; (b) broadcasting a message to the followers; and (c) local (not related to the net... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
_ingoing_, we write \(\mu \) with a _left-pointing arrow_ on top (!Image 19 is _outgoing_, we write \(\mu \) with a _right-pointing arrow_ on top (\(\vec {\mu }\)). The leader’s inbox corresponding to a message !Image 20 we introduce the following notation. Transitions in which the leader _reacts to an inbox_!Image 22,... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
{\mu }\) denotes the transition in which the leader broadcasts \(\mu \). _Local_ transitions are simply denoted with a plain label (no arrow on top). Similar notation is used for followers reacting to a message (!Image 34), as well as for their local transitions (no arrow on top). For examples using the above notation ... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
is unable to take any other transition. We define the _size_ of _L_, denoted \(\Vert L\Vert \), to be the quantity \(|Q^L|+|T^L|+|\delta ^L|\). For some example leaders see Sect.5 set _A_, whose elements are to be viewed as representing followers in the leader’s network. Let _L_ be a leader as above and \(A = \{ a_1, \... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
(!Image 56 !Image 58 !Image 61\) as an _enabled_ transition. Intuitively, \(\tau \in enb ( {\mathfrak {c}} )\) if \(\tau \) is one of the available transitions for _L_ when _L_’s configuration is \({\mathfrak {c}}\). Thus, all transitions in which a message is broadcast and all local transitions are enabled, whereas tr... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
\{ \langle {\mathfrak {c}}_n, \tau _n \rangle \}_{n \in {\mathbb {N}}}\), where !Image 74) is an l-configuration and \(\tau _n \in T^L\) (\(n \in {\mathbb {N}}\)), such that: \(q_0 \in Q^L_\text {init}\), !Image 75); for all \(n \in {\mathbb {N}}\), \(\iota ({\mathfrak {c}}_n) \preceq ^{\tau _n} \iota ({\mathfrak {c}}_... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
* \(Q^F\) is a finite set, the set of _states_ of \(F\); * \(Q^F_\text {init} \subseteq Q^F\) are the _initial states_ of \(F\); * \(T^F= T^F_\text {in} \cup T^F_\text {out} \cup T^F_\text {local} \cup \{ \textit{idle}\}\) is the set of _transitions_ of \(F\); and * \(\delta ^F\subseteq Q^F\times (T^F\setminus \{ \text... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
that \(\langle q, \tau , q' \rangle \in \delta ^F\), for some \(q' \in Q^F\), and either (a) \(\tau \in T^F_\text {out} \cup T^F_\text {local}\) or (b) !Image 87\) if \(\tau \) is one of the available transitions for _F_ when _F_’s configuration is \({\mathfrak {c}}\). Thus, all transitions in which a message is sent a... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
(b) \( enb ( {\mathfrak {c}}_n ) = \emptyset \), \(\tau _n = \textit{idle}\), and \(q_n = q_{n+1}\). Intuitively, a run describes a valid execution for _F_: _F_ starts at an initial state with its inbox empty, and, at each moment of time, chooses an enabled (at that time) transition or becomes idle if none exists. Mess... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
avoid ambiguities in the logical translation presented in Sect.4 be a distributed machine and \(A = \{ a_1, \ldots , a_k \}\) (\(k > 0\)) be a set, referred to as the _universe_ of _M_. Intuitively, each \(a \in A\) is identified with a (replicated) follower _F_. A _run_ for _M_ over _A_ is a \((k+1)\)-tuple \({\mathfr... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
been broadcast by the leader at some point in the past. Similarly, (A2) states that if a follower \(a \in A\) sends a message \(\vec {\mu }\) to the leader, _a_ will eventually appear in the inbox !Image 106 has been sent by _a_ to the leader at some point in the past. Conditions (A1) and (A2) describe an asynchronous ... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
machine when the delivery of a message from a follower to the leader coincides with the leader deleting the content of the corresponding inbox or when the delivery of a message from the leader to a follower coincides with the follower reacting to it and thus deleting it (the message could already be present in the foll... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
\in T^L\); and a unary predicate \({{\textsf{t}}}{{\textsf{f}}}_{\tau }(\cdot )\) for each \(\tau \in T^F\). For each \(q \in Q^L\), \({{\textsf{s}}}{{\textsf{l}}}_{q}\) (short for _state leader_) is to be viewed as stating that the leader is at state _q_. For each \(q \in Q^F\), \({{\textsf{s}}}{{\textsf{f}}}_{q}(a)\)... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
\{ q \}} \!\!\!\! \lnot {{\textsf{s}}}{{\textsf{l}}}_{q'} \big ), \\ \textsf {utransl}&\,:=\, \bigvee _{\tau \in T^L} \big ( {{\textsf{t}}}{{\textsf{l}}}_{\tau } \,\wedge \!\!\!\! \bigwedge _{\tau ' \in T^L \setminus \{ \tau \}} \!\!\!\! \lnot {{\textsf{t}}}{{\textsf{l}}}_{\tau '} \big ). \end{aligned}$$ The next formu... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
{O}}(\Vert L\Vert ^2)\). ### 4.2 The followers’ execution Next, we write a collection of formulas describing the execution of each follower. The following formulas (short for _unique state follower_ and _unique transition follower_ respectively) state that the states and transitions of follower _x_ are unique: $$\begin... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
whole operation. It is clear that \(\Vert \textsf {follower}(x)\Vert = {\mathcal {O}}(\Vert F\Vert ^2)\). ### 4.3 The distributed machine’s execution Next, we write a collection of formulas describing the network of the leader and its followers, and, combining these formulas with the ones in the previous two subsection... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
predicate \(\textsf {past}_{\vec {\mu }}(\cdot )\)) appearing in the second conjunct of bcastla (resp.sendfa) exists. Finally, the following formula \(\textsf {neta}\) (short for _network asynchronous_) describes the operation of the asynchronous network comprising the leader and its followers: $$\begin{aligned} \texts... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
from a previous round, leaving the follower in an inconsistent state.) At the time of writing, the authors know of no way of enforcing delivery of messages exactly once within the current approach. One possibility could be to parameterize each message delivery to a recipient _x_ with an identifier _y_. Then, one could ... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
i \le k\)), where \({\mathcal {I}}^i_n \subseteq T^F_\text {in}\) (\(1 \le i \le k\)). Let \(\Sigma ^M\) be as in the beginning of this section. We construct from \({\mathfrak {R}}\) a sequence \({\mathfrak {M}}= \{ {\mathfrak {A}}_n \}_{n \in {\mathbb {N}}}\), where each \({\mathfrak {A}}_n\) (\(n \in {\mathbb {N}}\))... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
(a), (b), and (d) that \({\mathfrak {A}}_0 \models \textsf {initl}\) and, for all \(n \in {\mathbb {N}}\), \({\mathfrak {A}}_n \models \textsf {ustatel}\) and \({\mathfrak {A}}_n \models \textsf {utransl}\). To show that, for all \(n \in {\mathbb {N}}\), \({\mathfrak {A}}_n \models \textsf {persl}\), let !Image 152, !I... | {
"page_id": null,
"source": 7332,
"title": "from dpo"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.