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A statement which holds after the execution of a sequence of statements. |
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When something happens with only a constant amount of extra space, it is said to happen in-place. |
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|algorithms|satisfiability|3-sat|sat| |
As is often the case, using a formal definition is helpful:
Let $V$ a finite set. $(V,E)$ is
* a *graph* if $E \subseteq \left\{\{v_1, v_2\} \mid v_1, v_2 \in V \right\}$ and
* a *digraph* if $E \subseteq \left\{(v_1,v_2) \mid v_1, v_2 \in V\right\}$.
Note the central difference: edges are sets in graphs and... |
In coding theory, 'how good a code is' means how many channel errors can be corrected, or better put, the maximal noise level that the code can deal with.
In order to get better codes, the codes are designed using a large alphabet (rather than binary one). And then, the code is good if it can deal with a large rate ... |
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[Cache-oblivious algorithms and data structures](http://en.wikipedia.org/wiki/Cache-oblivious_algorithm) are a rather new thing, introduced by Frigo et al. in [Cache-oblivious algorithms, 1999](http://userweb.cs.utexas.edu/~pingali/CS395T/2009fa/papers/coAlgorithms.pdf). Prokop's [thesis](http://www.google.fi/url?sa=t&... |
Research on evaluating the performance of cache-obliviousness in practice |
|algorithms|data-structures|reference-request| |
You've already covered background research on cache-oblivious algorithms quite well. In terms of benchmarking and practical results, I see this recent paper by Intel is an interesting read:
[A Synergetic Approach to Throughput Computing on x86-based Multicore Desktops][1]
[1]: http://software.intel.com/sites/... |
Here are a few papers that talk about the cache implications of generational garbage collectors:
* [Caching Considerations for Generational Garbage Collection][1]
* [The Effect of Garbage Collection on Cache Performance][2]
From what I can gather, the primary issue is that garbage collected systems trade off spa... |
null |
As is often the case, using a formal definition is helpful:
Let $V$ a finite set. $G=(V,E)$ is
* a *graph* if $E \subseteq \left\{\{v_1, v_2\} \mid v_1, v_2 \in V \right\}$ and
* a *digraph* if $E \subseteq \left\{(v_1,v_2) \mid v_1, v_2 \in V\right\}$.
Note the central difference: edges are sets in graphs a... |
|algorithms|data-structures|reference-request|cpu-cache| |
null |
How does the password that we enter (to connect to a wireless network) encrypt the data on the wireless network?
Through my reading I am not sure if the password that we enter is the same as the passphrase. If that is right then how can the passphrase generate the four WEP keys?
I understand how the four keys wor... |
How does a wifi password encrypt data using WEP and WPA? |
You've already covered background research on cache-oblivious algorithms quite well. In terms of benchmarking and practical results, I see this recent paper by Intel as an interesting read:
[A Synergetic Approach to Throughput Computing on x86-based Multicore Desktops][1]
[1]: http://software.intel.com/sites/... |
A property which holds after the execution of a sequence of statements. |
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Probability theory is the branch of mathematics concerned with modelling and analysing random phenomena. |
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λ-calculus is a formal system for function definition, function application and recursion which forms the mathematical basis of functional programming.
|
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Model checking refers to the following problem: given a model of a system, test automatically whether this model meets a given specification. |
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Model checking refers to the following problem: given a model of a system, test automatically whether this model meets a given specification.
Typically, the systems one has in mind are hardware or software systems, and the specification contains safety requirements such as the absence of deadlocks and similar critic... |
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Many widely used codes for binary data are [concatenated codes,](http://en.wikipedia.org/wiki/Concatenated_error_correction_code) which are composed by using two error-correcting codes. The *inner code* is over a binary alphabet, and the *outer code* is over an alphabet whose symbols correspond to the codewords of the ... |
Many widely used codes for binary data are [concatenated codes,](http://en.wikipedia.org/wiki/Concatenated_error_correction_code) which are composed by using two error-correcting codes. The *inner code* is over a binary alphabet, and the *outer code* is over an alphabet whose symbols correspond to the codewords of the ... |
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There have been.
One such example is [McEliece cryptosystem](http://en.wikipedia.org/wiki/McEliece_cryptosystem) which is based on hardness of decoding a linear code.
A second example is [NTRUEncrypt](http://en.wikipedia.org/wiki/NTRUEncrypt) which is based on the shortest vector problem which I believe is known... |
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Quantum computers might have some advantage over classical computers for some cases. The most remarkable example is [Shor's Algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm) which can factor a large number in polynomial time (while classically, the [best known algorithm](https://en.wikipedia.org/wiki/Number_... |
|cryptography|quantum-computing|hashing| |
Quantum computers might have some advantage over classical computers for some cases. The most remarkable example is [Shor's Algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm) which can factor a large number in polynomial time (while classically, the [best known algorithm](https://en.wikipedia.org/wiki/Number_... |
A fast memory limited in space close to the CPU. A cache is designed to reduce the average time to access memory. |
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Classifies problems based on how hard it is to express the problem in some logical formalism. |
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It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automata. But, apparently, Büchi automata is a more powerful, expressive model. I've heard somewhere that Büchi automata are equivalent to linear-time $\mu$-calculus (that is, $\mu$-calculus with usual fixpoints and only one temporal operator... |
Equivalence of Büchi automata and linear $\mu$-calculus |
Let $\Sigma$ be some finite set of characters of fixed size. Let $\alpha$ be some string over $\Sigma$. We say that a nonempty substring $\beta$ of $\alpha$ is a *repeat* if $\beta = \gamma \gamma$ for some string $\gamma$.
Now, my question is whether the following holds:
> For every $\Sigma$, there exists some ... |
Does every large enough string have repeats? |
|strings| |
|combinatorics|strings| |
|strings|word-combinatorics| |
|information-theory|coding-theory| |
|algorithms|data-structures|computer-architecture|reference-request|cpu-cache| |
|cryptography|computer-networks|encryption|security| |
No, unfortunately not. There are even infinite [*square-free*][1] words if your alphabet has at least three symbols.
This apparently natural border (two-element alphabets have only finitely many square-free words) is observed in many places, for instance:
* $\{xyyz \mid x,y,z\in \Sigma^+\}$ is co-finite for $|\S... |
Worst-case Hardness of NP-complete problems is not sufficient for cryptography. Even if NP-complete problems are hard in the worst-case (P≠NP ), they still could be efficiently solvable in the average-case. Cryptography assumes the existence of average-case intractable problems in NP. Also, proving the existence of ha... |
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|programming-languages|computer-architecture|operating-systems|cpu-cache| |
Satisfiability (often written in all capitals or abbreviated SAT) is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE.
SAT was the first known example of an NP-complete problem. Further, a wide range of other naturally occurr... |
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Satisfiability (often written in all capitals or abbreviated SAT) is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. |
|formal-languages|computability|automata|pushdown-automata| |
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|algorithms|complexity-theory|time-complexity| |
Formal methods are a particular kind of mathematically-based techniques for the specification, development and verification of software and hardware systems. |
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[Formal methods](http://en.wikipedia.org/wiki/Formal_methods) are a particular kind of mathematically-based techniques for the specification, development and verification of software and hardware systems.
The use of formal methods for software and hardware design is motivated by the expectation that, as in other eng... |
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Satisfiability (SAT) is the problem of determining whether there is a variable assignment that fulfills a given Boolean formula. |
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If we have a [divide and conquer algorithm][1], and we make only one recursive call for a subproblem, and it is the second case in [Master theorem](http://en.wikipedia.org/wiki/Master_theorem), i.e. the time complexity of the non-recursive part is $\Theta(\lg^k n)$, then the complexity of the algorithm will be $\Theta(... |
|combinatorics|strings|word-combinatorics| |
The [Post Correspondence Problem][1] (PCP) is undecidable.
The *bounded version of the PCP* is $\mathrm{NP}$-complete and the *marked version of the PCP* (the words of one of the two lists are required to differ in the first letter) is in $\mathrm{PSPACE}$ \[1\].
1. Are these restricted versions used to prove so... |
|computability|complexity-theory| |
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|algorithms|formal-languages|finite-automata|regular-expressions| |
Machine learning provides computer algorithms that automatically discover patterns in data and make intelligent decisions from them.
Classic Problems:
- Classification (e.g., supervised, unsupervised)
- Regression
- Density estimation
- Sampling
- Reinforcement Learning
Relevant Algorithms:
- Principal... |
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Machine learning provides computer algorithms that automatically discover patterns in data and make intelligent decisions from them. |
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Parallel computing seeks to reduce the running times of programs by allowing many computations to be carried out simultaneously. |
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|formal-languages|computability|automata|turing-machines|pushdown-automata| |
|algorithms|probability-theory|randomness|randomized-algorithms| |
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