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*Let <math>F_C = F_A \and F_B</math> be the Bloom filter formed by computing the bitwise AND of <math>F_A</math> and <math>F_B</math>. Argue that <math> ...

= Computing Graph Expansion = ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...

...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation :何昆：Kun HE received his Ph.D. degree from the Institute of Computing Technology, Chinese Academy of Sciences in 2019. Currently he is a postdoct ...

* [https://arxiv.org/abs/1907.09415 Ronald de Wolf. Quantum Computing: Lecture Notes.] ...

The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...

Besides directly computing the probability <math>\Pr[X\ge t]</math>, we want to have some general way ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...d store the results in memory. Afterwards he can decrypt the ciphertext by computing ''D_K''(''C'') for each ''K''. Any matches between these two resu ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...

|data17 = '''Probability and Computing''' (2E) <br> Michael Mitzenmacher and Eli Upfal <br> Cambridge University * '''[MU]''' ''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...mal language] (not entirely the same thing as the c language). The task of computing <math>f(x)</math> is equivalent to that of determining whether <math>x\in L ...nomial size certificate, the algorithm <math>A</math> verifies (instead of computing) the <math>f(x)</math> for any positive instance <math>x</math> in polynomi ...

A naive way of checking the equality is first computing <math>AB</math> and then comparing the result with <math>C</math>. The (asy ...

;The Monte Carlo method for computing <math>\mathrm{e}</math> ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

* [[Computer language]] for application of formal languages in computing ...

...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...

...ok.html|title = Proceedings of the Third Annual ACM Symposium on Theory of Computing|pages = 151–158}}</ref> ...ust 1% of the worst-case number of computation and that saves a ''lot'' of computing, but that is still <math>0.01 \times (2^n)</math> computations. And every e ...

|data17 = '''Probability and Computing''' (2E) <br> Michael Mitzenmacher and Eli Upfal <br> Cambridge University * '''[MU]''' ''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis ...

Computing the moment generating function <math>\mathbf{E}[e^{\lambda X}]</math>: We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let ...

...tudies of algorithms for elimination orderings in combinatorial scientific computing, our result is the first rigorous incorporation of randomized tools in this :Huacheng Yu (俞华程) is a postdoctoral researcher in the Theory of Computing group at Harvard University. He obtained his PhD from Stanford University i ...

We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let ...

...> multiplications, which is too expensive. We describe an efficient way of computing the [http://en.wikipedia.org/wiki/Modular_exponentiation modular exponent] ...ed a number instead of a list of all colorings, we expect cleverer ways of computing this number than the brute force enumeration. ...

...he search for new Mersenne primes is the goal of the [[GIMPS]] distributed computing project. *[http://www.oddperfect.org OddPerfect.org] A projected distributed computing project to search for odd perfect numbers. ...

|data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...

[[Decryption]] of a ciphertext <math>(R_n, L_n)</math> is accomplished by computing for <math>i=n,n-1,\ldots,1</math> ...

...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...

|data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...

...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...

* '''Reading assignment''': Mitzenmacher and Upfal, ''Probability and Computing, second edition'', '''Chapter 17''' "Balanced Allocations and Cuckoo Hashin ...

|data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...

...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation ...

...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation ...

== Computing graph expansion == ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...

...ber of perfect matchings of <math>G</math>. This problem can be reduced to computing the '''permanent''' of a square matrix. ...his problem can be reduced to computing the permanent, thus the problem of computing the permanents is also '''#P-hard'''. ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...

...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...