Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Probabilistic, nondeterministic, and alternating decision trees (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Unbounded fan-in circuits and associative functions
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
NP is as easy as detecting unique solutions
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Are search and decision programs computationally equivalent?
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the theory of average case complexity
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On the hardness of computing the permanent of random matrices (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Making zero-knowledge provers efficient
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Computational complexity and knowledge complexity (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The amazing power of pairwise independence (abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Knowledge on the average—perfect, statistical and logarithmic
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On the relative complexity of approximate counting problems
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
On the Derandomization of Constant Depth Circuits
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
A theorem on probabilistic constant depth Computations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Inapproximability of the Tutte polynomial
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandomness for Approximate Counting and Sampling
Computational Complexity
The matching problem for bipartite graphs with polynomially bounded permanents is in NC
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Inapproximability of the Tutte polynomial
Information and Computation
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Learning parities in the mistake-bound model
Information Processing Letters
The leakage-resilience limit of a computational problem is equal to its unpredictability entropy
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
A scalable and nearly uniform generator of SAT witnesses
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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There are several computational problems that can be formulated as problems of counting the number of objects having a certain property. Valiant [22] has introduced the class #P which includes a variety of counting problems such as counting the number of perfect matchings in a graph, computing the permanent of a matrix [22], finding the size of a backtrack search tree [14], and computing the probability that a network remains connected when links can fail with a certain probability [23]. We define and study a class of restricted, but very natural, probabilistic sampling methods motivated by the particular counting problems mentioned above. Instead of “singleton sampling” the algorithm is allowed to sample a large set S ample; U in one step; the information returned from the sample is whether S contains any element having the property being counted. We attempt to classify the complexity of computing approximate solutions to problems in #P. The classification is done in terms of the polynomial-time hierarchy (for short, P-hierarchy) [21]. We give a relativization result that complements a recent result of Sipser and Gaacute;c [19] that BPP is contained in the second level of the P-hierarchy.