Self-testing/correcting with applications to numerical problems
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This article is published in Journal of Computer and System Sciences.The article was published on 1993-12-01 and is currently open access. It has received 676 citations till now.read more
Citations
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Journal ArticleDOI
Some optimal inapproximability results
TL;DR: It is proved optimal, up to an arbitrary ε > 0, inapproximability results for Max-E k-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting.
Journal ArticleDOI
Proof verification and the hardness of approximation problems
TL;DR: It is proved that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP = P, and there exists a positive ε such that approximating the maximum clique size in an N-vertex graph to within a factor of Nε is NP-hard.
Journal ArticleDOI
Property testing and its connection to learning and approximation
TL;DR: This paper considers the question of determining whether a function f has property P or is ε-far from any function with property P, and devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a clique of density p-Clique with respect to the vertex set.
Journal ArticleDOI
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
TL;DR: A "reversal" of the connection between probabilistically checkable proofs (PCPs) and the approximability of NP-optimization problems is presented and any NP-hardness of approximation result for MaxClique yields a proof system for NP.
Book ChapterDOI
The LEDA Platform of Combinatorial and Geometric Computing
TL;DR: An overview of the LEDA platform for combinatorial and geometric computing and an account of its development are given and some recent theoretical developments are discussed.
References
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Journal ArticleDOI
The knowledge complexity of interactive proof systems
TL;DR: A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.
Journal ArticleDOI
Gaussian elimination is not optimal
TL;DR: In this paper, Cook et al. gave an algorithm which computes the coefficients of the product of two square matrices A and B of order n with less than 4. 7 n l°g 7 arithmetical operations (all logarithms in this paper are for base 2).
Journal ArticleDOI
How to generate cryptographically strong sequences of pseudo-random bits
Manuel Blum,Silvio Micali +1 more
TL;DR: In this article, the authors give a set of conditions that allow one to generate 50-50 unpredictable bits, and present a general algorithmic scheme for constructing polynomial-time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo-random bits.
Journal ArticleDOI
Monte-Carlo approximation algorithms for enumeration problems
TL;DR: The emphasis is on the development and analysis of a much more efficient ϵ, δ approximation algorithm for the DNF counting problem, which is substantially faster than the fastest known deterministic solution for the problem.
Journal ArticleDOI
Efficient Generation of Random Nonsingular Matrices
TL;DR: This work presents an efficient algorithm for generating an n × n nonsingular matrix uniformly over a finite field, and introduces efficient algorithms for related problems such as uniformly generating singular matrices or matrices with fixed determinant.
Related Papers (5)
Robust Characterizations of Polynomials withApplications to Program Testing
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