Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
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Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Derandomizing homomorphism testing in general groups
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Decomposing finite Abelian groups
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We construct an efficient probabilistic algorithm that, given a finite set with a binary operation, tests if it is an abelian group. The distance used is an analogue of the edit distance for strings. The query complexity of the tester is polylogarithmic in the size of the set. Previous testers used Hamming type distances and had superlinear query complexity. A building block for our construction is a constant query complexity homomorphism tester for functions mapping an given finite group into an arbitrary set equipped with a binary operation.