STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Designing programs that check their work
Journal of the ACM (JACM)
Efficient checkers for number-theoretic computations
Information and Computation
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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In this paper we design a nonadaptive NC checker for permutation group intersection, sharpening a result from Blum and Kannan. This is a consequence of two results. First we show that a nontrivial permutation in the intersection of two given permutation groups (described by lists of generators) can be computed by an NC algorithm with one round of parallel queries to the Group Intersection problem. Next we design a two-round interactive proof system for the complement of the Group Intersection problem, for which the honest prover can be simulated by an NC algorithm with one round of parallel queries to Group Intersection. As a consequence we also have nonadaptive NC checkers for some related group-theoretic problems. On the technical side, we define a generalization of wreath products of permutation groups. This product plays a crucial role in the design of the nonadaptive checkers.