Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
On isomorphism testing of a class of 2-Nilpotent groups
Journal of Computer and System Sciences
Journal of Computer and System Sciences
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
On Resource-Bounded Measure and Pseudorandomness
Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science
Derandomization That Is Rarely Wrong from Short Advice That Is Typically Good
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Derandomizing Arthur-Merlin Games Using Hitting Sets
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the nlog n isomorphism technique (A Preliminary Report)
STOC '78 Proceedings of the tenth 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
Solvable Group Isomorphism is (almost) in NP " CoNP
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On the complexity of trial and error
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The Group Isomorphism problem consists in deciding whether two input groups G1 and G2 given by their multiplication tables are isomorphic. We first give a 2-round Arthur-Merlin protocol for the Group Nonisomorphism problem such that on input groups (G1, G2) of size n, Arthur uses O(log6 n) random bits and Merlin uses O(log2 n) nondeterministic bits. We derandomize this protocol for the case of solvable groups showing the following two results: (a) We give a uniform NP machine for solvable Group Nonisomorphism, that works correctly on all but 2logO(1)(n) inputs of any length n. Furthermore, this NP machine is always correct when the input groups are nonisomorphic. The NP machine is obtained by an unconditional derandomization of the aforesaid AM protocol. (b) Under the assumption that EXP \not\subseteq i.o--PSPACE we get a complete derandomization of the aforesaid AM protocol. Thus, EXP \not\subseteq i.o--PSPACE implies that Group Isomorphism for solvable groups is in NP ∩ coNP.