Abstract
We investigate the complexity of strong nondeterministic circuit minimization problem (SNCMP in short) in relation to derandomizing Arthur-Merlin games. We show derandomization results for Arthur-Merlin games under both easiness and hardness assumptions about the complexity of SNCMP. Assuming SNCMP is non-uniformly easy, we present derandomization of Arthur-Merlin games using weaker hardness assumptions than what is currently known. On the other hand, we show that establishing SNCMP is hard for SAT or Graph Isomorphism problem under certain natural reductions will show that Graph Nonisomorphism problem has subexponential proofs of membership. We combine known constructions of pseudorandom and hitting set generators to prove our results.
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