Derandomizing Arthur-Merlin Games using Hitting Sets

Peter Bro Miltersen, Vinodchandran N. Variyam
1999 BRICS Report Series  
We prove that AM (and hence Graph Nonisomorphism) is in NP<br />if for some epsilon > 0, some language in NE intersection coNE requires nondeterministic<br />circuits of size 2^(epsilon n). This improves recent results of Arvind<br />and K¨obler and of Klivans and Van Melkebeek who proved the same<br />conclusion, but under stronger hardness assumptions, namely, either<br />the existence of a language in NE intersection coNE which cannot be approximated<br />by nondeterministic circuits of size
more » ... less than 2^(epsilon n) or the existence<br />of a language in NE intersection coNE which requires oracle circuits of size 2^(epsilon n)<br />with oracle gates for SAT (satisfiability).<br />The previous results on derandomizing AM were based on pseudorandom<br />generators. In contrast, our approach is based on a strengthening<br />of Andreev, Clementi and Rolim's hitting set approach to derandomization.<br />As a spin-off, we show that this approach is strong enough<br />to give an easy (if the existence of explicit dispersers can be assumed<br />known) proof of the following implication: For some epsilon > 0, if there is<br />a language in E which requires nondeterministic circuits of size 2^(epsilon n),<br />then P=BPP. This differs from Impagliazzo and Wigderson's theorem<br />"only" by replacing deterministic circuits with nondeterministic<br />ones.
doi:10.7146/brics.v6i47.20117 fatcat:2ecf3j6i55cqnfvfernj4dxguy