Derandomizing Arthur-Merlin games using hitting sets
Miltersen, P.B.
Vinodchandran, N.V.
Dept. of Comput. Sci., Aarhus Univ.;
This paper appears in: Foundations of Computer Science, 1999. 40th Annual Symposium on
Publication Date: 1999
On page(s): 71-80
Meeting Date: 10/17/1999 - 10/19/1999
Location: New York City, NY, USA
ISBN: 0-7695-0409-4
References Cited: 35
INSPEC Accession Number: 6431096
Digital Object Identifier: 10.1109/SFFCS.1999.814579
Current Version Published: 2002-08-06
Abstract
We prove that AM (and hence Graph Nonisomorphism) is in NP if for
some ε>0, some language in NE∩ coNE requires
nondeterministic circuits of size 2en. This improves results
of Arvind and Kobler (1997) and of Klivans and Van Melkebeek (1999) who
have proven the same conclusion, but under stronger hardness
assumptions, namely, either the existence of a language in NE∩ coNE
which cannot be approximated by nondeterministic circuits of size less
than 2en or the existence of a language in NE∩ coNE which
requires oracle circuits of size 2en with oracle gates for
SAT (satisfiability). The previous results on derandomizing AM were
based on pseudorandom generators. In contrast, our approach is based on
a strengthening of Andreev, Clementi and Rolim's (1996) hitting set
approach to derandomization. As a spin-off we show that this approach is
strong enough to give an easy (if the existence of explicit dispersers
can be assumed known) proof of the following implication: for some
ε>0, if there is a language in E which requires
nondeterministic circuits of size 2en, then P=BPP. This
differs from Impagliazzo and Wigderson's (1995) theorem
“only” by replacing deterministic circuits with
nondeterministic ones
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