Affiliation:
1. LogicBlox Inc.
2. University at Buffalo, Buffalo, NY
Abstract
We investigate autoreducibility properties of complete sets for NEXP under different polynomial-time reductions. Specifically, we show under some polynomial-time reductions that there are complete sets for NEXP that are not autoreducible. We obtain the following main results:
—For any positive integers
s
and
k
such that 2
s
− 1 >
k
, there is a ≤
s-T
p
-complete set for NEXP that is not ≤
k-tt
p
-autoreducible.
—For every constant
c
> 1, there is a ≤
2-T
p
-complete set for NEXP that is not autoreducible under nonadaptive reductions that make no more than three queries, such that each of them has a length between
n
1/c
and
n
c
, where
n
is input size.
—For any positive integer
k
, there is a ≤
k-tt
p
-complete set for NEXP that is not autoreducible under ≤
k-tt
p
-reductions whose truth table is not a disjunction or a negated disjunction.
Finally, we show that settling the question of whether every ≤
dtt
p
-complete set for NEXP is ≤
NOR-tt
p
-autoreducible either positively or negatively would lead to major results about the exponential time complexity classes.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
1 articles.
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