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Structural Properties of Nonautoreducible Sets

Published:11 May 2016Publication History
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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 2s − 1 > k, there is a ≤s-Tp-complete set for NEXP that is not ≤k-ttp-autoreducible.

—For every constant c > 1, there is a ≤2-Tp-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 n1/c and nc, where n is input size.

—For any positive integer k, there is a ≤k-ttp-complete set for NEXP that is not autoreducible under ≤k-ttp-reductions whose truth table is not a disjunction or a negated disjunction.

Finally, we show that settling the question of whether every ≤dttp-complete set for NEXP is ≤NOR-ttp-autoreducible either positively or negatively would lead to major results about the exponential time complexity classes.

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        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 8, Issue 3
        May 2016
        105 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/2936308
        Issue’s Table of Contents

        Copyright © 2016 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 11 May 2016
        • Accepted: 1 March 2016
        • Received: 1 September 2015
        Published in toct Volume 8, Issue 3

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