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View all- Glaßer CNguyen DSelman AWitek M(2016)Introduction to Autoreducibility and MitoticityComputability and Complexity10.1007/978-3-319-50062-1_5(56-78)Online publication date: 1-Dec-2016
Structural Properties of Nonautoreducible Sets
Article No.: 11, Pages 1 - 24
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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Index Terms
- Structural Properties of Nonautoreducible Sets
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Publication History
Published: 11 May 2016
Accepted: 01 March 2016
Received: 01 September 2015
Published in TOCT Volume 8, Issue 3
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View all- Glaßer CNguyen DSelman AWitek M(2016)Introduction to Autoreducibility and MitoticityComputability and Complexity10.1007/978-3-319-50062-1_5(56-78)Online publication date: 1-Dec-2016
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