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Do there exist complete sets for promise classes?

Beyersdorff, O and Sadowski, Z (2011) Do there exist complete sets for promise classes? Mathematical logic quarterly, 57 (6). 535 - 550 . ISSN 0942-5616


In this paper we investigate the following two questions: Q1: Do there exist optimal proof systems for a given language L? Q2: Do there exist complete problems for a given promise class ? For concrete languages L (such as TAUT or SAT) and concrete promise classes (such as , , , disjoint -pairs etc.), these questions have been intensively studied during the last years, and a number of characterizations have been obtained. Here we provide new characterizations for Q1 and Q2 that apply to almost all promise classes and languages L, thus creating a unifying framework for the study of these practically relevant questions. While questions Q1 and Q2 are left open by our results, we show that they receive affirmative answers when a small amount of advice is available in the underlying machine model. For promise classes with promise condition in, the advice can be replaced by a tally -oracle.

Item Type: Article
Keywords: Computational complexity, optimal proof systems, promise classes
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 19 Jul 2012 11:45
Last Modified: 15 Sep 2014 03:38
Published Version: http://dx.doi.org/10.1002/malq.201010021
Status: Published
Publisher: Wiley-VCH Verlag Berlin
Identification Number: 10.1002/malq.201010021
URI: http://eprints.whiterose.ac.uk/id/eprint/74436

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