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2009
Springer

Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes

8 years 7 months ago
Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
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 C? For concrete languages L (such as TAUT or SAT) and concrete promise classes C (such as NP∩coNP, UP, BPP, disjoint NP-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 C 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 on advice is available in the underlying machine model. This continues a recent line of research on proof systems with advice started by Cook and Kraj´ıˇcek [6].
Olaf Beyersdorff, Zenon Sadowski
Added 04 Sep 2010
Updated 04 Sep 2010
Type Conference
Year 2009
Where CSR
Authors Olaf Beyersdorff, Zenon Sadowski
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