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DOI: 10.4230/LIPIcs.ICALP.2016.94
URN: urn:nbn:de:0030-drops-62290
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6229/
Chen, Hubie
Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness
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Abstract
We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essentially) a sequence of proof systems where, for each, proof checking can be performed in the polynomial hierarchy. We introduce a proof system ensemble called relaxing QU-res which is based on the established proof system QU-resolution.Our main results include an exponential separation of the tree-like and general versions of relaxing QU-res, and an exponential lower bound for relaxing QU-res; these are analogs of classical results in propositional proof complexity.
BibTeX - Entry
@InProceedings{chen:LIPIcs:2016:6229,
author = {Hubie Chen},
title = {{Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {94:1--94:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6229},
URN = {urn:nbn:de:0030-drops-62290},
doi = {10.4230/LIPIcs.ICALP.2016.94},
annote = {Keywords: proof complexity, polynomial hierarchy, quantified propositional logic}
}
| Keywords: | proof complexity, polynomial hierarchy, quantified propositional logic | |
| Seminar: | 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 23.08.2016 |
