Title: Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness
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.
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: article
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Cited By Count: 9
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