Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness

Hubie Chen

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arXiv · 1410.5369

Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness

Hubie Chen

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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.

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Hubie Chen. 2014-10-20. Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness. https://arxiv.org/abs/1410.5369

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