Affiliation:
1. Universidad del Paí Vasco and IKERBASQUE, Basque Foundation for Science, Spain
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
that is based on the established proof system
QU-resolution
. Our main results include an exponential separation of the treelike 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.
Funder
Basque Government Project
University of the Basque Country
Spanish Project FORMALISM
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Reference30 articles.
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