Year: 2016 | |

12/2 | [elc] ELC Seminar (Prof. Hubie Chen) |

Place : CELC seminar room | |

Date: Dec. 2nd (Fri) 10:30-11:45 Place: ELC Seminar room (Tokyo Tech. CIC Tamachi) Speaker: Professor Hubie Chen (Universidad del Pais Vasco) Title: Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness Abstract: If one looks at typical proof systems for QBF, such as Q-resolution, a dilemma is encountered: lower bounds for Q-resolution are implied immediately by lower bounds for resolution, yet this says nothing about Q-resolution's ability to cope with quantifier alternation--- and moreover clashes severely with the contemporary QBF view of SAT as "easy". In this talk, we will discuss this dilemma and present a possible way to escape it. In particular, 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 technical 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. This talk will focus on a conceptual discussion of the work's motivation, the framework and the main definitions. (host: Osamu Watanabe, watanabe@is.titech.ac.jp) |

horiyama@al.ics.saitama-u.ac.jp