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Lower bound techniques for QBF proof systems. (English) Zbl 07228393

Niedermeier, Rolf (ed.) et al., 35th symposium on theoretical aspects of computer science, STACS 2018, Caen, France, February 28 – March 3, 2018. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 96, Article 2, 8 p. (2018).
Summary: How do we prove that a false QBF is inded false? How big a proof is needed? The special case when all quantifiers are existential is the well-studied setting of propositional proof complexity. Expectedly, universal quantifiers change the game significantly. Several proof systems have been designed in the last couple of decades to handle QBFs. Lower bound paradigms from propositional proof complexity cannot always be extended – in most cases feasible interpolation and consequent transfer of circuit lower bounds works, but obtaining lower bounds on size by providing lower bounds on width fails dramatically. A new paradigm with no analogue in the propositional world has emerged in the form of strategy extraction, allowing for transfer of circuit lower bounds, as well as obtaining independent genuine QBF lower bounds based on a semantic cost measure.
This talk will provide a broad overview of some of these developments.
For the entire collection see [Zbl 1381.68010].

MSC:

03F20 Complexity of proofs
03B35 Mechanization of proofs and logical operations
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)

Software:

CAQE; QuBE++; QUBE; Quaffle
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