## Unified QBF certification and its applications.(English)Zbl 1284.68516

Summary: Quantified Boolean formulae (QBF) allow compact encoding of many decision problems. Their importance motivated the development of fast QBF solvers. Certifying the results of a QBF solver not only ensures correctness, but also enables certain synthesis and verification tasks. To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic clause-resolution proof. The semantic certificate for a false QBF is missing, and the syntactic and semantic certificates are somewhat unrelated. This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates by showing that, given a true QBF, its Skolem-function model is derivable from its cube-resolution proof of satisfiability as well as from its clause-resolution proof of unsatisfiability under formula negation. Consequently Skolem-function derivation can be decoupled from special Skolemization-based solvers and computed from standard search-based ones. Experimental results show strong benefits of the new method.

### MSC:

 68T15 Theorem proving (deduction, resolution, etc.) (MSC2010) 03B35 Mechanization of proofs and logical operations 68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) 68T27 Logic in artificial intelligence

### Software:

MiniSat; ABC ; Quaffle
Full Text:

### References:

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