FZQSAT: A QSAT Solver for QBFs in Prenex NNF (A Useful Tool for Circuit Verification)

In this paper we present FZQSAT, which is an algorithm for evaluating quantified Boolean formulas presented in negation normal form (NNF). QBF is a language that extends propositional logic in such a way that many advanced forms of verification, such as bounded model checking, can be easily formulated and evaluated. FZQSAT is based on ZDD which is a variant of BDD, and is an adopted version of the DPLL algorithm. The capability of ZDDs in storing sets of subsets efficiently, enabled us to store the formula very compact and led us to implement the search algorithm in such a way that we could store and reuse the results of all already solved subformulas. This idea which we call it ’embedding memorization to the semantic tree method in deciding QBFs) along some other techniques, specially the possibility of accepting QBFs in their prenex NNF (instead of requiring to transform them to prenex CNF) enabled FZQSAT to solve the ’sequential depth of circuits’ problem, which is an important problem in bounded model checking, much faster than best existing solvers. FZQSAT also accepts the standard prenex CNF formulas. It manages to solve some standard QBF benchmark problems faster than best existing