Representation and Evaluation of QBFs in Prenex-NNF

Theoretical and practical investigations have shown that some forms of reasoning such as belief revision, nonmonotonic reasoning, reasoning about knowledge, and STRIPS-like planning can be formulated by quantified Boolean formulas (QBFs) and can be solved as instances of quantified satisfiability problem (QSAT). Almost all existing QSAT solvers only accept QBFs represented in prenex-CNF. Formulating problems into QBFs usually does not yield prenex-CNF. Therefore, they are required to transform the obtained formula into prenex-CNF before launching it to a QSAT solver. This task usually cannot be done efficiently. In this paper we show how Zero-Suppressed Binary Decision Diagram (abbreviated by ZBDD or ZDD) can be used to represent QBFs given in prenex-NNF and evaluate them efficiently. Transforming any QBF into its equivalent in prenex-NNF usually can be done efficiently.