A Generic Method for Theorem Proving based on Counting Satisfiability

Theorem proving is a challenging task for formal verification of systems. There exist many efforts to efficiently solve this problem, based for example on rewriting rules and/or SAT-based techniques. We propose an alternative of SAT-based techniques by using instead a counting SAT-based technique (denoted also #SAT). A SAT solver tests if a propositional formula F has at least one truth assignment, while a #SAT solver returns the number of truth assignments of F. For efficiency reasons, many of the existing SAT-based techniques are applied incrementally, that is, using the satisfiability of some sub-formulas to determine the satisfiability of a given formula. While there exist incremental SAT solvers, to the best of our knowledge, our paper presents first time the theoretical background for the incremental counting satisfiability problem. Being a more general technique than the existing works, our approach can be used to handle all the problems solved by SAT solvers. Moreover, our #SAT solver outperforms a SAT solver when considering the challeging problems of re-design or debugging of systems. ∗Lamar University, Department of Computer Science, Texas, USA, [email protected] †University of Houston, Department of Computer Science, Texas, USA, [email protected] ‡Cuza University of Iasi, Department of Computer Science, Romania, [email protected] §Lamar University, Department of Computer Science, Texas, USA, os-