Bounded Model Checking for Partial Kripke Structures

Partial Kripke structures model incomplete state spaces with unknown parts. The evaluation of temporal logic formulae on partial Kripke structures is thus based on three-valued interpretations; the additional truth value ⊥ stands for “unknown whether property true or false”. There are existing model checking algorithms as well as tools employing this three-valued interpretation. In this paper we study the applicability of bounded model checking techniques to partial Kripke structures. To this end, we generalise the translation of Kripke structure and temporal logic formula to propositional logic as to include the value ⊥, and define a new notion of satisfiability for propositional formulae containing ⊥ as constants. We show that a check for this kind of satisfiability can be reduced to two checks for ordinary two-valued satisfiability, thus allowing for the use of standard SAT solvers.