RegSTAB: A SAT Solver for Propositional Schemata

We describe the system RegStab (for regular schemata tableau) that solves the satisfiability problem for a class of propositional schemata. Our formalism extends propositional logic by considering indexed propositions (such as $P_1,P_{{\tt i}},P_{{\tt j}+1},\ldots$) and iterated connectives (e.g. $\bigvee_{i={\tt i}}^{\tt n} \phi$). The indices and bounds are linear arithmetic expressions (possibly containing variables, interpreted as integers). Our system allows one to check the satisfiability of sequences of formulae such as $(\bigvee_{{\tt i}=1}^{\tt n} P_{\tt i}) \wedge (\bigwedge_{{\tt i}=1}^{\tt n} \neg P_{\tt i})$.