An Optimal On-the-fly Tableau-based Decision Procedure for PDL satisfiability

Abstract

We give an optimal (exptime), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic. Our main contribution is a sound method to track unfulfilled eventualities "on the fly" which allows us to detect "bad loops" sooner rather than in multiple subsequent passes. We achieve this by propagating and updating the "status" of nodes throughout the underlying graph as soon as is possible. We give sufficient details to enable an easy implementation by others. Preliminary experimental results from our unoptimised OCaml implementation indicate that our algorithm is feasible.