An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability

Authors:
Rajeev Goré;Florian Widmann
Affiliations:
Logic and Computation Group, The Australian National University, Canberra, Australia ACT 0200;Logic and Computation Group and NICTA, The Australian National University, Canberra, Australia ACT 0200
Venue:
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Year:
2009

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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.