Journal of Symbolic Logic

PDL with intersection and converse: satisfiability and infinite-state model checking

Stefan Göller, Markus Lohrey, and Carsten Lutz

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study satisfiability and infinite-state model checking in ICPDL, which extends Propositional Dynamic Logic (PDL) with intersection and converse operators on programs. The two main results of this paper are that (i) satisfiability is in 2EXPTIME, thus 2EXPTIME-complete by an existing lower bound, and (ii) infinite-state model checking of basic process algebras and pushdown systems is also 2EXPTIME-complete. Both upper bounds are obtained by polynomial time computable reductions to ω-regular tree satisfiability in ICPDL, a reasoning problem that we introduce specifically for this purpose. This problem is then reduced to the emptiness problem for alternating two-way automata on infinite trees. Our approach to (i) also provides a shorter and more elegant proof of Danecki's difficult result that satisfiability in IPDL is in 2EXPTIME. We prove the lower bound(s) for infinite-state model checking using an encoding of alternating Turing machines.

Article information

J. Symbolic Logic Volume 74, Issue 1 (2009), 279-314.

First available in Project Euclid: 4 January 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Göller, Stefan; Lohrey, Markus; Lutz, Carsten. PDL with intersection and converse: satisfiability and infinite-state model checking. J. Symbolic Logic 74 (2009), no. 1, 279--314. doi:10.2178/jsl/1231082313.

Export citation