Journal of Symbolic Logic

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

Stefan Göller, Markus Lohrey, and Carsten Lutz

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Abstract

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

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

Dates
First available in Project Euclid: 4 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1231082313

Digital Object Identifier
doi:10.2178/jsl/1231082313

Mathematical Reviews number (MathSciNet)
MR2499431

Zentralblatt MATH identifier
1181.03034

Citation

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. https://projecteuclid.org/euclid.jsl/1231082313.


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