March 2009 PDL with intersection and converse: satisfiability and infinite-state model checking
Stefan Göller, Markus Lohrey, Carsten Lutz
J. Symbolic Logic 74(1): 279-314 (March 2009). DOI: 10.2178/jsl/1231082313


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.


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Stefan Göller. Markus Lohrey. Carsten Lutz. "PDL with intersection and converse: satisfiability and infinite-state model checking." J. Symbolic Logic 74 (1) 279 - 314, March 2009.


Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1181.03034
MathSciNet: MR2499431
Digital Object Identifier: 10.2178/jsl/1231082313

Rights: Copyright © 2009 Association for Symbolic Logic


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Vol.74 • No. 1 • March 2009
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