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

Published online by Cambridge University Press:  12 March 2014

Stefan Göller ,
Markus Lohrey  and
Carsten Lutz
Stefan Göller
Affiliation:
Universität Leipzig, Institut für Informatik, Abteilung Algebraische und Logische Grundlagen der Informatik, Johannisgasse 26, 04103 Leipzig, Germany, E-mail: goeller@informatik.uni-leipzig.de
Markus Lohrey
Affiliation:
Universität Leipzig, Institut für Informatik, Abteilung Algebraische und Logische Grundlagen der Informatik, Johannisgasse 26, 04103 Leipzig, Germany, E-mail: lohrey@informatik.uni-stuttgart.de
Carsten Lutz
Affiliation:
Dresden University of Technology, Institute for Theoretical Computer Science, Department of Computer Science, Nöthnitzer Str. 46, 01062 Dresden, Germany, E-mail: lutz@tcs.inf.tu-dresden.de
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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 2ΕΧΡΤΙΜΕ, thus 2ΕΧΡΤΙΜΕ-complete by an existing lower bound, and (ii) infinite-state model checking of basic process algebras and pushdown systems is also 2ΕΧΡΤΙΜΕ-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 2ΕΧΡΤΙΜΕ. We prove the lower bound(s) for infinite-state model checking using an encoding of alternating Turing machines.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 1 , March 2009 , pp. 279 - 314
Copyright
Copyright © Association for Symbolic Logic 2009

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