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2-Exp Time lower bounds for propositional dynamic logics with intersection

Published online by Cambridge University Press:  12 March 2014

Martin Lange  and
Carsten Lutz
Martin Lange
Affiliation:
Department of Computer Science, University of Munich, Oettingenstr. 67, 80538 Munich, Germany, E-mail: Martin.Lange@ifi.lmu.de
Carsten Lutz
Affiliation:
Department of Computer Science, Dresden University of Technology, Hans-Grundig-Str. 25, 01062 Dresden, Germany, E-mail: lutz@tcs.inf.tu-dresden.de
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Abstract

In 1984. Danecki proved that satisfiability in IPDL, i.e., Propositional Dynamic Logic (PDL) extended with an intersection operator on programs, is decidabie in deterministic double exponential time. Since then, the exact complexity of IPDL has remained an open problem: the best known lower bound was the ExpTime one stemming from plain PDL until, in 2004. the first author established ExpSpace-hardness. In this paper, we finally close the gap and prove that IPDL is hard for 2-ExpTime. thus 2-ExpTime-complete. We then sharpen our lower bound, showing that it even applies to IPDL without the test operator interpreted on tree structures.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1072 - 1086
Copyright
Copyright © Association for Symbolic Logic 2005

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