PDL with Intersection and Converse Is 2EXP-Complete

  • Stefan Göller
  • Markus Lohrey
  • Carsten Lutz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4423)


We study the complexity of satisfiability in the expressive extension ICPDL of PDL (Propositional Dynamic Logic), which admits intersection and converse as program operations. Our main result is containment in 2EXP, which improves the previously known non-elementary upper bound and implies 2EXP-completeness due to an existing lower bound for PDL with intersection. The proof proceeds by showing that every satisfiable ICPDL formula has a model of tree-width at most two and then giving a reduction to the (non)-emptiness problem for alternating two-way automata on infinite trees. In this way, we also reprove in an elegant way Danecki’s difficult result that satisfiability for PDL with intersection is in 2EXP.


Description Logic Tree Decomposition Atomic Proposition Epistemic Logic Kripke Structure 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stefan Göller
    • 1
  • Markus Lohrey
    • 1
  • Carsten Lutz
    • 2
  1. 1.Universität Stuttgart, FMIGermany
  2. 2.Institute for Theoretical Computer Science, TU DresdenGermany

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