Reasoning about the past with two-way automata

  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)


The Μ-calculus can be viewed as essentially the “ultimate” program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the Μ-calculus is EXPTIME-complete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the Μ-calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on infinite trees.


Model Check Exponential Time Atomic Proposition Acceptance Condition Kripke Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Moshe Y. Vardi
    • 1
  1. 1.Department of Computer ScienceRice UniversityHoustonUSA

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