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Specification in PDL with Recursion

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 7226)

Abstract

By extending regular Propositional Dynamic Logic (PDL) with simple recursive propositions, we obtain a language which has enough expressiveness to allow interesting applications while still enjoying a relatively simple decision procedure. More specifically, it is strictly more expressive than the regular PDL and not more expressive than the single alternation fragment of the modal μ-calculus. We present a decision procedure for satisfiability of a large class of so called simple formulas. The decision procedure has a time complexity which is polynomial in the size of the programs and exponential in the number of the sub-formulas. We show a way to solve process equations of weak bisimulation as an application.

Keywords

  • specification
  • labeled transition systems
  • propositional dynamic logic
  • modal μ-calculus
  • fixed point
  • satisfiability

Research supported by ANR-NSFC 61161130530.

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Liu, X., Xue, B. (2012). Specification in PDL with Recursion. In: Goodloe, A.E., Person, S. (eds) NASA Formal Methods. NFM 2012. Lecture Notes in Computer Science, vol 7226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28891-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-28891-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28890-6

  • Online ISBN: 978-3-642-28891-3

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