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A Decidable Non-Regular Modal Fixpoint Logic

Authors Florian Bruse, Martin Lange

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Author Details

Florian Bruse
  • School of Electrical Engineering and Computer Science, Universität Kassel, Germany
Martin Lange
  • School of Electrical Engineering and Computer Science, Universität Kassel, Germany

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Florian Bruse and Martin Lange. A Decidable Non-Regular Modal Fixpoint Logic. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CONCUR.2021.23

Abstract

Fixpoint Logic with Chop (FLC) extends the modal μ-calculus with an operator for sequential composition between predicate transformers. This makes it an expressive modal fixpoint logic which is capable of formalising many non-regular program properties. Its satisfiability problem is highly undecidable. Here we define Visibly Pushdown Fixpoint Logic with Chop, a fragment in which fixpoint formulas are required to be of a certain form resembling visibly pushdown grammars. We give a sound and complete game-theoretic characterisation of FLC’s satisfiability problem and show that the games corresponding to formulas from this fragment are stair-parity games and therefore effectively solvable, resulting in 2EXPTIME-completeness of this fragment. The lower bound is inherited from PDL over Recursive Programs, which is structurally similar but considerably weaker in expressive power.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Program specifications
Keywords
  • formal specification
  • temporal logic
  • expressive power

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