License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.23
URN: urn:nbn:de:0030-drops-144003
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14400/
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Bruse, Florian ; Lange, Martin

A Decidable Non-Regular Modal Fixpoint Logic

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LIPIcs-CONCUR-2021-23.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{bruse_et_al:LIPIcs.CONCUR.2021.23,
  author =	{Bruse, Florian and Lange, Martin},
  title =	{{A Decidable Non-Regular Modal Fixpoint Logic}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14400},
  URN =		{urn:nbn:de:0030-drops-144003},
  doi =		{10.4230/LIPIcs.CONCUR.2021.23},
  annote =	{Keywords: formal specification, temporal logic, expressive power}
}

Keywords: formal specification, temporal logic, expressive power
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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