License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2016.28
URN: urn:nbn:de:0030-drops-61643
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David, Amélie ; Laroussinie, Francois ; Markey, Nicolas

On the Expressiveness of QCTL

LIPIcs-CONCUR-2016-28.pdf (0.6 MB)


QCTL extends the temporal logic CTL with quantification over atomic propositions. While the algorithmic questions for QCTL and its fragments with limited quantification depth are well-understood (e.g. satisfiability of QkCTL, with at most k nested blocks of quantifiers, is (k+1)-EXPTIME-complete), very few results are known about the expressiveness of this logic.
We address such expressiveness questions in this paper. We first consider the distinguishing power of these logics (i.e., their ability to separate models), their relationship with behavioural equivalences, and their ability to capture the behaviours of finite Kripke structures with so-called characteristic formulas. We then consider their expressive power (i.e., their ability to express a property), showing that in terms of expressiveness the hierarchy QkCTL collapses at level 2 (in other terms, any QCTL formula can be expressed using at most two nested blocks of quantifiers).

BibTeX - Entry

  author =	{Am{\'e}lie David and Francois Laroussinie and Nicolas Markey},
  title =	{{On the Expressiveness of QCTL}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Jos{\'e}e Desharnais and Radha Jagadeesan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-61643},
  doi =		{10.4230/LIPIcs.CONCUR.2016.28},
  annote =	{Keywords: Specification, Verification, Temporal Logic, Expressiveness, Tree automata}

Keywords: Specification, Verification, Temporal Logic, Expressiveness, Tree automata
Collection: 27th International Conference on Concurrency Theory (CONCUR 2016)
Issue Date: 2016
Date of publication: 24.08.2016

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