Model-Checking Counting Temporal Logics on Flat Structures

Authors Normann Decker, Peter Habermehl, Martin Leucker, Arnaud Sangnier, Daniel Thoma

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Normann Decker
Peter Habermehl
Martin Leucker
Arnaud Sangnier
Daniel Thoma

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Normann Decker, Peter Habermehl, Martin Leucker, Arnaud Sangnier, and Daniel Thoma. Model-Checking Counting Temporal Logics on Flat Structures. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show that decidability can be recovered by considering flat Kripke structures where each state belongs to at most one simple loop. Most decision procedures are based on results on (flat) counter systems where counters are used to implement the evaluation of counting operators.
  • Counting Temporal Logic
  • Model checking
  • Flat Kripke Structure


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