Model Checking Flat Freeze LTL on One-Counter Automata

Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, James Worrell

Research output: Contribution to journalArticlepeer-review


Freeze LTL is a temporal logic with registers that is suitable for specifying properties of data words. In this paper we study the model checking problem for Freeze LTL on one-counter automata. This problem is known to be undecidable in general and PSPACE-complete for the special case of deterministic one-counter automata. Several years ago, Demri and Sangnier investigated the model checking problem for the flat fragment of Freeze LTL on several classes of counter automata and posed the decidability of model checking flat Freeze LTL on one-counter automata as an open problem. In this paper we resolve this problem positively, utilising a known reduction to a reachability problem on one-counter automata with parameterised equality and disequality tests. Our main technical contribution is to show decidability of the latter problem by translation to Presburger arithmetic.
Original languageEnglish
Article numberlmcs:5019
Number of pages21
JournalLogical Methods in Computer Science
Issue number4:20
Publication statusPublished - 7 Dec 2018


  • One-counter automata
  • disequality tests
  • reachability
  • Freeze LTL
  • Presburger arithmetic
  • computer science
  • logic in computer science
  • Formal Languages and Automata Theory


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