The complexity of linear-time temporal logic over the class of ordinals

Demri St́ephane*, Alexander Rabinovich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a pspace-complete satisfiability problem over the class of ordinals. Among the consequences of our proof, we show that given the code of some countable ordinal α and a formula, we can decide in PSPACE whether the formula has a model over α. In order to show these results, we introduce a class of simple ordinal automata, as expressive as Büchi ordinal automata. The pspace upper bound for the satisfiability problem of the temporal logic is obtained through a reduction to the nonemptiness problem for the simple ordinal automata.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalLogical Methods in Computer Science
Issue number4
StatePublished - 2010


  • Automaton
  • Linear-time temporal logic
  • Ordinal
  • Polynomial space


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