The complexity of temporal logic with until and since over ordinals

  • Authors:

  • Stéphane Demri;Alexander Rabinovich

  • Affiliations:

  • LSV, ENS Cachan, CNRS, INRIA;Tel Aviv University, Ramat Aviv

  • Venue:
  • LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
  • Year:
  • 2007

Quantified Score

Hi-index 0.01

Visualization

Abstract

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 thanks to 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.