Point algebras for temporal reasoning: algorithms and complexity

  • Authors:

  • Mathias Broxvall;Peter Jonsson

  • Affiliations:

  • Department of Technology, Örebro University, S-70182 Örebro, Sweden;Department of Computer and Information Science, Linköping University, S-581 83 Linköping, Sweden

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2003

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Abstract

We investigate the computational complexity of temporal reasoning in different time models such as totally-ordered, partially-ordered and branching time. Our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions--for these problems, we identify all tractable subclasses. We also provide a number of additional results; for instance, we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks, we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras.