One-pass tableaux for computation tree logic

  • Authors:

  • Pietro Abate;Rajeev Goré;Florian Widmann

  • Affiliations:

  • The Australian National University, Canberra, ACT, Australia;The Australian National University, Canberra, ACT, Australia;The Australian National University, Canberra, ACT, Australia and Canberra Research Laboratory, NICTA, Australia

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

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Abstract

We give the first single-pass ("on the fly") tableau decision procedure for computational tree logic (CTL). Our method extends Schwendimann's single-pass decision procedure for propositional linear temporal logic (PLTL) but the extension is non-trivial because of the interactions between the branching inherent in CTL-models, which is missing in PLTL-models, and the "or" branching inherent in tableau search. Our method extends to many other fix-point logics like propositional dynamic logic (PDL) and the logic of common knowledge (LCK). The decision problem for CTL is known to be EXPTIME-complete, but our procedure requires 2EXPTIME in the worst case. A similar phenomenon occurs in extremely efficient practical single-pass tableau algorithms for very expressive description logics with EXPTIME-complete decision problems because the 2EXPTIME worst-case behaviour rarely arises. Our method is amenable to the numerous optimisation methods invented for these description logics and has been implemented in the Tableau Work Bench (twb.rsise.anu.edu.au) without these extensive optimisations. Its one-pass nature also makes it amenable to parallel proof-search on multiple processors.