Model Checking Knowledge and Linear Time: PSPACE Cases

  • Authors:

  • Kai Engelhardt;Peter Gammie;Ron Meyden

  • Affiliations:

  • School of Computer Science and Engineering, The University of New South Wales, and National ICT Australia , Sydney, NSW 2052, Australia;School of Computer Science and Engineering, The University of New South Wales, and National ICT Australia , Sydney, NSW 2052, Australia;School of Computer Science and Engineering, The University of New South Wales, and National ICT Australia , Sydney, NSW 2052, Australia

  • Venue:
  • LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
  • Year:
  • 2007

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Abstract

We present a general algorithm scheme for model checking logics of knowledge, common knowledge and linear time, based on bisimulations to a class of structures that capture the way that agents update their knowledge. We show that the scheme leads to PSPACE implementations of model checking the logic of knowledge and linear time in several special cases: perfect recall systems with a single agent or in which all communication is by synchronous broadcast, and systems in which knowledge is interpreted using either the agents' current observation only or its current observation and clock value. In all these results, common knowledge operators may be included in the language. Matching lower bounds are provided, and it is shown that although the complexity bound matches the PSPACE complexity of the linear time temporal logic LTL, as a function of the model size the problems considered have a higher complexity than LTL.