Hyperfinite approximations to labeled markov transition systems

  • Authors:
  • Ernst-Erich Doberkat

  • Affiliations:
  • Chair for Software Technology, University of Dortmund

  • Venue:
  • AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
  • Year:
  • 2006

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Abstract

The problem of finding an approximation to a labeled Markov transition system through hyperfinite transition systems is addressed. It is shown that we can find for each countable family of stochastic relations on Polish spaces a family of relations defined on a hyperfinite set that is infinitely close. This is applied to Kripke models for a simple modal logic in the tradition of Larsen and Skou. It follows that we can find for each Kripke model a hyperfinite one which is infinitely close.