Approximating labelled Markov processes

  • Authors:

  • Josée Desharnais;Vineet Gupta;Radha Jagadeesan;Prakash Panangaden

  • Affiliations:

  • Département d'Informatique, Université Laval, Qué., Canada G1K 7P4;Google Inc., 2400 Bayshore Parkway, Mountain View, CA;School of CTI, DePaul University, 243 S. Wabash Street, Chicago, IL;School of Computer Science, McGill University, Montréal, Canada H3A 2A7

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. In this paper, we study approximation techniques for continuousstate labelled Markov processes.We show that the collection of labelled Markov processes carries a Polish-space structure with a countable basis given by finite-state Markov chains with rational probabilities: thus permitting the approximation of quantitative observations (e.g., an integral of a continuous function) of a continuous-state labelled Markov process by the observations on finite-state Markov chains. The primary technical tools that we develop to reach these results are • A variant of a finite-model theorem for the modal logic used to characterize bisimulation, and • an isomorphism between the poset of Markov processes (ordered by simulation) with the ω-continuous dcpo Proc (defined as the solution of the recursive domain equation Proc = ΠL PPr(Proc)). The isomorphism between labelled Markov processes and Proc can be independently viewed as a full-abstraction result relating an operational (labelled Markov process) and a denotational (Proc) model and yields a logic complete for reasoning about simulation for continuous-state processes.