Approximating labelled Markov processes

Josée Desharnais, Vineet Gupta, Radha Jagadeesan, Prakash Panangaden
2003 Information and Computation  
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
more » ... 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 = L P Pr (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.
doi:10.1016/s0890-5401(03)00051-8 fatcat:haprjbaejnc67bxzun5cnraery