Approximating Markov Processes by Averaging

Author:

Chaput Philippe1,Danos Vincent2,Panangaden Prakash1,Plotkin Gordon2

Affiliation:

1. McGill University

2. University of Edinburgh

Abstract

Normally, one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition. We, however, take a dual view of Markov processes as transformers of bounded measurable functions. This is very much in the same spirit as a “predicate-transformer” view, which is dual to the state-transformer view of transition systems. We redevelop the theory of labelled Markov processes from this viewpoint; in particular, we explore approximation theory. We obtain three main results. (i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximations. (iii) We show that there is a minimal process bisimulation-equivalent to a given process, and this minimal process is obtained as the limit of the finite approximants.

Funder

Natural Sciences and Engineering Research Council of Canada

Office of Naval Research

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

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