Logic in Computer Science, Symposium on (2000)
Santa Barbara, California
June 26, 2000 to June 29, 2000
Josée Desharnais , McGill University
Prakash Panangaden , McGill University
Radha Jagadeesan , Loyola University-Lake Shore Campus
Vineet Gupta , PurpleYogi.com
We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we develop to reach these results are: A finite-model theorem for the modal logic used to characterize bisimulation A categorical equivalence between the category of Markov processes (with simulation morphisms) with the w-continuous dcpo Proc , defined as the solution of the recursive domain equation Proc = ?Labels PProb ( Proc )1.The correspondence between labeled Markov processes and Proc yields logic complete for reasoning about simulation for continuous-state processes.
P. Panangaden, V. Gupta, R. Jagadeesan and J. Desharnais, "Approximating Labeled Markov Processes," Logic in Computer Science, Symposium on(LICS), Santa Barbara, California, 2000, pp. 95.