## Paper: Approximating Labeled Markov Processes (at LICS 2000)

**Josée Desharnais Prakash Panangaden Radha Jagadeesan Vineet Gupta**

### Abstract

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.

### BibTeX

@InProceedings{DesharnaisPanangade-ApproximatingLabele, author = {Josée Desharnais and Prakash Panangaden and Radha Jagadeesan and Vineet Gupta}, title = {Approximating Labeled Markov Processes}, booktitle = {Proceedings of the Fifteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2000)}, year = {2000}, month = {June}, pages = {95--106}, location = {Santa Barbara, CA, USA}, publisher = {IEEE Computer Society Press} }