Testing Labelled Markov Processes

Larsen and Skou introduced a notion of bisimulation for probabilistic transition systems. They characterized probabilistic bisimilarity in terms of a probabilistic modal logic and also in terms of 'button pressing' tests. Desharnais et al. extended the notion of probabilistic bisimulation and the logical characterization of probabilistic bisimilarity to labelled Markov processes. These processes generalize probabilistic transition systems in that they also allow continuous state spaces. We extend the characterization of probabilistic bisimilarity in terms of testing to labelled Markov processes. One of our main technical contributions is the construction of a final object in a category of labelled Markov processes and the identification of a natural metric on the state space of the final labelled Markov process. This metric provides us with another characterization of probabilistic bisimilarity: states are probabilistic bisimilar if and only if they have distance 0.

[1]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[2]  Radha Jagadeesan,et al.  Metrics for partial labeled markov systems , 1999 .

[3]  Albert R. Meyer,et al.  Experimenting with Process Equivalence , 1992, Theor. Comput. Sci..

[4]  Jan Rutten,et al.  On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces , 1998, Mathematical Structures in Computer Science.

[5]  Samson Abramsky,et al.  Observation Equivalence as a Testing Equivalence , 1987, Theor. Comput. Sci..

[6]  K. Parthasarathy,et al.  Probability measures on metric spaces , 1967 .

[7]  Václav Koubek,et al.  Least Fixed Point of a Functor , 1979, J. Comput. Syst. Sci..

[8]  James Worrell,et al.  Towards Quantitative Verification of Probabilistic Transition Systems , 2001, ICALP.

[9]  James Worrell,et al.  An Algorithm for Quantitative Verification of Probabilistic Transition Systems , 2001, CONCUR.

[10]  G. A. Edgar.  Integral, probability, and fractal measures , 1997 .

[11]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[12]  Radha Jagadeesan,et al.  Metrics for Labeled Markov Systems , 1999, CONCUR.

[13]  W. Arveson.  An Invitation To C*-Algebras , 1976 .

[14]  Michèle Giry,et al.  A categorical approach to probability theory , 1982 .

[15]  P. Billingsley,et al.  Probability and Measure , 1980 .

[16]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[17]  Abbas Edalat,et al.  Bisimulation for Labelled Markov Processes , 2002, Inf. Comput..

[18]  Abbas Edalat,et al.  A logical characterization of bisimulation for labeled Markov processes , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[19]  Pierre America,et al.  Solving Reflexive Domain Equations in a Category of Complete Metric Spaces , 1989, J. Comput. Syst. Sci..

[20]  Jan J. M. M. Rutten,et al.  On the Foundation of Final Semantics: Non-Standard Sets, Metric Spaces, Partial Orders , 1992, REX Workshop.