#
Weak Bisimulation is Sound and Complete for PCTL*

Josée Desharnais, Vineet Gupta, Radha Jagadeesan, Prakash Panangaden
### Abstract

We investigate weak bisimulation of probabilistic
systems in the presence of nondeterminism, i.e. labelled concurrent
Markov chains (LCMC) with silent transitions. We build on the work of
Philippou, Lee and Sokolsky for finite state LCMCs.
Their definition of weak bisimulation destroys the additivity property
of the probability distributions, yielding instead *capacities*.
The mathematics behind capacities naturally captures the intuition
that when we deal with nondeterminism we must work with estimates on
the possible probabilities.
Our analysis leads to three new developments:
- We identify an axiomatization of "image finiteness" for
countable state systems and present a new definition of weak
bisimulation for these LCMCs. We prove that our definition
coincides with that of Philippou, Lee and Sokolsky for finite
state systems.

- We show that bisimilar states have matching computations.
The notion of matching involves
*linear combinations* of transitions.
This idea is closely related to the use of randomized schedulers.

- We study a minor variant of the probabilistic logic pCTL*
- the variation arises from an extra path formula to address action
labels. We show that bisimulation is sound and complete for this
variant of pCTL*.

© Springer Verlag, 2002. Published in the
Lecture Notes in Computer Science Series.

@InProceedings{weak-bisim-pctl,
author = "Josee Desharnais and Vineet Gupta and Radha Jagadeesan and Prakash Panangaden",
title = "Weak Bisimulation is Sound and Complete for PCTL*",
booktitle = "Proceedings of CONCUR 2002",
editor= "Petr Jancar and Mojmir Kretinsky",
series = "Lecture Notes in Computer Science 2421",
publisher = "Springer Verlag",
year = "2002",
month = "August"
}

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