Article

# Branching bisimulation for probabilistic systems: Characteristics and decidability.

Theoretical Computer Science (Impact Factor: 0.49). 01/2006; 356:325-355. DOI: 10.1016/j.tcs.2006.02.010

Source: DBLP

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**ABSTRACT:**We develop a general testing scenario for probabilistic processes, giving rise to two theories: probabilistic may testing and probabilistic must testing. These are applied to a simple probabilistic version of the process calculus CSP. We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer valid in our probabilistic setting; even for non-probabilistic CSP processes, the distinguishing power of probabilistic tests is much greater than that of standard tests. We develop a method for deriving inequations valid in probabilistic may testing based on a probabilistic extension of the notion of simulation. Using this, we obtain a complete axiomatisation for non-probabilistic processes subject to probabilistic may testing.Electronic Notes in Theoretical Computer Science. 01/2007; -
##### Conference Paper: Branching Bisimulations for Higher Order p-Calculus

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**ABSTRACT:**In this paper, we introduce branching context bisimulation, branching normal bisimulation and branching barbed congruence for higher order pi-calculus. Moreover we prove the equivalence of the three branching bisimulations. At last, we compare branching context bisimulations with other bisimulations for higher order pi-calculus.Information Technology and Computer Science, 2009. ITCS 2009. International Conference on; 08/2009 - [Show abstract] [Hide abstract]

**ABSTRACT:**Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a one-step state-to-state reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label. The state reachability distribution is a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. They can be defined on ULTraS by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability/stochasticity coexist; then new equivalences pop up.Information and Computation 04/2013; 225:29–82. · 0.70 Impact Factor

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