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A uniform framework for modeling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences

Bernardo, Marco and De Nicola, Rocco and Loreti, Michele A uniform framework for modeling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences. Information and Computation, 225. 29 - 82. ISSN 0890-5401 (2013)

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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.

Item Type: Article
Identification Number: 10.1016/j.ic.2013.02.004
Uncontrolled Keywords: Labeled transition systems; Discrete-/continuous-time Markov chains; Discrete-/continuous-time Markov decision processes; Bisimulation equivalences; Trace equivalences; Testing equivalences
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 16 Jun 2014 13:17
Last Modified: 16 Jun 2014 13:17
URI: http://eprints.imtlucca.it/id/eprint/2207

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