tcs97 - Composition and Behaviors of Probabilistic I/O...

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Composition and Behaviors of Probabilistic I/O Automata Sue-Hwey Wu, Scott A. Smolka, Eugene W. Stark Department of Computer Science State University of New York at Stony Brook Stony Brook, NY 11794 USA Abstract We augment the I/O automaton model of Lynch and Tuttle with probability, as a step toward the ultimate goal of obtaining a useful tool for specifying and reasoning about asynchronous probabilistic systems. Our new model, called probabilistic I/O automata , preserves the fundamental properties of the I/O automaton model, such as the asymmetric treatment of input and output and the pleasant notion of asyn- chronous composition. For certain classes of probabilistic I/O automata, we show that probabilistic behavior maps , which are an abstract representation of I/O au- tomaton behavior in terms of a certain expectation operator, are compositional and fully abstract with respect to a natural notion of probabilistic testing. 1 Introduction I/O Automata are a kind of state machine that have been proposed by Lynch and Tuttle [LT87] as a tool for specifying and reasoning about asynchronous systems. The distin- guishing features of the I/O automaton model are: (1) an asymmetric treatment of input and output actions, (2) a notion of asynchronous composition that takes a “compatible” collection of I/O automata and produces a new I/O automaton as a result, (3) a simple correspondence between computations of a composite I/O automaton and certain collec- tions of computations of its component automata, (4) the treatment of liveness properties through the introduction of a “fairness partition” on the action set of an automaton, and (5) the use of simulation-based techniques for proving that the set of action sequences that A preliminary version of this paper appeared in the Proceedings of CONCUR’94 – Fifth International Conference on Concurrence Theory, Lecture Notes in Computer Science, volume 836. The research of the first and second authors was supported in part by NSF Grants CCR-9120995 and CCR-9208585, and AFOSR Grant F49620-93-1-0250. The research of the third author was supported in part by NSF Grant CCR-8902215. E-mail addresses: [email protected] , [email protected] , [email protected]
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can be produced by one I/O automaton is a subset of the set of action sequences that can be produced by another. In this paper, we consider the problem of augmenting I/O automata with probability information, as a step toward the ultimate goal of obtaining a useful tool for specifying and reasoning about asynchronous probabilistic systems. As much as possible, we would like to preserve the characteristic features of the I/O automa- ton model, especially the asymmetric treatment of input and output and the associated pleasant notion of composition.
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