Date: 22 Aug 2001

Compositional Methods for Probabilistic Systems

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We present a compositional trace-based model for probabilistic systems. The behavior of a system with probabilistic choice is a stochastic process, namely, a probability distribution on traces, or “bundle.” Consequently, the semantics of a system with both nondeterministic and probabilistic choice is a set of bundles. The bundles of a composite system can be obtained by combining the bundles of the components in a simple mathematical way. Refinement between systems is bundle containment. We achieve assume-guarantee compositionality for bundle semantics by introducing two scoping mechanisms. The first mechanism, which is standard in compositional modeling, distinguishes inputs from outputs and hidden state. The second mechanism, which arises in probabilistic systems, partitions the state into probabilistically independent regions.

This research was supported in part by the SRC contract 99-TJ-683.003, the AFOSR MURI grant F49620-00-1-0327, the MARCO GSRC grant 98-DT-660, the NSF Theory grant CCR-9988172, and the DARPA SEC grant F33615-C-98-3614.