Chapter

CONCUR 2001 — Concurrency Theory

Volume 2154 of the series Lecture Notes in Computer Science pp 351-365

Date:

Compositional Methods for Probabilistic Systems

  • Luca de AlfaroAffiliated withElectrical Engineering and Computer Sciences, University of California
  • , Thomas A. HenzingerAffiliated withElectrical Engineering and Computer Sciences, University of California
  • , Ranjit JhalaAffiliated withElectrical Engineering and Computer Sciences, University of California

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Abstract

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.