Compositional Methods for Probabilistic Systems

We present a compositional trace based model for proba bilistic systems The behavior of a system with probabilistic choice is a stochastic process namely a probability distribution on traces or bun dle Consequently the semantics of a systemwith 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 Re nement between systems is bundle containment We achieve assume guarantee compositionality for bundle semantics by introducing two scoping mechanisms The rst mechanism which is standard in compositional modeling distinguishes inputs from outputs and hidden state The second mechanism which arises in prob abilistic systems partitions the state into probabilistically independent