A Compositional Trace-Based Semantics for Probabilistic Automata

We extend the trace semantics for labeled transition systems to a ran-domized model of concurrent computation. The main objective is to obtain a com-positional semantics. The role of a trace in the randomized model is played by a probability distribution over traces, called a trace distribution. We show that the preorder based on trace distribution inclusion is not a precongruence, and we build an elementary context, called the principal context, that is suuciently powerful to characterize the coarsest precongruence that is contained in the trace distribution preorder. Finally, we introduce a notion of a probabilistic forward simulation and we prove that it is sound for the trace distribution precongruence. An important characteristic of probabilistic forward simulations is that they relate states to probability distributions over states.