Axiomatizations for Probabilistic Finite-State Behaviors

We study a process calculus which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioral equivalences, and we provide complete axiomatizations for finite-state processes, restricted to guarded definitions in case of the weak equivalences. We conjecture that in the general case of unguarded recursion the “natural” weak equivalences are undecidable. This is the first work, to our knowledge, that provides a complete axiomatization for weak equivalences in the presence of recursion and both nondeterministic and probabilistic choice.