Probabilistic i/o automata: theories of two equivalences

Working in the context of a process-algebraic language for Probabilistic I/O Automata (PIOA), we study the notion of PIOA behavior equivalence by obtaining a complete axiomatization of its equational theory and comparing the results with a complete axiomatization of a more standard equivalence, weighted bisimulation. The axiomatization of behavior equivalence is achieved by adding to the language an operator for forming convex combinations of terms.