Axiomatization of trace semantics for stochastic nondeterministic processes

We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion. The axiomatization is given for two different semantics of the process algebra that are consistent with the alternating model of Hansson and the nonalternating model of Segala, respectively. It is shown that the two semantics coincide up to trace distribution precongruence.