When is partial trace equivalence adequate?

Two processes arepartial trace equivalent iff they can perform the same sequences of actions in isolation. Partial trace equivalence is perhaps the simplest possible notion of process equivalence. In general, it is too simple: it is not usually an adequate semantics. We investigate the circumstances under which it is adequate, which are surprisingly rich. We give two substantial classes of languages for which partial traces are adequate. In one class, partial trace equivalence suffices for total correctness, and operations such as true sequencing are possible; but all processes are determinate and silent moves are not possible. The other class — which includes many standard process calculi, such as CCS and CSP — admits indeterminacy and silent moves, but partial traces only suffice for partial correctness and true sequencing is not definable.