Determinacy - (Observation Equivalence = Trace Equivalence)

If an experiment s is conducted on a parallel process p, then, in general, different processes may result from the experiment, due to the nondeterministic behaviour of p (in the notation of Milner (1980): p ~ p' for different p'). Process p is called determinate if the resulting processes are all equivalent (i.e., if p A=> p' and p ~ p", then p' and p" are equivalent). This means that, although p behaves nondeterministically, this cannot be detected by an observer of p. Let -denote observation equivalence, used in CCS (Milner, 1980), let f denote (the much weaker) failure equivalence, used for CSP (Hoare et al., 1981 ; Brookes, 1983), and let t denote (the still weaker) trace equivalence. We show that the three corresponding notions of determinacy are the same, and that for determinate processes -~, f , and t are the same. Determinacy is preserved under and ~--f, but not under t -