On Syntactic and Semantic Action Refinement

The semantic de nition of action re nement on labelled event structures is compared with the notion of syntactic substitution which can be used as another notion of action re nement in a process algebraic setting This is done by studying a process algebra equipped with the ACP sequential composition parallel composition with an explicit synchronization set and an operator for action re nement On the one hand the language including the re nement operator is given a ow event structure semantics On the other hand a reduction procedure transforms a process term P into a at term i e with the re nement operator not occurring in it red P by means of syntactic substitution de ned in a structural inductive way The main aim of the paper is to nd general conditions under which the terms P and red P have the same semantics The results we present are essentially dependent on the question whether the re ned action can be synchronized or not In the latter case P and red P give rise to isomorphic ow event structures under mild assumptions The former case is considerably more di cult We give necessary and su cient semantic conditions under which re nement can be distributed over synchronization up to isomorphic domains of con gurations Subsequently we also give su cient but not necessary syntactic conditions for reducible terms