Full Abstraction in Structural Operational Semantics

This paper explores the connection between semantic equivalences for concrete sequential processes, represented by means of transition systems, and formats of transition system speciications using Plotkin's structural approach. For several equivalences in the linear time { branching time spectrum a format is given, as general as possible, such that this equivalence is a congruence for all operators speciiable in that format. And for several formats it is determined what is the coarsest congruence with respect to all operators in this format that is ner than partial or completed trace equivalence. 1 Preorders and equivalences on labelled transition systems Deenition 1 A labelled transition system (LTS) is a pair (I P; ?!) with I P a set (of processes) and ?!! I P A I P for A a set (of actions). Notation: Write p a ?! q for (p; a; q) 2?! and p a ?! for 9q 2 I P : p a ?! q. The elements of I P represent the processes we are interested in, and p a ?! q means that process p can evolve into process q while performing the action a. By an action any activity is understood that is considered as a conceptual entity on a chosen level of abstraction. Diierent activities that are indistinguishable on the chosen level of abstraction are interpreted as occurrences of the same action a 2 A. Actions may be instantaneous or durational and are not required to terminate, but in a nite time only nitely many actions can be carried out (i.e. only discrete systems are considered). Below several semantic preorders and equivalences will be deened on processes represented by means of labelled transition systems. These preorders can be deened in terms of the observations that an experimentator could make during a session with a process.