Syntactic Formats for Free: An Abstract Approach to Process Equivalence

Abstract

Abstract. A framework of Plotkin and Turi's, originally aimed at providing an abstract notion of bisimulation, is modified to cover other operational equivalences and preorders. Combined with bialgebraic methods, it yields a technique for the derivation of syntactic formats for transition system specifications which guarantee that various operational preorders are precongruences. The technique is applied to the trace preorder, the completed trace preorder and the failures preorder. In the latter two cases, new syntactic formats guaranteeing precongruence properties are introduced.

Bialgebraic methods and modal logic in structural operational semantics

“…In particular, novel formats for completed trace and failures equivalences on LTSs were obtained. That work is closely related to the present paper, and indeed the following sections can be seen as a refinement of the approach described in [39,35,33].…”

“…For example, interesting formats for various "decorated trace" equivalences were proposed in [9]. A considerably more complex format for completed trace equivalence was defined in [39,35]. For a detailed study of various congruence formats and their properties, see [1,23].…”

“…In [39,35], abstract GSOS is interpreted in certain fibered categories. This allows one to derive congruence formats for process equivalences other than the canonical coalgebraic notion of bisimilarity.…”