A domain equation for bisimulation
Samson Abramsky · Information and Computation · 1991
Some basic topics in the theory of concurrency are studied from the point of view of denotational semantics, and particularly the “domain theory in logical form” developed by the author. A domain of synchronization trees is defined by means of a recursive domain equation involving the Plotkin powerdomain. The logical counterpart of this domain is described, and shown to be related to it by Stone duality. The relationship of this domain logic to the standard Hennessy-Milner logic for transition systems is studied; the domain logic can be seen as a rational reconstruction of Hennessy-Milner logic from the standpoint of a very general and systematic theory. Finally, a denotational semantics for SCCS based on the domain of synchronization trees is given, and proved fully abstract with respect to bisimulation.