Structured operational semantics and bisimulation as a congruence

AbstractIn this paper we are interested in general properties of classes of transition system specifications in Plotkin style. The discussion takes place in a setting of labelled transition systems. The states of the transition systems are terms generated by a single sorted signature and the transitions between states are defined by conditional rules over the syntax. It is argued that in this setting it is natural to require that strong bisimulation equivalence be a congruence on the states of the transition systems. A general format, called the tyft/tyxt format, is presented for the rules in a transition system specification, such that bisimulation is always a congruence when all the rules fit this format. With a series of examples it is demonstrated that the tyft/tyxt format cannot be generalized in any obvious way. Another series of examples illustrates the usefulness of our congruence theorem. Briefly we touch upon the issue of modularity of transition system specifications. It is argued that certain pathological tyft/tyxt rules (the ones which are not pure) can be disqualified because they behave badly with respect to modularization. Next we address the issue of full abstraction. We characterize the completed trace congruence induced by the operators in pure tyft/tyxt format as 2-nested simulation equivalence. The pure tyft/tyxt format includes the format given by de Simone (Theoret. Comput. Sci. 37, 245–267 (1985)) but is incomparable to the GSOS format of Bloom, Istrail, and Meyer (in “Conference Record of the 15th Annual Symposium on Principles of Programming Languages, San Diego, California, 1988,” pp. 229–239). However, it turns out that 2-nested simulation equivalence strictly refines the completed trace congruence induced by the GSOS format