Structured operational semantics and bisimulation as a congruence

Abstract

In this paper the question is considered in which cases a transition system specification in Plotkin style has ‘good’ properties and deserves the predicate ‘structured’. 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. We argue that in this setting it is natural to require that strong bisimulation equivalence is a congruence on the states of the transition systems. A general format, called the tyft/tyxt format, is presented for the conditional rules in a transition system specification, such that bisimulation is always a congruence when all the rules fit into this format. With a series of examples it is demonstrated that the tyft/tyxt format cannot be generalized in any obvious way. Briefly we touch upon the issue of modularity of transition system specifications. We show that certain pathological tyft/tyxt rules (the ones which are not pure) can be disqualified because they behave badly with respect to modularisation. 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 [16, 17] but is incomparable to the GSOS format of Bloom, Istrail & Meyer [7]. However, it turns out that 2-nested simulation equivalence strictly refines the completed trace congruence induced by the GSOS format.