A Characterization of Finitary Bisimulation

Following a paradigm put forward by Milner and Plotkin, a primary criterion to judge the appropriateness of denotational models for programming and specification languages is that they be in agreement with operational intuition about program behaviour. Of the “good fit” criteria for such models that have been discussed in the literature, the most desirable one is that of full abstraction. Intuitively, a fully abstract denotational model is guaranteed to relate exactly all those programs that are operationally indistinguishable with respect to some chosen notion of observation. Because of its prominent role in process theory, bisimulation [ 121 has been a natural yardstick to assess the appropriateness of denotational models for several process description languages. In particular, when proving full abstraction results for denotational semantics based on the Scott-Strachey approach for CCS-like languages, several preorders based on bisimulation have been considered; see, e.g., [ 6,3,4]. In this paper, we shall study one such bisimulation-based preorder whose connections with domain-theoretic models are by now well understood, viz. the prebisimulution preorder 5 investigated in, e.g., [ 6,3]. Intuitively, p 5 q holds of processes p and q if p and q can simulate each other’s behaviour, but at times the behaviour of p may be less specified than that of q. A common problem in relating denotational semantics for process description languages, based on Scott’s theory of domains or on the theory of algebraic semantics, with behavioural semantics based on bisiniulation is that the chosen behavioural theory is, in general, too concrete. The reason for this phenomenon is that two programs are related by a standard denotational interpretation if, in some precise sense, they afford the same finite observations. On the other hand, bisimulation can make distinctions between the behaviours of two processes based on injinite observations. (Cf. the seminal study [ 1 ] for a detailed analysis of this phenomenon.)