Deriving Denotational Models for Bisimulation from Struc- Tured Operational Semantics

systems, metric spaces and ready sets in the semantics of uniform concur-rency. We have deened an order theoretic interpretation for L and have proved that it is a complete model for the equational theory of ACP. Some remarks seem appropriate. First of all, traditionally ACP is interpreted over so-called process graphs modulo strong bisimu-lation BW91]. A canonical model for the algebra of nite terms (i.e. without procedure variables) is the set of nitely branching trees of nite depth. These trees precisely correspond to nite an toatal (i.e. not containing ?) elements in P. Next, a recursively speciied process X can be given meaning in the projective limit model BW91]. This is essentially similar to how the denotation of X is obtained in P. Next, P contains a lot of`junk', i.e. elements p 6 2 P. Moreover, P itself contains junk: no non-total process (that is, a process containing ?) can be obtained as the denotation of a closed term. Moreover, consider the innnite process fh1; ai : a 2 Ag f?g. Since the recursion is guarded, this process can never be obtained as the denotation of a program. An important feature of process algebras is the so-called silent move , which is used to model a step or a sequence of steps local to a process BW91, dBK90, Mil89]. Axioms for include ; x + x = ; x. It is readily seen that this axiom prevents us from modeling the semantic choice operator by a continuous function. Hence we cannot extend our model to cover this extension of the algebra. It is an interesting question which kind of structure we should use in order to model this.