Abstract
This paper investigates full abstraction of denotational model w.r.t. operational ones for two concurrent languages. The languages are nonuniform in the sense that the meaning of atomic statements generally depends on the current state. The first language, L 1 , has parallel composition but no communication, whereas the second one, L 2 , has CSP-like communications in addition. For each of L i ( i = 1, 2), an operational model O i is introduced in terms of a Plotkin-style transition system, while a denotational model D i for L i is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in appropriate complete metric spaces. The full abstraction is shown by means of a context with parallel composition: Given two statements s 1 and s 2 with different denotational meanings, a suitable statement T is constructed such that the operational meanings of s 1 ∥ T and s 2 ∥ T are distinct. A combinatorial method for constructing such T is proposed. Thereby the full abstraction of D 1 and D 2 w.r.t. O 1 and O 2 , respectively, is established. That is, D i is most abstract of those models C which are compositional and satisfy O i = α ∘ C for some abstraction function α ( i = 1, 2).
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