The expressive power of implicit specifications

Abstract

The results of this paper provide insight in the contest behavioural versus logical specification formalisms. In general, behavioural specifications are strictly less expressive than logical ones. However, resorting to implicit behavioural specifications gives you the full expressive power of a logical specification formalism. In particular, implicit behavioural specifications may be combined under logical connectives such as conjunction and disjunction.

The paper leaves as an open problem the characterization of the expressive power of implicit specifications of the form:

$$\left( {A\left| {P\left[ \Phi \right]} \right.} \right)\backslash L \sim B$$

where A and B are regular processes. That is, what is the expressive power of the implicit specification formalism I[CCS_T,T]? Based on the monotonicity of I[,] and main theorem 6.1, we know that I[CCS_T,T] can be no more expressive than H _v . The question is whether I[CCS_T,T] equals H _v in expressive power. Related to this question is the question of complexityfor the consistency problem of I[CCS_T,T]. We know from [JL91] that this decision problem is PSPACE-hard, but whether it is in PSPACE or is an inherent DEXPTIME-problem is still an open problem.