Congruence from the Operator's Point of View: Compositionality Requirements on Process Semantics

Abstract

One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus on a number of process operators, and for each of them attempt to find the widest possible class of congruences. To this end, we impose restrictions on sublanguages of Hennessy-Milner logic, so that a semantics whose modal characterization satisfies a given criterion is guaranteed to be a congruence with respect to the operator in question. We investigate action prefix, alternative composition, two restriction operators, and parallel composition

Fixed-point Characterization of Compositionality Properties of Probabilistic Processes Combinators

“…Second, we will explore compositionality with respect to behavioral pseudometrics based on trace semantics [11] and testing semantics. Finally, we will investigate how the denotational approach to decide the compositionality properties of operators relates to the logical approach to derive rule formats of [4,22]. Besides this general line, we want to investigate how our structural syntactic approach to compositionality relates to the algorithmic computational approach in [1].…”

All Linear-Time Congruences for Familiar Operators

“…Clearly N ′ 0 has no effect on the behaviour. With N ′ 0 , independently of what Σ N is, also the hiding with Σ [3] N has no effect. Figure 9: A switchable LTS for detecting the infinite trace e 1 e 2 · · · .…”

“…, a m } = Σ [2] L . When j ∈ {1, 2}, let N ′ j = T ξ || d.⌈N j ⌉ [3] , where T ξ is the LTS in Fig. 9 with the alphabet {c, d} ∪ Σ [2] L ∪ Σ [3] N .…”

“…Figure 10: An LTS for detecting an infinite trace with only finitely many nondivergent prefixes. The thick arrows with Σ [3] L denote that there is a transition from each start state of the thick arrows to their common end state for each a ∈ Σ [3] L .…”

“…Each transition of Una(L) whose label a is visible is replaced by a [2] c 1 , if it starts in a certainly nondiv. and ends in a potentially divergent state; a [2] c 2 , if it starts and ends in a potentially divergent state; a [3] , if it starts in a potentially divergent and ends in a certainly nondiv. state; a [2] , if it starts and ends in a certainly nondivergent state.…”