On the discriminating power of passivation and higher-order interaction

Abstract

This paper studies the discriminating power offered by higherorder concurrent languages, and contrasts this power with those offered by higher-order sequential languages (à la λ-calculus) and by first-order concurrent languages (à la CCS). The concurrent higherorder languages that we focus on are Higher-Order π-calculus (HOπ), which supports higher-order communication, and an extension of HOπ with passivation, a simple higher-order construct that allows one to obtain location-dependent process behaviours.The comparison is carried out by providing embeddings of firstorder processes into the various languages, and then examining the resulting contextual equivalences induced on such processes. As first-order processes we consider both ordinary Labeled Transition Systems (LTSs) and Reactive Probabilistic Labeled Transition Systems (RPLTSs).The hierarchy of discriminating powers so obtained for RPLTSs is finer than that for LTSs. For instance, in the LTS case, the additional discriminating power offered by passivation in concurrency is captured, in sequential languages, by the difference between the call-by-name and call-by-value evaluation strategies of an extended typed λ-calculus.

Higher-Order Languages: Bisimulation and Coinductive Equivalences (Extended Abstract)

“…Contextual equivalence is a 'may' of form of testing that, in first-order languages (e.g., CCS) is quite different from bisimilarity or even simulation equivalence. Indeed, in general, higherorder languages have a stronger discriminating power than first-order languages [BSV14]. For instance, if we use higher-order languages to test first-order languages, using (may-like) contextual equivalence, then the equivalences induced is often finer than the equivalences induced by first-order languages (usually trace equivalence); moreover, the natural definition of the former equivalences is coinductive, whereas that for the latter equivalences is inductive.…”

“…The same discriminating power can also be obtained in callby-value λ-calculi (that is, without concurrency or nondeterminism) extended with a location-like construct akin to a store of imperative λ-calculi, and operators for reading the content of this location, overriding it, and, if the location contains a process, for consuming such process (i.e., performing observations on the process actions). When the tested first-order processes are probabilistic, the difference in discriminating power between first-order and higher-order languages increases further: in higher-order languages equipped with passivation, or in a call-by-value λ-calculus, bisimilarity may be recovered [BSV14].…”

A general SOS theory for the specification of probabilistic transition systems

“…deterministic) probabilistic transition systems were already introduced in [20]. Also, the recent paper [37] has shown that an extension of the higher order π calculus that includes action refusal and passivation (called HOπ pass,ref ) is powerful enough to distinguish bisimulation in reactive probabilistic transition systems. However, in these two cases, the achieved full abstraction is with respect to probabilistic trace equivalence rather than the weaker possibilistic trace equivalence used in Theorem 16.…”