Bisimulation for Higher-Order Process Calculi

Abstract

A higher-order process calculus is a calculus for communicating systems which contains higher-order constructs like communication of terms. We analyse the notion of bisimulation in these calculi. We argue that both the standard de nition of bisimulation (i.e., the one for CCS and related calculi), as well as higher-order bisimulation AGR88, Bou89, Tho90] are in general unsatisfactory, because of their overdiscrimination. We propose and study a new form of bisimulation for such calculi, called context bisimulation, which yields a more satisfactory discriminanting power. A drawback of context bisimulation is the heavy use of universal quanti cation in its de nition, which is hard to handle in practice. To resolve this di culty we introduce triggered bisimulation and normal bisimulation, and we prove that they both coincide with context bisimulation. In the proof, we exploit the factorisation theorem: When comparing the behaviour of two processes, it allows us to \isolate" subcomponents which might give di erences, so that the analysis can be concentrated on them.

Modal characterization of weak bisimulation for higher-order processes

“…Such a communication scheme is called late which makes ~ is a late bisimulation. For a conceptual discussion and practical application of this combination, see [13,5]. We do not know whether the results of this paper could be obtained for classically weak and/or non-late, that is, early forms of bisimulation.…”

Reversibility in the higher-order π-calculus

“…The rules in Figure B.16 are a direct adaptation of the rules in [21] to the asynchronous higher-order π, with the use of concretions and abstractions, following Milner and Sangiorgi [15,17]. A concretion takes the form νã.…”

“…The same reasons that motivated the introduction of the π-calculus [15] apply to motivate the study of a reversible π-calculus. As a first contribution in that study, we introduced in [16] a causally-consistent reversible extension of an asynchronous variant of the higher-order π-calculus [17], where we showed how to preserve the usual properties of the π-calculus operators (e.g., associativity and commutativity of parallel composition), and that one could faithfully encode (up to weak barbed bisimilarity) our reversible higher-order π, called rhoπ, into a variant of the higher-order π-calculus with abstractions and join patterns. The operational semantics of rhoπ was given in [16] by way of a reduction semantics.…”

A Testing Theory for a Higher-Order Cryptographic Language

“…However, unlike [21,23,25], in order to keep the LTS first-order we severely restrict the ability of the observer to construct higher-order values. The soundness of our technique in Section 5 shows that this restriction does not compromise the possible observations made in the LTS.…”