On Unique Decomposition of Processes in the Applied π-Calculus

Abstract

Abstract. Unique decomposition has been a subject of interest in process algebra for a long time (for example in BPP [2] or CCS [11,13]), as it provides a normal form with useful cancellation properties. We provide two parallel decomposition results for subsets of the Applied π-Calculus: we show that any closed normed (i.e. with a finite shortest complete trace) process P can be decomposed uniquely into prime factors Pi with respect to strong labeled bisimilarity, i.e. such that P ∼ l P1| . . . |Pn. We also prove that closed finite processes can be decomposed uniquely with respect to weak labeled bisimilarity.

Unique parallel decomposition in branching and weak bisimulation semantics

“…We leave for future investigations to what extent our theory of unique decomposition can be applied to variants of π-calculus. The article [10], in which unique parallel decomposition is established for a fragment of Applied π-calculus, will serve as a good starting point. A complication, illustrated in [10], is that parallel components may fuse into a single indecomposable process due to scope extrusion.…”

“…The article [10], in which unique parallel decomposition is established for a fragment of Applied π-calculus, will serve as a good starting point. A complication, illustrated in [10], is that parallel components may fuse into a single indecomposable process due to scope extrusion. As a consequence, precompositionality fails for the order induced on equivalence classes of π-terms by the transition relation.…”

“…Unique parallel decomposition could be of practical interest too, e.g., to devise methods for finding the maximally parallel implementation of a behaviour [8], or for improving verification methods [14]. In [10], unique parallel decomposition results are established for the Applied π-calculus, as a tool in the comparison of different security notions in the context of electronic voting. This article is organised as follows.…”

Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics

“…In fact, it is to be expected that our condition, similarly as in [15], can also be used to prove unique decomposition results in settings with more complicated notions of parallel composition operator allowing, e.g., synchronisation between components. We leave for future investigations to what extent our theory of unique decomposition can be applied to variants of πcalculus; the report [7], in which unique parallel decomposition is established for a fragment of Applied π-calculus, will serve as a starting point.…”

On the existence and decidability of unique decompositions of processes in the applied π-calculus

“…It is of particular importance for unique decomposition since two parallel processes sharing a restricted channel might not be decomposable and hence a simple reduction might "fuse" two prime factors, which is not possible in BPP or CCS. An extended abstract presenting the results of Sections 5 and 6 without the detailed proofs was presented at FoSSaCS 2013 [21].…”