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

Unique Parallel Decomposition for the Pi-calculus

“…In particular, these examples show that item 4 in Lemma 3 of [7] (norm is additive) is false, and, as a consequence, some proofs in [7] are flawed. The authors of [7] proposed a solution to this problem that we discuss in the conclusion of this paper. So, to facilitate inductive reasoning, we will consider finite processes and depth.…”

“…In Section 4 we showed with two examples that norm is not additive for the π-calculus and therefore some proofs in [7] are flawed. After pointing out this problem to Dreier et al, they proposed us an alternative definition of norm to solve it.…”

“…This is the reason why we restrict ourselves to finite processes in the strong setting. The proof of the weak case in [7] follows the proof technique attributed to Milner. The general techniques from [15] cannot be applied directly in the setting of the applied π-calculus due to the active substitutions.…”

“…The paper [7] studies unique parallel decomposition w.r.t. both strong bisimilarity and weak bisimilarity for the applied π-calculus.…”

“…Because the variables in a transition are observable but the 'memories' are not, it is possible to mask sensitive information. The proof of the result for the strong case in [7] relies on induction over the norm of a process and the fact that the norm of the arguments of a parallel composition is less than the norm of the parallel composition. Unfortunately, this property is not true because of the restriction operator (see Section 4 for a counter example).…”