Is It a "Good" Encoding of Mixed Choice?

This technical report contains the proofs to the lemmata and theorems of [PN12] as well as some additional material. As main contributions [PN12] presents an encoding of mixed choice in the context of the π-calculus and a criterion to measure whether the degree of distribution in process networks is preserved. 1 Technical Preliminaries 1.1 The π-Calculus Our source language is the monadic π-calculus as described for instance in [SW01]. As already demonstrated in [Pal03] the most interesting operator for a comparison of the expressive power between the full π-calculus and its asynchronous variant is mixed choice, i.e., choice between input and output capabilities. Thus we denote the full π-calculus also by πm. Let N denote a countably infinite set of names with τ / ∈ N and N the set of co-names, i.e., N = {n | n ∈ N}. We use lower case letters a, a, a1, . . . , x, y, . . . to range over names. Definition 1 (πm). The set of process terms of the synchronous π-calculus (with mixed choice), denoted by Pm, is given by P ::= (ν n)P | P1 | P2 | [ a = b ]P | y ∗ (x) .P | ∑