Bas Luttik ; Fei Yang - The $\pi$-Calculus is Behaviourally Complete and Orbit-Finitely Executable

lmcs:6047 - Logical Methods in Computer Science, February 10, 2021, Volume 17, Issue 1 - https://doi.org/10.23638/LMCS-17(1:14)2021
The $\pi$-Calculus is Behaviourally Complete and Orbit-Finitely Executable

Authors: Bas Luttik ; Fei Yang

Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour (finitely) executable if, and only if, it is equivalent to the behaviour of a (finite) reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the $\pi$-calculus. We establish that every finitely executable behaviour can be specified in the $\pi$-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended) limitations of the model of reactive Turing machines. That is, the $\pi$-calculus allows the specification of behaviour that is not finitely executable up to divergence-preserving branching bisimilarity. We shall prove, however, that if the finiteness requirement on reactive Turing machines and the associated notion of executability is relaxed to orbit-finiteness, then the $\pi$-calculus is executable up to (divergence-insensitive) branching bisimilarity.

Volume: Volume 17, Issue 1
Published on: February 10, 2021
Accepted on: December 3, 2020
Submitted on: January 23, 2020
Keywords: Computer Science - Logic in Computer Science