A hierarchy of behavioral equivalences in the $\pi$-calculus with noisy channels

TL;DR

This paper extends the $ ext{pi}$-calculus to noisy channels, introduces an early semantics, and develops a hierarchy of behavioral equivalences to better verify agent behaviors under realistic communication conditions.

Contribution

It presents an early semantics for the $ ext{pi}_N$-calculus and extends six behavioral equivalences into this noisy channel framework, forming a useful hierarchy.

Findings

Behavioral equivalences form a hierarchy in $ ext{pi}_N$-calculus.

Noisy channels break the coincidence of certain equivalences.

The hierarchy aids in verifying agent behavioral equivalence.

Abstract

The $\pi$-calculus is a process algebra where agents interact by sending communication links to each other via noiseless communication channels. Taking into account the reality of noisy channels, an extension of the $\pi$-calculus, called the $\pi_N$-calculus, has been introduced recently. In this paper, we present an early transitional semantics of the $\pi_N$-calculus, which is not a directly translated version of the late semantics of $\pi_N$, and then extend six kinds of behavioral equivalences consisting of reduction bisimilarity, barbed bisimilarity, barbed equivalence, barbed congruence, bisimilarity, and full bisimilarity into the $\pi_N$-calculus. Such behavioral equivalences are cast in a hierarchy, which is helpful to verify behavioral equivalence of two agents. In particular, we show that due to the noisy nature of channels, the coincidence of bisimilarity and barbed equivalence, as well as the coincidence of full bisimilarity and barbed congruence, in the $\pi$-calculus does not hold in $\pi_N$.