Separability in the Ambient Logic

TL;DR

This paper investigates the discriminating power of the Ambient Logic in process calculi, providing characterizations, axiomatizations, and decidability results for process equivalences in Mobile Ambients and related calculi.

Contribution

It offers new operational characterizations of Ambient Logic equivalence, axiomatizations for subcalculi, and analyzes decidability and separation properties.

Findings

$_=L$ is strictly finer than barbed congruence

Axiomatizations of $_=L$ are provided for subcalculi of MA

Decidability of $_=L$ varies between MA and its subcalculi

Abstract

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the discriminating power of AL, focusing on the equivalence on processes induced by the logic $(=_L>)$. As underlying calculi besides MA we consider a subcalculus in which an image-finiteness condition holds and that we prove to be Turing complete. Synchronous variants of these calculi are studied as well. In these calculi, we provide two operational characterisations of $_=L$: a coinductive one (as a form of bisimilarity) and an inductive one (based on structual properties of processes). After showing $_=L$ to be stricly finer than barbed congruence, we establish axiomatisations of $_=L$ on the subcalculus of MA (both the asynchronous and the synchronous version), enabling us to relate $_=L$ to structural congruence. We also present some (un)decidability results that are related to the above separation properties for AL: the undecidability of $_=L$ on MA and its decidability on the subcalculus.