Expressiveness of Process Algebras

AbstractWe examine ways to measure expressiveness of process algebras, and recapitulate and compare some related results from the literature

Analysing and Comparing Encodability Criteria

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of different criteria and different variants of criteria in order to reason in different settings. This leads to incomparable results. Moreover it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. We show how to formally reason about and compare encodability criteria by mapping them on requirements on a relation between source and target terms that is induced by the encoding function. In particular we analyse the common criteria full abstraction, operational correspondence, divergence reflection, success sensitiveness, and respect of barbs; e.g. we analyse the exact nature of the simulation relation (coupled simulation versus bisimulation) that is induced by different variants of operational correspondence. This way we reduce the problem of analysing or comparing encodability criteria to the better understood problem of comparing relations on processes.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.06347. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/Encodability_Process_Calculi.shtm

Musings on Encodings and Expressiveness

This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition with other definitions of encoding and expressiveness found in the literature, and illustrate it on a case study: comparing the expressive power of CCS and CSP.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Comparing Process Calculi Using Encodings

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch of different criteria and different variants of criteria in order to reason in different settings. This leads to incomparable results. Moreover, it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. This paper provides a short survey on often used encodability criteria, general frameworks that try to provide a unified notion of the quality of an encoding, and methods to analyse and compare encodability criteria.Comment: In Proceedings EXPRESS/SOS 2019, arXiv:1908.0821

On the expressiveness of linearity vs persistence in the asychronous pi-calculus

We present an expressiveness study of linearity and persistence of processes. We choose the π-calculus, one of the main representatives of process calculi, as a framework to conduct our study. We consider four fragments of the π-calculus. Each one singles out a natural source of linearity/persistence also present in other frameworks such as Concurrent Constraint Programming (CCP), Linear CCP, and several calculi for security. The study is presented by providing (or proving the non-existence of) encodings among the fragments, a processes-as-formulae interpretation and a reduction from Minsky machines.

Static analysis of an actor-based process calculus by abstract interpretation

Le modèle des Acteurs, introduit par HEWITT et AGHA à la fin des années 80, décrit un système concurrent comme un ensemble d'agents autonomes au comportement non uniforme et communiquant de façon point-à-point par l'envoi de messages étiquetés. Le calcul CAP, proposé par COLAÇO, est un calcul de processus basé sur ce modèle qui permet de décrire sans encodage complexe des systèmes réalistes non triviaux. Ce calcul permet, entre autre, la communication de comportements via les messages et est, en ce sens, un calcul d'ordre supérieur. L'analyse de propriétés sur ce calcul a déjà fait l'objet de plusieurs travaux, essentiellement par inférence de type en utilisant des types comportementaux et du sous-typage. Par ailleurs, des travaux plus récents, effectués par VENET puis FERET, proposent une utilisation de l'interprétation abstraite pour l'analyse de calculs de processus. Ces approches permettent de calculer des propriétés non uniformes : elles permettent, par exemple, de différencier les instances récursives d'un même processus. Cette thèse s'inscrit donc dans la suite de ces deux approches, en appliquant l'interprétation abstraite à l'analyse de CAP. Suivant le cadre proposé par FERET, CAP est, tout d'abord, exprimé dans une forme non standard facilitant les analyses. L'ensemble des configurations atteignables est ensuite sur-approximé via une représentation, correcte par construction, dans des domaines abstraits. Des domaines abstraits généraux sont ensuite introduits afin d'améliorer les analyses existantes ou de représenter des propriétés locales à un sous-terme. Des propriétés spécifiques à CAP, la linéarité des termes et l'absence de messages orphelins, sont alors étudiées dans ce cadre. Des domaines spécifiques sont définis et utilisés pour vérifier ces propriétés. Le cadre présenté permet de lever toutes les restrictions existantes des analyses précédentes quant à la forme des termes ou l'utilisation du passage de comportement. L'intégralité des analyses présentées a été implantée dans un prototype. ABSTRACT : The Actor model, introduced by HEWITT and AGHA in the late 80s, describes a concurrent communicating system as a set of autonomous agents, with non uniform interfaces and communicating by the use of labeled messages. The CAP process calculus, proposed by COLAÇO, is based on this model and allows to describe non trivial realistic systems, without the need of complex encodings. CAP is a higher-order calculus: messages can carry actor behaviors. Multiple works address the analysis of CAP properties, mainly by the use of inferencebased type systems using behavioral types and sub-typing. Otherwise, ore recent works, by VENET and later FERET, propose the use of abstract interpretation to analyze process calculi. These approaches allow to compute non-uniform properties. For example, they are able to differentiate recursive instances of the same thread. This thesis is at the crossroad of these two approaches, applying abstract interpretation to the analysis of CAP. Following the framework of FERET, CAP is firstly expressed in a non standard form, easing its analysis. The set of reachable states is then over-approximated via a sound by construction representation within existing abstract domains. New general abstract domains are then introduced in order to improve the accuracy of existing analyses or to represent local properties. CAP specific properties such as the linearity of terms or the absence of orphan messages, are then considered in this framework. Specific abstract domains are defined and used to check these properties. The proposed framework is able to relax any existing restriction of previous analyses such as constraints on the shape of terms or limitation in the use of CAP behavior passing. The whole analyses have been implemented in a prototyp