A framework is defined within which reactive systems can be studied formally. The framework is based upon s-categories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors. The framework

G-relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct GRPOs in a category of ‘bunches and wirings. ’ We then examine the approach based on Milner’s precategories and Leifer’s functorial reactive systems, and show that it can be recast in a much simpler way into the 2-categorical theory of GRPOs.

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The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism based on borrowed contexts (bcs), proposed by Ehrig and König (which are an instance of relative pushouts, originally introduced by Milner and Leifer). The bc mechanism allows the effective construction of an lts that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of the lts distilled by exploiting the encoding of ccs processes: besides offering some technical contributions towards the simplification of the bc mechanism, the key result of our work is the proof that the bisimilarity on processes obtained via bcs coincides with the standard strong bisimilarity for ccs.

For historical, sociological and technical reasons, -calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, -calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equally convincing formal foundation for distributed computing has not been forthcoming. This thesis seeks to contribute towards ameliorating that omission. To this end, guided by the assumption that distributed computing is concurrent computing with partial failures of various kinds, we extend the asynchronous -calculus with a notion of sites, the possibility of site failure, a persistence mechanism to deal with site failures, the distinction between inter-site and intra-site communication, the possibility of message loss in inter-site communication and a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.

We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation of bigraphical reactive systems.

... often, models are required to be executable, as a simulation, on a computer. In this paper, we present some contributions to the process-theoretic and logical foundations of discrete-event modelling with resources and processes. We present a process calculus with an explicit representation of resources in which processes and resources co-evolve. The calculus is closely connected to a logic that may be used as a specification language for properties of models. The logic is strong enough to allow requirements that a system has certain structure; for example, that it is a parallel composite of subsystems. This work consolidates, extends, and improves upon aspects of earlier work of ours in this area. An extended example, consisting of a semantics for a simple parallel programming language, indicates a connection with separating logics for concurrency.

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Abstract. We propose a methodology for the analysis of open systems based on process calculi and bisimilarity. Open systems are seen as coordinators (i.e. terms with place-holders), that evolve when suitable components (i.e. closed terms) fill in their place-holders. The distinguishing feature of our approach is the definition of a symbolic operational semantics for coordinators that exploits spatial/modal formulae as labels of transitions and avoids the universal closure of coordinators w.r.t. all components. Two kinds of bisimilarities are then defined, called strict and large, which differ in the way formulae are compared. Strict bisimilarity implies large bisimilarity which, in turn, implies the one based on universal closure. Moreover, for process calculi in suitable formats, we show how the symbolic semantics can be defined constructively, using unification. Our approach is illustrated on a toy process calculus with ccs-like communication within ambients. 1

Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.