. We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the well-known characterisation of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particular, we show that term graphs over a signature \Sigma are one-to-one with the arrows of the free gs-monoidal category generated by \Sigma. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator r), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of r and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively. Keywords: algebraic theories, directed acyclic graphs, gs-monoidal categories, symmetric monoidal categories, term graphs. Mathematical Subject Clas...

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

The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possible ways; the only alternatives considered in the literature relying on Larsen and Xinxin's context systems and Rensink's conditional transition systems. We propose a different approach based on tile logic, where both closed and open terms are managed analogously. In particular, we analyze the `bisimilarity as congruence' property for several tile formats that accomplish di erent concepts of subterm sharing.

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Abstract. In this paper, we give novel and more liberal notions of operational and equational conservativity for language extensions. We motivate these notions by showing their practical application in existing formalisms. Based on our notions, we formulate and prove meta-theorems that establish conservative extensions for languages defined using Structural

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.

Abstract. The conceptual separation between computation and coordination in distributed computing systems motivates the use of peculiar entities commonly called connectors, whose task is managing the interaction among distributed components. Different kinds of connectors exist in the literature, at different levels of abstraction. We focus on a basic algebra of connectors which is expressive enough to model, e.g., all the architectural connectors of CommUnity. We first define the operational, observational and denotational semantics of connectors, then we show that the observational and denotational semantics coincide and finally we give a complete normal-form axiomatization. 1 Introduction The advent of modern communication technologies shifted the focus of computer science researchers from isolated computing systems to distributed communicating systems, in which interaction plays the prominent role. In Milner's words [21], "computing has grown into informatics and Turing's logical computing machines are matched by a logic of interaction". In this perspective, the analysis of global computing systems is facilitated by approaches, techniques and paradigms that exploit a clean conceptual separation between computation and coordination. This is much evident at several levels of abstraction (architecture, software, processes), where issues like reusability, maintenance, heterogeneity call for modular specifications, theories and models. When separating coordination from computation, the notion of a connector emerges in different contexts, with slightly different meaning, expressiveness and functionalities. The common trait is the role of a connector: a component that mediates the interaction of other computational components and connectors. In particular, connectors have been studied within both algebraic and categorical approaches to system modeling.

Abstract. Behavioural equivalences on open systems are usually defined by comparing system behaviour in all environments. Due to this “universal ” quantification over the possible hosting environments, such equivalences are often difficult to check in a direct way. Here, working in the setting of process calculi, we introduce a hierarchy of behavioural equivalences for open systems, building on a previously defined symbolic approach. The hierarchy comprises both branching, bisimulation-based, and non-branching, trace-based, equivalences. Symbolic equivalences are amenable to effective analysis techniques (e.g., the symbolic transition system is finitely branching under mild assumptions), which result to be sound, but often not complete due to redundant information. Two kinds of redundancy, syntactic and semantic, are discussed and and one class of symbolic equivalences is identified that deals satisfactorily with syntactic redundant transitions, which are a primary source of incompleteness. 1

h ground and open terms in a uniform way. To this aim, transition labels become pairs, whose components are called triggers (expressing the interaction of a context with its arguments) and effect (representing the behavior offered to the rest of the system, i.e. a possible context). Tiles can be represented as rectangles where the horizontal dimension is devoted to the assembling of states and the vertical dimension is dedicated to the evolution of components. Thus, triggers and effects form the left and right sides of tiles, respectively. The vertices of tiles are called interfaces, connecting the input and output observations to the initial (before the step) and final (after the step) configurations. Thanks to the abstract notions of configuration and observation, tiles allow us to develop a theoretical framework parametric in such structures (e.g. graphs or hypergraphs or trees or l-terms rather than terms), and able to capture analogies in the structures by means of suitable auxili

Abstract. This paper is an informal summary of different encoding techniques from process calculi and distributed formalisms to graphic frameworks. The survey includes the use of solo diagrams, term graphs, synchronized hyperedge replacement systems, bigraphs, tile models and interactive systems, all presented at the Dagstuhl Seminar 04241. The common theme of all techniques recalled here is having a graphic presentation that, at the same time, gives both an intuitive visual rendering (of processes, states, etc.) and a rigorous mathematical framework. 1