. Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature \Sigma as cartesian functors from the algebraic theory of \Sigma , Th(\Sigma), to Set. The functors we introduce are based on variations of the notion of theory, having a structure weaker than cartesian, and their target is Rel, the category of sets and relations. We argue that this functorial presentation provides an original abstract syntax for partial and multi-algebras. 1 Introduction Nondeterminism is a fundamental concept in Computer Science. It arises not only from the study of intrinsically nondeterministic computational models, like Turing machines and various kinds of automata, but also in the study of the behaviour of deterministic sys...

Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. Starting from a functorial presentation of multi-algebras based on gs-monoidal theories, we argue that speci cations for multi-algebras should be based on the notion of term graphs instead of on standard terms. We consider the simplest case of (term graph) equational specification, showing that it enjoys an unrestricted form of substitutivity. We discuss the expressive power of equational specification for multialgebras, and we sketch possible extensions of the calculus.

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We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the well-accepted operational definition proposed in [3] -- but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2-categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.

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.

This paper extends our approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on a graphical encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph. Behavioral and structural properties of π-calculus processes expressed in a spatial logic are verified on the graphical encoding of a process rather than on its textual representation. For this purpose we introduce a modal logic for graphs and define a faithful translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula.

The paper introduces a novel approach to the verification of spatial properties for finite #-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of #-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula).

Abstract. As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design points for this language are to only describe data flow, have built-in facilities for redundancies, and still have code that looks like assembler, by virtue of consisting mainly of assembly instructions, we are basing the theoretical foundations on data-flow graph theory, and have to accommodate also relational aspects. Using functorial semantics into a Kleene category of “hyper-paths”, we formally capture the data-flow-with-choice aspects of this language and its implementation, providing also the framework for the necessary correctness proofs. 1

Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, tree-like presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, but an exhaustive comparison between them is sometimes difficult, because their presentations can be quite dissimilar. This work is a first step towards a unified view: Focusing on the primitive ingredients of distributed spaces (namely interfaces, links and basic modules), we introduce a general schema for describing a normal form presentation of many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable monoidal categories.

The paper introduces a novel approach to the verification of spatial properties for finite π-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of π-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula).