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Cartesian Closed Double Categories, their LambdaNotation, and the PiCalculus
, 1999
"... We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between s ..."
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Cited by 22 (12 self)
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We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed calculus and cartesian closed categories, we define a new typed framework, called double notation, which is able to express the abstraction /application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the ßcalculus, where the double  notation straightforwardly handles name passing and creation, concludes the presentation.
Symmetric Monoidal and Cartesian Double Categories as a Semantic Framework for Tile Logic
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2002
"... Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing acti ..."
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Cited by 14 (9 self)
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Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing actions (called configurations and observations, respectively, in our terminology) are monoidal categories having the same objects (the interfaces of the system). In particular, configurations and observations based on netprocesslike and term structures are usually described in terms of symmetric monoidal and cartesian categories, where the auxiliary structures for the rearrangement of interfaces correspond to suitable natural transformations. In this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (for example, for configurations or for observations, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four double functors (rather than two). As a consequence, the concepts of symmetric monoidal and cartesian (with consistently chosen products) double categories arise in a natural way from the corresponding ordinary versions, giving a very good relationship between the auxiliary structures of configurations and observations. Moreover, the Kelly–Mac Lane coherence axioms can be lifted to our setting without effort, thanks to the characterization of two suitable diagonal categories that are always present in a double category. Then, symmetric monoidal and cartesian double categories are shown to offer an adequate semantic setting for process and term tile systems.
An Interactive Semantics of Logic Programming
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We apply to logic programming some recently emerging ideas from the field of reductionbased 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 ..."
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Cited by 13 (6 self)
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We apply to logic programming some recently emerging ideas from the field of reductionbased 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.
A connector algebra for P/T nets interactions
 CONCUR, volume 6901 of LNCS
, 2011
"... Abstract. A quite flourishing research thread in the recent literature on componentbased system is concerned with the algebraic properties of various kinds of connectors for defining wellengineered systems. In a recent paper, an algebra of stateless connectors was presented that consists of five k ..."
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Cited by 9 (1 self)
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Abstract. A quite flourishing research thread in the recent literature on componentbased system is concerned with the algebraic properties of various kinds of connectors for defining wellengineered systems. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, plus their duals. The connectors can be composed in series or in parallel and employing a simple 1state buffer they can model the coordination language Reo. Pawel Sobocinski employed essentially the same stateful extension of connector algebra to provide semanticspreserving mutual encoding with some sort of elementary Petri nets with boundaries. In this paper we show how the tile model can be used to extend Sobocinski’s approach to deal with P/T nets, thus paving the way towards more expressive connector models. 1
Open Ended Systems, Dynamic Bisimulation and Tile Logic
, 2000
"... The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence pro ..."
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Cited by 8 (4 self)
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The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence property with such axioms and with the specication of open ended systems, where states can be recongured at runtime, at the cost of an innitary operation at the metalevel. We show that the compositional framework oered by tile logic is suitable to deal with structural axioms and open ended systems specications, allowing for a nitary presentation of context closure. Keywords: Bisimulation, sos formats, dynamic bisimulation, tile logic. Introduction The semantics of dynamic systems can be conveniently expressed via labelled transition systems (lts) whose states are terms over a certain algebra and whose labels describe some abstract behavioral information. Provided such informatio...
Connector Algebras, Petri Nets, and BIP ⋆
"... Abstract. In the area of componentbased software architectures, the term connector has been coined to denote an entity (e.g. the communication network, middleware or infrastructure) that regulate the interaction of independent components. Hence, a rigorous mathematical foundation for connectors is ..."
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Abstract. In the area of componentbased software architectures, the term connector has been coined to denote an entity (e.g. the communication network, middleware or infrastructure) that regulate the interaction of independent components. Hence, a rigorous mathematical foundation for connectors is crucial for the study of coordinated systems. In recent years, many different mathematical frameworks have been proposed to specify, design, analyse, compare, prototype and implement connectors rigorously. In this paper, we overview the main features of three notable frameworks and discuss their similarities, differences, mutual embedding and possible enhancements. First, we show that Sobocinski’s nets with boundaries are as expressive as Sifakis et al.’s BI(P), the BIP component framework without priorities. Second, we provide a basic algebra of connectors for BI(P) by exploiting Montanari et al.’s tile model and a recent correspondence result with nets with boundaries. Finally, we exploit the tile model as a unifying framework to compare BI(P) with other models of connectors and to propose suitable enhancements of BI(P). 1
Appligraph: Applications of Graph Transformation  Fourth Annual Progress Report
, 2001
"... This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and devel ..."
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Cited by 1 (0 self)
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This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and development of systems, languages, and tools and to improve the awareness of its industrial relevance
Towards a Videoconference Interface Formalisation, The
 4th International Arab Conference on computer science and Information Technology, CSIT06
, 2006
"... The definition of the manmachine interaction in the interfaces controlled by the user is a difficult task. The use of a formal specification technique is of a big utility while providing complete, unambiguous and coherent models. The major objective of our contribution is the formalisation of a vid ..."
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The definition of the manmachine interaction in the interfaces controlled by the user is a difficult task. The use of a formal specification technique is of a big utility while providing complete, unambiguous and coherent models. The major objective of our contribution is the formalisation of a videoconference interface encouraging its a validation. Rewriting logic is proved to be an adequate formalism for specifying this type of applications. Indeed, it permits to argue on the complex possible changes of a videoconference interface system. These changes correspond to the atomic actions specified by the rewriting rules. Besides, Maude system based on rewriting logic concepts offers formal analysis techniques to prove some properties related to this system type. So, the practical realization of this videoconference interface is inspired from its prototype which is designed and tested under the Maude environment. A theoretical extent of this survey will permit the deduction of a meta model that will be able to develop graphic interfaces generator.
Modeling a Service and Session Calculus with Hierarchical Graph Transformation ∗
"... Abstract: Graph transformation techniques have been applied successfully to the modelling of process calculi, for example for equipping them with a truly concurrent semantics. Recently, there has been an increasing interest towards hierarchical structures both at the level of graphbased models, in ..."
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Abstract: Graph transformation techniques have been applied successfully to the modelling of process calculi, for example for equipping them with a truly concurrent semantics. Recently, there has been an increasing interest towards hierarchical structures both at the level of graphbased models, in order to represent explicitly the interplay between linking and containment (like in Milner’s bigraphs), and at the level of process calculi, in order to deal with several logical notions of scoping (ambients, sessions and transactions, among others). In this paper we show how to encode a sophisticated calculus of services and nested sessions by exploiting a suitable flavour of hierarchical graphs. For the encoding of the processes of this calculus we benefit from a recently proposed algebra of graphs with nesting.