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The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 66 (24 self)
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In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the others, the structured operational semantics [Plo81], the context systems [LX90] and the structured transition systems [CM92] approaches. Our model recollects many properties of these sources: first, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is defined, equipping the system under analysis with a concurrent semantics, ...
An Algebraic Presentation of Term Graphs, via GSMonoidal Categories
 Applied Categorical Structures
, 1999
"... . We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the wellknown characterisation of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particula ..."
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Cited by 38 (25 self)
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. We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the wellknown 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 onetoone with the arrows of the free gsmonoidal 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, gsmonoidal categories, symmetric monoidal categories, term graphs. Mathematical Subject Clas...
Algebra of Flownomials; Part 1: Binary Flownomials; Basic Theory
"... ' morphism for connecting flowgraphs are used in [CaU82] and in all of our subsequent papers on flowchart schemes and flownomials, see [Ste87a, Ste87b, CaS88a, CaS90a, CaS92]. This chapter folows Chapter B, sec. 36 of [Ste91]. The main result is based on a series of papers dealing with the al ..."
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Cited by 16 (0 self)
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' morphism for connecting flowgraphs are used in [CaU82] and in all of our subsequent papers on flowchart schemes and flownomials, see [Ste87a, Ste87b, CaS88a, CaS90a, CaS92]. This chapter folows Chapter B, sec. 36 of [Ste91]. The main result is based on a series of papers dealing with the algebraization of flowchart schemes, including [CaU82, BlEs85, Ste86/90, Bar87a, CaS88a, CaS90b]. With different sets of operators various algebras for flowgraphs appear in [Mil79, Parr87, CaS90b, CaS88b]. In the classical algebraic calculus for regular languages it is often the case that certain abstract semirings are used instead of the Boolean f0; 1g semiring, e.g. by using formal series with such coefficients. 5 This property is similar to the universal property of the polynomials over a ring. Chapter 6 Graph isomorphism with various constants In this chapter we extend the axiomatistion for flowgraphs modulo isomorphism to the case where more constants for generating relations are present i...
Normal Forms for Partitions and Relations
 Recent Trends in Algebraic Development Techniques, volume 1589 of Lect. Notes in Comp. Science
, 1999
"... Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" ..."
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Cited by 14 (11 self)
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Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" field, but an exhaustive comparison between them is difficult because their presentations can be quite dissimilar. This work is a first step towards a unified view, which is able to recast all those formalisms into a more general one, where they can be easily compared. We introduce a general schema for describing a characteristic normal form for many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable concrete monoidal categories.
Rewriting On Cyclic Structures: Equivalence Between The Operational And The Categorical Description
, 1999
"... . We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, fo ..."
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Cited by 13 (6 self)
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. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms. R'esum'e. Nous pr'esentons une formulation cat'egorique de la r'e'ecriture des graphes cycliques des termes, bas'ee sur une variante de 2theorie alg'ebrique. Nous prouvons que cette pr'esentation est 'equivalente `a la d'efinition op'erationnelle propos'ee par Barendregt et d'autres auteurs, mais pas dons le cas des radicaux circulaires, pour lesquels nous proposons (et justifions formellem...
Reaction and Control I. Mixing Additive and Multiplicative Network Algebras
 Logic Journal of the IGPL
, 1996
"... . This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomi ..."
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Cited by 9 (2 self)
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. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomiallike calculus for representing flowgraphs and their behaviours. An `additive' interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a `multiplicative' interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The role of this first paper is to present a few motivating examples. To appear in Journal of IGPL....
The algebra of stream processing functions
, 1996
"... Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing funct ..."
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Cited by 8 (1 self)
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Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing functions. The algebraic theory is provided by the calculus of flownomials which gives a unified presentation of regular algebra and iteration theories. The kernel of the calculus is an equational axiomatization called Basic Network Algebra (BNA) for flowgraphs modulo graph isomorphism. We show that the algebra of stream processing functions called SPF (used for deterministic networks) and the algebra of sets of stream processing functions called PSPF (used for nondeterministic networks) are BNA algebras. As a byproduct this shows that both semantic models are compositional. We also identify the additional axioms satisfied by the branching components that correspond to constants in these two algebraic theories. For the deterministic case we study in addition the coarser equivalence relation on networks given by the inputoutput behaviour and provide a correct and complete axiomatization.
Towards a Calculus for UMLRT Specifications
, 1998
"... The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most importantstandards for the specification and design of objectoriented systems. This standard is currently tuned for realtime applications in the form of a new proposal, ..."
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Cited by 7 (0 self)
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The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most importantstandards for the specification and design of objectoriented systems. This standard is currently tuned for realtime applications in the form of a new proposal, UML for RealTime (UMLRT), by Rational Software Corporation and ObjecTime Limited. Because of the importance of UMLRTwe are investigating its formal foundation in a joint project between ObjecTime Limited, Technische Universitat Munchen and the University of Bucharest. In this paper we present part of this foundation, namely the theory of flowgraphs.
WHAT IS BEHIND UMLRT?
, 1999
"... The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most important standards for the specification and design of object oriented systems. This standard is currently tuned for real time applications in the form of a new proposal, UML ..."
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Cited by 6 (0 self)
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The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most important standards for the specification and design of object oriented systems. This standard is currently tuned for real time applications in the form of a new proposal, UML for RealTime (UMLRT), by Rational Software Corporation and ObjecTime Limited. Because of the importance of UMLRT we are investigating its formal foundation in a joint project between ObjecTime Limited, Technische Universität München and the University of Bucharest. Our results clearly show that the visual notation of UMLRT is not only very intuitive but it also has a very deep mathematical foundation. In a previous paper (see [GBSS98]) we presented part of this foundation, namely the theory of flow graphs. In this paper we use flow graphs to define the more powerful theory of interaction graphs.