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On the Structure of Highlevel Nets
 Helsinki University of Technology
, 1995
"... : The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is ..."
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: The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is shown that nets given in these formalisms can be transformed into equivalent Algebraic nets. Then the semantics of nets in terms of universal constructions is discussed. A definition of Algebraic nets in terms of structured transition systems is proposed. The semantics of the Algebraic net is then given as a free completion of this structured transition system to a category. As an alternative also a sheaf semantics of nets is examined. Here the semantics of the net arises as a limit of a diagram of sheaves. Next Algebraic nets are characterized as encodings of special morphisms called foldings. Each algebraic net gives rise to a surjective morphism between Petri nets and conversely each sur...
Marked Petri Nets Within a Categorial Framework
 RITA  Revista de Informática Teórica e Aplicada
, 1995
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A Sheaf Semantics for Petri Nets
, 1993
"... : The semantics of Petri Nets are discussed within the "Objects are sheaves" paradigm. Transitions and places are represented as sheaves and nets are represented as diagrams of sheaves. Both an interleaving semantics, and a noninterleaving semantics are shown to arise as the limit of the ..."
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: The semantics of Petri Nets are discussed within the "Objects are sheaves" paradigm. Transitions and places are represented as sheaves and nets are represented as diagrams of sheaves. Both an interleaving semantics, and a noninterleaving semantics are shown to arise as the limit of the sheaf diagram representing the net. This work was supported by the Information Technology Promotion Agency, Japan, as part of the R & D of Basic Technology for Future Industries "New Models of Software Architecture" project sponsored by NEDO (New Energy and Industrial Technology Developments Organization). Printing: TKK Monistamo; Otaniemi 1993 Helsinki University of Technology Phone: 90 +3580 4511 Department of Computer Science Digital Systems Laboratory Telex: 125 161 htkk sf Otaniemi, Otakaari 1 Telefax: +3580465 077 SF02150 ESPOO, FINLAND Email: lab@hutds.hut.fi  1  1 Introduction Sheaf theory is a mathematical tool that has been successfully applied to the solution of difficult m...
DuoInternal Labeled Graphs with Distinguished Nodes: a Categorial Framework for Graph Based Anticipatory Systems
 CASYS'99  Third International Conference on Computing Anticipatory Systems, International Journal of Computing Anticipatory Systems
, 2000
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An Algebra of Graph Derivations Using Finite (co) Limit Double Theories
"... Graph transformation systems have been introduced for the formal specication of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specication. Operations on graph derivations provide means to reason about the distribution ..."
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Graph transformation systems have been introduced for the formal specication of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specication. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph derivations as a descriptive model of graph transformation systems. For that purpose we use a categorical three level approach for the construction of models of computations based on structured transition systems. Categorically the algebra of graph derivations can then be characterized as a free double category with nite horizontal colimits.
Compositional Reification of Concurrent, Interacting Systems
 Proc. of International Conf. on Parallel and Distributed Processing Techniques and Application PDPTA’98, v.4, Las Vegas
, 1998
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Web Courses are Automata: a Categorial Framework
 II Workshop on Formal Methods, Florianpolis
, 1999
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Categorical rewriting of termlike structures 1 Abstract
"... The article surveys a recent series of papers by the authors investigating the categorical foundations of various rulebased formalisms. The starting point is the wellknown representation of term rewriting systems as cartesian 2categories, based on the characterization of finite terms as arrows of ..."
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The article surveys a recent series of papers by the authors investigating the categorical foundations of various rulebased formalisms. The starting point is the wellknown representation of term rewriting systems as cartesian 2categories, based on the characterization of finite terms as arrows of a Lawvere theory. We first show that many termlike structures (including cyclic term graphs, µterms and rational terms) can be characterized as arrows of suitable theories. Next we represent rules as cells over a theory, and we show that the free 2category generated by these cells faithfully represents the rewrite sequences of the original rewriting system. Key words: Term graphs; rational terms; µterms; term graph rewriting; algebraic, gsmonoidal, traced monoidal and iteration theories; 2theories. 1