A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Theorique et Applications/Theoretical Informatics and Applications, 33:467{ 493, 1999. Home/Search Document Details and Download
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Appligraph: Applications of Graph Transformation - Third.. - Kreowski, (eds.) (2000) (Correct)
....is proved. The authors argue that term graph equations are more expressive than standard equations for the speci cation of multi algebras, but they admit that inequations (interpreted as inclusions of the corresponding relations) are more adequate for the speci cation of non determinism. Paper [CG99b] has been accepted for publication in Theoretical Informatics and Applications; this is a full version of paper [CG98] which was already described in the Second Annual Report. 4.3.7 Application to Neural Networks In [BFK00] attributed graph transformation is used to model neural networks. The ....
A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Theoretical Informatics and Applications, 33:467-493, 1999.
Some Algebraic Laws for Spans (and Their Connections With.. - Bruni, Gadducci (2001) Self-citation (Gadducci) (Correct)
....how, our taxonomy can be extended and generalized to (complete and cocomplete) categories other than Set. We are thinking in particular of Graph, given the importance of the resulting categories in the modeling of the operational behaviour of rewriting systems and of automata, as pointed out in [8,14] and [16,17] respectively. 15 ....
A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Theorique et Applications/Theoretical Informatics and Applications, 33:467{ 493, 1999.
A Bi-Categorical Axiomatisation of Concurrent Graph.. - Gadducci, Heckel.. (1999) (5 citations) Self-citation (Gadducci) (Correct)
....important role in the theory since it allows for definitions and proofs by structural induction. From a categorical view point, such inductive definitions have been given for various formalisms via the construction of free categories equipped with an orthogonal (algebraic or categorical) structure [3,7,8,10,16,25 27,29,30]. Often such categorical models of rewriting do not only axiomatise the rewrite relation but impose an equivalence on rewriting sequences which captures the basic concurrency properties of the system. In the double pushout (DPO) approach to graph transformation [11,15] the operational definition ....
....of graph derivations. The restriction to iso cells is necessary since cells are meant to represent rewrite steps which have to be explicitly specified by productions. 5 From DPO rewrites to bi categories We already mentioned how most of the categorical descriptions of productionbased systems [7,8,16,18,20,25,27,29,30] simulate computations via cells. To a certain extent, they all share the same view, representing such a system as a computad [31] namely, a category (in our case, a discrete bi category) augmented with a graph structure over hom sets (informally, a set S of cells 4 Actually, in [5] the authors ....
A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Th'eorique et Applications/Theoretical Informatics and Applications, 1999. To appear.
Some Algebraic Properties of (Co)Spans - Bruni, Gadducci (2000) Self-citation (Gadducci) (Correct)
....introducing the ownomial calculus [13,14] proposed as a calculus for owgraphs. Similar considerations arose independently also in di erent contexts, such as the allegories of circuits [3] based on the relational language ruby for circuit design [29] or the languages for (term) graph rewriting [10,11,20] and contextual net processes [22] or the calculi for concurrent and distributed processes [21,24,28] mostly arising from the work on pre monoidal categories [36] On the other hand, these structures have been used as suitable semantic models, that is, as suitable algebras for modeling the ....
....consider the bicategorical enrichment [2,6] over (co)spans. For the time being, we conclude the paper by presenting a table that summarizes the equational properties of the structured categories we presented, and relating our results of to the ongoing work on spans over the category of graphs [10,11,20]. 2 1 Preliminaries We introduce now the terminology and the notation that will be used in the rest of the paper, assuming the reader already familiar with the basic concepts of category theory. Abusing the notation we will often denote the arrow id a by the object name a itself. Sequential ....
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A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. Informatique Theorique et Applications/Theoretical Informatics and Applications, 33:467-493, 1999.
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