Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Fundamenta Informaticae

2 2006

Powiadomienia systemowe

Sesja wygasła!

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Critical Pair Lemma

Sortuj według:

Ogranicz wyniki do:

Fundamental Theory for Typed Attributed Graphs and Graph Transformation based on Adhesive HLR Categories

Ehrig H., Ehrig K., Prange U., Taentzer G.

Fundamenta Informaticae

2006

Vol. 74, nr 1

31-61

The concept of typed attributed graphs and graph transformation is most significant for modeling and meta modeling in software engineering and visual languages, but up to now there is no adequate theory for this important branch of graph transformation. In this article we give a new formalization of typed attributed graphs, which allows node and edge attribution. The first main result shows that the corresponding category is isomorphic to the category of algebras over a specific kind of attributed graph structure signature. This allows to prove the second main result showing that the category of typed attributed graphs is an instance of ''adhesive HLR categories''. This new concept combines adhesive categories introduced by Lack and Soboci\'nski with the well-known approach of high-level replacement (HLR) systems using a new simplified version of HLR conditions. As a consequence we obtain a rigorous approach to typed attributed graph transformation providing as fundamental results the Local Church-Rosser, Parallelism, Concurrency, Embedding and Extension Theorem and a Local Confluence Theorem known as Critical Pair Lemma in the literature.

Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation

Ehrig H., Padberg J., Prange U.

Fundamenta Informaticae

2006

Vol. 74, nr 1

1-29

Adhesive high-level replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to high-level structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.