A Uniform Approach to Graph Rewriting: The Pullback Approach

Most of the works in the theory of graph rewriting can be put into two main categories: edge (or hyperedge) rewriting and node rewriting. Each has been described by a specific formalism, both have given rise to many significant developments and many works have been devoted to the comparison of both approaches. In this paper, we describe a new categorical formalism, which provides a common framework to both approaches and makes their comparison much clearer.

[1]  Michel Bauderon,et al.  Infinite Hypergraphs I. Basic Properties , 1991, Theor. Comput. Sci..

[2]  Walter Vogler,et al.  On Hyperedge Replacement and BNLC Graph Grammars , 1989, Discret. Appl. Math..

[3]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[4]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[5]  Grzegorz Rozenberg,et al.  On the structure of node-label-controlled graph languages , 1980, Inf. Sci..

[6]  Joost Engelfriet,et al.  A Comparison of Boundary Graph Grammars and Context-Free Hypergraph Grammars , 1990, Inf. Comput..

[7]  Michel Bauderon.  A Category-Theoretical Approach to Vertex Replacement: The Generation of Infinite Graphs , 1994, TAGT.

[8]  D. A. Waller,et al.  Kronecker Products and Local Joins of Graphs , 1977, Canadian Journal of Mathematics.

[9]  Grzegorz Rozenberg,et al.  Graph grammars with node-label controlled rewriting and embedding , 1982, Graph-Grammars and Their Application to Computer Science.

[10]  Annegret Habel,et al.  Hyperedge Replacement: Grammars and Languages , 1992, Lecture Notes in Computer Science.

[11]  Grzegorz Rozenberg,et al.  Graph Grammars with Neighbourhood-Controlled Embedding , 1982, Theor. Comput. Sci..

[12]  Joost Engelfriet,et al.  Graph Grammars Based on Node Rewriting: An Introduction to NLC Graph Grammars , 1990, Graph-Grammars and Their Application to Computer Science.

[13]  S. Maclane,et al.  Categories for the Working Mathematician , 1971 .

[14]  Michel Bauderon.  Infinite Hypergraphs II: Systems of Recursive Equations , 1992, Theor. Comput. Sci..

[15]  Bruno Courcelle.  An Axiomatic Definition of Context-Free Rewriting and its Application to NLC Graph Grammars , 1987, Theor. Comput. Sci..