On Hyperedge Replacement and BNLC Graph Grammars

It is shown that up to vertex labelling BNLC grammars of bounded nonterminal degree generate the same languages of simple graphs as hyperedge replacement grammars. This does not hold if the vertex labelling is taken into account. Vice versa hyperedge replacement grammars generate the same languages of simple graphs as BNLC grammars of bounded nonterminal degree. Furthermore the generation of loops and multiple edges by hyperedege replacement grammars is discussed.

[1]  Detlef Seese,et al.  Problems Easy for Tree-Decomposable Graphs (Extended Abstract) , 1988, ICALP.

[2]  Azriel Rosenfeld,et al.  Web Grammars , 1969, IJCAI.

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

[4]  Annegret Habel,et al.  Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement , 1987, STACS.

[5]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs , 1990, Inf. Comput..

[6]  Clemens Lautemann,et al.  Decomposition Trees: Structured Graph Representation and Efficient Algorithms , 1988, CAAP.

[7]  Grzegorz Rozenberg,et al.  Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity , 1986, Inf. Control..

[8]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[9]  Andrzej Ehrenfeucht,et al.  Restrictions on NLC Graph Grammars , 1984, Theor. Comput. Sci..

[10]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1982, Lecture Notes in Computer Science.

[11]  Grzegorz Rozenberg,et al.  Combinatorial properties of boundary NLC graph languages , 1987, Discret. Appl. Math..

[12]  Annegret Habel,et al.  Characteristics of Graph Languages Generated by Edge Replacement , 1987, Theor. Comput. Sci..

[13]  Clemens Lautemann,et al.  Efficient Algorithms on Context-Free Graph Grammars , 1988, ICALP.

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

[15]  Hartmut Ehrig,et al.  Graph-Grammars and Their Application to Computer Science and Biology , 1978, Lecture Notes in Computer Science.

[16]  Joost Engelfriet,et al.  Apex Graph Grammars , 1986, Graph-Grammars and Their Application to Computer Science.

[17]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1986, Lecture Notes in Computer Science.

[18]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.