Abstract
Relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied. We define operations on structures that are compatible with monadic second-order logic, and that are powerful enough to represent context-free graph- and hypergraph-grammars of various types, namely, hyperedge replacement, C-edNCE, and separated handle replacement ones. Several results on monadic second-order properties of the generated sets are obtained in a uniform way.
Notes :(+) Laboratoire associé au CNRS. Email : courcell@geocub.greco-prog.fr.This work has been supported by the ESPRIT-Basic Research Action 3299 ("Computing by Graph Transformation").
Preview
Unable to display preview. Download preview PDF.
References
BAUDERON M., COURCELLE B., Graph expressions and graph rewritings, Mathematical System Theory 20 (1987) 83–127.
COURCELLE B., Equivalences and transformations of regular systems. Applications to recursive program schemes and grammars, Theor. Comp. Sci. 42 (1986), 1–122.
COURCELLE B., A representation of graphs by algebraic expressions and its use for graph rewriting systems, Proceedings of the 3rd International Workshop on Graph Grammars, L.N.C.S. 291, Springer, 1987, pp. 112–132.
COURCELLE B., On context-free sets of graphs and their monadic second-order theory, same volume as [3], pp. 133–146.
COURCELLE B., An axiomatic definition of context-free rewriting and its application to NLC graph grammars, Theoretical Computer Science 55 (1987) 141–181.
COURCELLE B., Graph rewriting: An algebraic and logic approach, in "Handbook of Theoretical Computer Science,Volume B", J. Van Leeuwen ed., Elsevier,1990, pp.193–242
COURCELLE B., The monadic second-order logic of graphs I, recognizable sets of finite graphs. Information and Computation 85 (1990) 12–75.
COURCELLE B., The monadic second-order logic of graphs V: On closing the gap between definability and recognizability, Research Report 89–91, Bordeaux I University, to appear in Theor. Comput. Sci.
COURCELLE B., The monadic second order logic of graphs VI: On several representations of graphs by relational structures, Report 89-99, (see also Logic in Computer Science 1990, Philadelphia).
COURCELLE B., The monadic second-order logic of graphs VII: Graphs as relational structures, in preparation.
COURCELLE B., ENGELFRIET J., A logical characterization of hypergraph languages generated by hyperedge replacement grammars, in preparation.
COURCELLE B., ENGELFRIET J., ROZENBERG G., Handle-rewriting hypergraph grammars, this volume.(Long version as research report 90-84, Bordeaux-I University, or reports 90-08 and 90-09 of the University of Leiden).
EHRIG H. et al., Transformations of structures, an algebraic approach, Math. Systems Theory 14 (1981) 305–334.
ENGELFRIET J., A characterization of context-free NCE graph languages by monadic-second order logic on trees, preprint, 1990.
ENGELFRIET J., ROZENBERG G., A comparison of boundary graph grammars and context-free hypergraph grammars,Information and Computation 84 (1990) 163–206.
HABEL A., KREOWSKI H.J., May we introduce to you: Hyperedge replacement, same volume as [3], pp. 15–26.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Courcelle, B. (1991). Graphs as relational structures : An algebraic and logical approach. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017393
Download citation
DOI: https://doi.org/10.1007/BFb0017393
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54478-4
Online ISBN: 978-3-540-38395-6
eBook Packages: Springer Book Archive