The modular decomposition of countable graphs: Constructions in monadic second-order logic

Lecture Notes in Computer Science

Volumn 3634, Issue , 2005, Pages 325-338

  Courcelle, Bruno ^a   Delhommé, Christian ^b  

^a UNIVERSITÉ DE BORDEAUX   (France)

^b UNIVERSITÉ DE LA RÉUNION   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DECOMPOSITION; FORMAL LOGIC; MATHEMATICAL MODELS;

COUNTABLE GRAPH; MODULAR DECOMPOSITIONS; RELATIONAL STRUCTURES; SECOND-ORDER LOGIC;

GRAPH THEORY;

EID: 26944463816     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11538363_23     Document Type: Conference Paper

References (17)

1. K. Barthelmann, When can an equational simple graph be generated by hyperedge replacement? Mathematical Foundations of Computer Science, Lec. Notes Comput. Sci. 960 (1998) 543-552.
2. A. Blumensath, E. Grädel, Finite presentations of infinite structures: Automata and interpretations, Theory of Computing Systems 37 (2004) 641-674.
3. D. Caucal, On the regular structure of prefix rewriting. Theoretical Computer Science 106 (1992) 61-86.
4. B. Courcelle, Fundamental properties of infinite trees, Theoretical Computer Science 25 (1983) 95-169.
5. B. Courcelle, Recursive applicative program schemes, in Handbook of Theoretical Computer Science vol. B, J. Van Leeuwen ed., Elsevier, 1990, pp.459-492.
6. B. Courcelle, Monadic second-order graph transductions: A survey. Theoretical Computer Science, 126 (1994)53-75.
7. B. Courcelle, The expression of graph properties and graph transformations in monadic second-order logic. In G. Rozenberg, editor, Handbook of graph grammars and computing by graph transformations, Vol. 1: Foundations, World Scientific, 1997, pp. 313-400.
8. B. Courcelle, The monadic second-order logic of graphs X: Linear orderings, Theoretical Computer Science 160 (1996) 87-143.
9. B. Courcelle, The monadic second-order logic of graphs XIV: Uniformly sparse graphs and edge set quantifications. Theoretical Computer Science 299 (2003) 1-36.
10. B. Courcelle, The monadic second-order logic of graphs XV: On a Conjecture by D. Seese, to appear in Journal of Applied Logic, see: http://www.labri.fr/~courcell/ActSci.html
11. B. Courcelle, C. Delhommé, The modular decomposition of countable graphs, 2005, see: http://www.labri.fr/~courcell/ActSci.html.
12. A. Ehrenfeucht, T. Harju, G. Rozenberg, Decomposition of infinite labeled 2-structures, Lec. Notes Comput. Sci. 812 (1994) 145-158.
13. A. Ehrenfeucht, T. Harju, G. Rozenberg, The theory of 2-structures. A framework for decomposition and transformation of graphs, World Scientific Publishing Co., River Edge, New-Jersey,1999.
14. R. Fraïssé, Theory of relations, Studies in logic vol. 118, North-Holland, 1986 (Second edition, Elsevier, 2000).
15. D. Kelly, Comparability graphs, in Graphs and order, I. Rival ed., D. Reidel Pub. Co., 1985, pp. 3-40.
16. B. Khoussainov, A. Nerode, Automatic presentations of structures, in Logic and Computational Complexity, Lec. Notes Comput. Sci. 960 (1995) 367-392.
17. R. Möhring, R. Radermacher, Substitution decomposition of discrete structures and connections with combinatorial optimization, Annals Discrete Maths 19 (1984) 257-356.