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Monadic second-order logic and context-free graph-grammars

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Mathematical Foundations of Computer Science 1989 (MFCS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 379))

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Abstract

Sets of finite graphs (and hypergraphs) can be defined in different ways : by context-free grammars, by conguences, by logical formulas. We compare these three types of definitions. In particular, we consider certain context-free graph-grammar, the parsing of which can be expressed in monadic second-order logic.

Notes: (+) Unité de Recherche Associée au Centre National de la Recherche Scientifique no726 • Electronic mail : courcell @geocub.greco-prog.fr or mcvax!inria!geocub!courcell (on UUCP network). • This work has been supported by the ESPRIT-Basic Research Action contract 3299 "Computing by Graph Transformation" and by the "Projet de Recherches Coordonnées: Mathématiques et Informatique".

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References

  1. BAUDERON M., COURCELLE B., Graph expressions and graph rewritings, Mathematical Systems Theory 20(1987) 83–127.

    Google Scholar 

  2. BÜCHI J., Weak second order logic and finite automata, S.Math. Logik Grundlagen Math. 5 (1960) 66–92.

    Google Scholar 

  3. COURCELLE B., Equivalence and transformations of regular systems. Applications to recursive program schemes and grammars, Theor. Comp. Sci. 42 (1986) 1–122.

    Google Scholar 

  4. COURCELLE B., An axiomatic definition of context-free rewriting and its application to NLC graph grammars, Theoretical Computer Science 55 (1987) 141–181.

    Google Scholar 

  5. COURCELLE B., A representation of graphs by algebraic expressions and its use for graph rewriting systems, Proceedings of the 3rd international workshop on grah grammars,-L.N.C.S. 291, 1987, pp. 112–132.

    Google Scholar 

  6. COURCELLE B., On context-free sets of graphs and their monadic second-order theory Proceedings fo te 3rd international workshop on graph grammars,-L.N.C.S. 291, 1987,pp. 133–146.

    Google Scholar 

  7. COURCELLE B., Some applications of logic, of universal algebra and of category theory to the theory of graph transformations, Bulleting of E.A.T.C.S. no 36, October 1988, pp. 161–218.

    Google Scholar 

  8. COURCELLE B., Graph rewriting: An algebraic and logical approach, in "Handbook of Computer Science", J. Van Leeuwen ed., North-Holland-Elsevier, to appear.

    Google Scholar 

  9. COURCELLE B., On the use of context-free graph grammars for analyzing recursive definitions, in "Programming of future generation computers II", K. Fuchi, L.Kott eds., Elsevier, 1988,pp. 83–122.

    Google Scholar 

  10. COURCELLE B., The monadic second-order logic of graphs:Definable sets of finite graphs, Workshop on graph Theoretical concepts in computer science,-L.N.C.S. 344, (1989) pp. 30–53.

    Google Scholar 

  11. COURCELLE B., The monadic second-order logic of graphs I: Recognizable sets of finite graphs, to appear in Information and Computation.

    Google Scholar 

  12. COURCELLE B., The monadic second-order logic of graphs II: Infinite graphs of bounded width, to appear in Mathematical Systems Theory.

    Google Scholar 

  13. COURCELLE B., The monadic second-order logic of graphs III: Tree-width, forbidden minors, and complexity issues, Report I-8852, 1988, Bordeaux-1 University, submitted.

    Google Scholar 

  14. COURCELLE B., The monadic second-order logic of graphs IV: Every equational graph is definable, Report I-8830, 1988, Submitted for publication.

    Google Scholar 

  15. COURCELLE B., The monadic second-order logic of graphs V: On context-free graph-grammars generating definable sets., Research report in preparation.

    Google Scholar 

  16. COURCELLE B., On recognizable sets and tree-automata, in "Resolution of equations in algebraic structures", H.Ait-Kaci and M.Nivat eds., Academic Press, 1989.

    Google Scholar 

  17. COURCELLE B., ENGELFRIET J., ROZENBERG.G., In preparation.

    Google Scholar 

  18. DONER J., Tree acceptors and some of their applications, J. Comput System Sci. 4(1970) 406–451.

    Google Scholar 

  19. EHRIG H. et al., eds, Graph-grammars and their applications in computer science and biology, L.N.C.S. Lecture Notes in Computer Science. Springer 73, 1979.

    Google Scholar 

  20. EHRIG. H. et al., eds, Graph-grammars and their applications to computer science, L.N.C.S. Lecture Notes in Computer Science. Springer 153, 1983.

    Google Scholar 

  21. EHRIG. H. et al., eds, Graph-grammars and their applications to computer science, L.N.C.S. Lecture Notes in Computer Science. Springer 291, 1987.

    Google Scholar 

  22. ENGELFRIET J., Private communication, October 1988.

    Google Scholar 

  23. GECSEG F., STEINBY M., Tree-automata, Akademia kiado, Budapest, 1984.

    Google Scholar 

  24. GOGUEN J., THATCHER J., WAGNER E., WRIGHT J., Initial algebra semantics and continuous algebras,-L.N.C.S. 24 (1977) 68–95.

    Google Scholar 

  25. HABEL A., KREOWSKI H.J., Characteristics of graph languages generated by edge replacement, Theoret. Comp. Sci 51 (1987) 81–115.

    Google Scholar 

  26. HABEL A., KREOWSKI H.J., May we introduce to you: hyperedge replacement,-L.N.C.S. 291, (1987), pp. 15–26.

    Google Scholar 

  27. JANSSENS D., ROZENBERG G., A survey of NLC grammars, in Proc. CAAP'83,-L.N.C.S. 159, (1983), pp. 114–128.

    Google Scholar 

  28. LAUTEMANN C., Efficient algorithms on context-free graph languages, ICALP'88, Tampere,-L.N.C.S. 317, (1988), pp. 362–378.

    Google Scholar 

  29. LENGAUER T., WANKE E., Efficient analysis of graph properties on context-free graph languages, ICAP'88,-L.N.C.S. 317, (1988), pp. 379–393.

    Google Scholar 

  30. MEZEI J., WRIGHT J., Algebraic automata and context-free sets, Information and control 11 (1967) 3–29.

    Google Scholar 

  31. MONTANARI U., ROSSI F., An efficient algorithm for the solution of hierarchical networks of constraints.-L.N.C.S. 291, (1987), pp. 440–457.

    Google Scholar 

  32. ROBERSTON N., SEYMOUR P., Some new results on the well-quasi-ordering of graphs, Annals of Discrete Mathematics 23 (1984) 343–354 (Elsevier Science Publisher).

    Google Scholar 

  33. SEESE D., The structure of the models of decidable monadic theories of graphs, Preprint 1987, to appear in the Journal of Pure and Applied Logic.

    Google Scholar 

  34. THOMAS W., Automata on infinite objects, "Handbook of Theoretical Computer Science", same volume as [8].

    Google Scholar 

  35. TRAHTENBROT B., Impossibility of an algorithm for the decision problem on finite classes, Doklady Nauk. SSR 70, (1950), 569–572.

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire d'Informatique(+), Université BORDEAUX-1, 351 cours de la Libération, 33405, Talence, France

    Bruno Courcelle

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  1. Bruno Courcelle
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Antoni Kreczmar Grazyna Mirkowska

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© 1989 Springer-Verlag Berlin Heidelberg

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Courcelle, B. (1989). Monadic second-order logic and context-free graph-grammars. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_54

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  • DOI: https://doi.org/10.1007/3-540-51486-4_54

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  • Print ISBN: 978-3-540-51486-2

  • Online ISBN: 978-3-540-48176-8

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