A String-Rewriting Characterization of Muller and Schupp’s Context-Free Graphs

  • Hugues Calbrix
  • Teodor Knapik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1530)


This paper introduces Thue specifications, an approach for string-rewriting description of infinite graphs. It is shown that strongly reduction-bounded and unitary reduction-bounded rational Thue specifications have the same expressive power and both characterize the context-free graphs of Muller and Schupp. The problem of strong reduction-boundedness for rational Thue specifications is shown to be undecidable but the class of unitary reduction-bounded rational Thue specifications, that is a proper subclass of strongly reduction-bounded rational Thue specifications, is shown to be recursive.


Normal Form Turing Machine Cayley Graph Order Theory Free Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barthelmann, K.: On equational simple graphs. Technical Report 9/97, Johannes Gutenberg Universität, Mainz (1997)Google Scholar
  2. 2.
    Book, R.V., Otto, F.: String–Rewriting Systems. Texts and Monographs in Computer Science. Springer, Heidelberg (1993)Google Scholar
  3. 3.
    Calbrix, H., Knapik, T.: On a class of graphs of semi–Thue systems having decidable monadic second–order theory. Technical Report INF/1998/01/01/a, IREMIA, Université de la Réunion (1998)Google Scholar
  4. 4.
    Caucal, D.: On the regular structure of prefix rewriting. Theoretical Comput. Sci. 106, 61–86 (1992)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Caucal, D.: On infinite transition graphs having a decidable monadic second– order theory. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 194–205. Springer, Heidelberg (1996)Google Scholar
  6. 6.
    Courcelle, B.: The monadic second–order logic of graphs, II: Infinite graphs of bounded width. Mathematical System Theory 21, 187–221 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Courcelle, B.: Graph rewriting: An algebraic and logic approach. In: van Leeuwen, J. (ed.) Formal Models and Semantics, Handbook of Theoretical Computer Science, vol. B, pp. 193–242. Elsevier, Amsterdam (1990)Google Scholar
  8. 8.
    Courcelle, B.: The monadic second–order theory of graphs IX: Machines and their behaviours. Theoretical Comput. Sci. 151, 125–162 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Engelfriet, J.: Contex–free graph grammars. In: Rozenberg, G., Salomaa, A. (eds.) Beyond Words, Handbook of Formal Languages, vol. 3, pp. 125–213. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial approach to the specification, correctness and implementation of abstract data types. In: Yeh, R.T. (ed.) Data Structuring, Current Trends in Programming Methodology, vol. 4, pp. 80–149. Prentice Hall, Englewood Cliffs (1978)Google Scholar
  11. 11.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison–Wesley, London (1979)zbMATHGoogle Scholar
  12. 12.
    Muller, D.E., Schupp, P.E.: The theory of ends, pushdown automata and second–order logic. Theoretical Comput. Sci. 37, 51–75 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Otto, F.: On the property of preserving regularity for string–rewriting systems. In: Comon, H. (ed.) RTA 1997. LNCS, vol. 1232, pp. 83–97. Springer, Heidelberg (1997)Google Scholar
  14. 14.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  15. 15.
    Sénizergues, G.: Formal languages and word rewriting. In: Comon, H., Jouannaud, J.-P. (eds.) TCS School 1993. LNCS, vol. 909, pp. 75–94. Springer, Heidelberg (1995)Google Scholar
  16. 16.
    Squier, C.C., Otto, F., Kobayashi, Y.: A finiteness condition for rewriting systems. Theoretical Comput. Sci. 131(2), 271–294 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Thue, A.: Probleme über veränderungen von zeichenreihen nach gegebenen regeln. Skr. Vid. Kristiania, I Mat. Natuv. Klasse 10, 34 (1914)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Hugues Calbrix
    • 1
  • Teodor Knapik
    • 2
  1. 1.College Jean LecanuetRouen CedexFrance
  2. 2.IREMIAUniversité de la RéunionSaint Denis Messageries Cedex 9

Personalised recommendations