On rational expressions representing infinite rational trees : Application to the structure of flow charts

  • Guy Cousineau
  • Maurice Nivat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 74)


Regular Expression Regular Tree Regular System Exit Statement Finite Tree 
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.
    Arsac J., Nolin L., Vasseur J.P. and G. Ruggiu: Le système de programmation structurée EXEL. Revue Thomson-CSF, Vol. 6 (1974).Google Scholar
  2. 2.
    Arsac J.: La construction de programmes structurés. Dunod, Paris (1977).Google Scholar
  3. 3.
    Ashcroft E. and Z. Manna: The translation of goto programs to while programs, in Proc. IFIP Cong, Amsterdam (1971).Google Scholar
  4. 4.
    Böhm C. and G. Jacopini: Flow diagrams, turing machines and languages with only two formation rules, Proc. IFIP Cong. Amsterdam (1971).Google Scholar
  5. 5.
    Casteran P.: Structures de contrôle: définitions opérationnelles et algébriques. Thèse de 3ème cycle, Université Paris VII (1979).Google Scholar
  6. 6.
    Courcelle B.: Recursive schemes, algebraic trees and deterministic languages, in Proc. 15th Symp. Found. Comp. Sci. (1974).Google Scholar
  7. 7.
    Courcelle B., G. Kahn and J. Vuillemin: Algorithmes d'équivalence et de réduction à des expressions minimales dans une classe d'équations récursives simples, in Automata, Languages and Programming (J. Loeckx ed.) LNCS no 14, Berlin (1974).Google Scholar
  8. 8.
    Cousineau G.: Arbres à feuilles indicées et transformations de programmes. Thèse d'Etat, Université Paris VII (1977).Google Scholar
  9. 9.
    Cousineau G.: An algebraic definition for control structures, to appear in Theoretical Computer Science (1979).Google Scholar
  10. 10.
    Doner J.E.: Tree acceptors and some of their applications, Jour. Comp. Syst. Sci. Vol 4 (1970), pp. 406–451.Google Scholar
  11. 11.
    Ershov A.P.: Theory of program schemata, in Proc. IFIP Cong., Amsterdam (1971).Google Scholar
  12. 12.
    Henry C.: Resolution d'équations algébriques sur le magma libre: application aux transformations de programmes, Thèse de 3ème cycle, Université Paris VII, (1978).Google Scholar
  13. 13.
    Ianov I.I.: The logical scheme of algorithms, english translation in Problems of Cybernetics, Vol. 1 (1960), pp. 82–140.Google Scholar
  14. 14.
    Igarashi S.: An axiomatic approach to the equivalence problem of algorithms, Report of the Computer Center, Univ. of Tokyo, vol. 1 (1969) pp. 1–101.Google Scholar
  15. 15.
    Jacob G.: Structural invariants for some classes of structured programs in Mathematical Foundations of Computer Science, LNCS no 64, Springer Verlag, Berlin (1978).Google Scholar
  16. 16.
    Kaplan D.M.: The formal theoretic analysis of strong equivalence for elemental programs, Ph D dissertation, Stanford (1968).Google Scholar
  17. 17.
    Kasai T.: Translatability of flow-charts into while programs. Jour. Comp. Syst. Sci., vol. 9 (1974), pp. 177–195.Google Scholar
  18. 18.
    Kasami T., W. Peterson and N. Tokura: On the capabilities of while, repeat and exit statements. Comm. Assoc. Comp. Mach. Vol. 16 (1973).Google Scholar
  19. 19.
    Knuth D.E. and R.W. Floyd: Notes on avoiding go to statements. Inf. Proc. Letters Vol. 1 (1971), pp. 23–31.CrossRefGoogle Scholar
  20. 20.
    Kosaraju R.: Analysis of structured programs, Jour. Compt. Syst. Sci., Vol. 9 (1974) pp. 232–255.Google Scholar
  21. 21.
    Milner R.: Equivalence on program schemes, Jour. Comp. Syst. Sci., vol. 4 (1970) pp. 205–219.Google Scholar
  22. 22.
    Mycielski J. and W. Taylor: A compactification of the algebra of terms, Alg. Univ. Vol. 6 (1976) pp. 159–163.Google Scholar
  23. 23.
    Nivat M.: Langages algébriques sur le magma libre et sémantique des schémas de programmes in Automata, languages and programming (M. Nivat ed.) Amsterdam (1973).Google Scholar
  24. 24.
    Nolin L. and G. Ruggiu: Formalization of EXEL, in Proc. ACM Symp. Princ. Prog. Lang., Boston (1973).Google Scholar
  25. 25.
    Paterson M.S.: Equivalence problems in a model of computation Ph. D dissertation Trinity College, Cambridge (1967).Google Scholar
  26. 26.
    Robinet B.: Un modèle fonctionnel des structures de contrôle, RAIRO Inf. The, Vol. 11 (1977) pp. 213–236.Google Scholar
  27. 27.
    Ruggiu G.: De l'organigramme à la formule, Thèse d'Etat, Université Paris VII, (1973).Google Scholar
  28. 28.
    Rutledge J.D.: On Ianov's program schemata. Journal Assoc. Comp. Mach. Vol. 11 (1964) pp. 1–9.Google Scholar
  29. 29.
    Scott D.: The lattice of flow diagrams, in Symposium on semantics of algorithmic languages (E. Engeler ed.), in Lecture Notes Math. no 188, Springer Verlag, Berlin (1971).Google Scholar
  30. 6 bis.
    Courcelle B. and M. Nivat: Algebraic families of interpretations, in Proc. 17th Symp. Found. Comp. Sci. (1976).Google Scholar
  31. 23 bis.
    Nivat M.: Chartes, arbres, programmes itératifs. Revue Thomson-CSF, Vol. 10 (1978) pp. 705–731.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Guy Cousineau
    • 1
  • Maurice Nivat
    • 1
  1. 1.Laboratoire d'Informatique Théorique et ProgrammationParis

Personalised recommendations