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A gap between linear and non linear term-rewriting systems

  • M. Dauchet
  • DE Comite
Families Of Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 256)

Abstract

We prove that every recursively enumerable set of terms is generated by a non linear t.r.s in 2 passes. Conversely, every set of terms which is generated by a linear t.r.s in a finite number of passes is recognizable.

Reference

  1. [1]
    A. ARNOLD et M. DAUCHET. "Caractérisation algébrique des ensembles d'arbres récursivement énumérables". 1er Colloque AFCET-SMF, Paris, (1978), T2, pp. 1–14.Google Scholar
  2. [2]
    M. DAUCHET et J. MONGY. "Transformation de noyaux reconnaissables, capacité générative des bimorphismes de forêts". FCT'79, Akademie-Verlag, Berlin, pp.99–104.Google Scholar
  3. [3]
    F. DE COMITE. "Simulation linéaire de systèmes de réécriture". Thèse de 3ème cycle, Université de Lille I, (1984).Google Scholar
  4. [4]
    N. DERSHOWITZ. "Termination, rewriting techniques and applications". Lecture Notes in Computer Science 202, (1985), pp. 180–224.Google Scholar
  5. [5]
    J. ENGELFRIET. "Bottom-up top-down tree transformations. A comparison". Math. Systems Theory 9, (1975), pp. 198–231.Google Scholar
  6. [6]
    J. ENGELFRIET et M. SCHMIDT. "IO and OI". Journal of Computer and Systems Science 15, (1977), pp. 328–353, 16, (1978), pp. 67–99Google Scholar
  7. [7]
    J.V. GUTTAG, D. KAPUR et D.R. MUSSER. "Derived pairs, overlap closure and rewrite rules. New tools foranalysing term rewriting systems". 9th Automata, Languages and Programming, Lecture Notes in Computer Science 140, (1982), pp. 300–312.Google Scholar
  8. [8]
    G. HUET ET D.C. OPPEN. "Equations and rewrite rules: a survey". In Formal Language Theory: Perspectives and Open Problems. Academic Press, (1980).Google Scholar
  9. [9]
    J.W. THATCHER. "Tree automata: an informal survey". In "Currents in the theory of computing". (A.V. Aho, Ed.), Prentice Hall, (1973), pp. 143–178.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • M. Dauchet
    • 1
  • DE Comite
    • 1
  1. 1.Universite Des Sciences Et Techniques De Lille Flanders-Artois Ufr D'Ieea — Informatique — Bât. M3Villeneuve D'Ascq Cedex

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