Proofs and reachability problem for ground rewrite systems

  • J. L. Coquidé
  • R. Gilleron
Part III Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 464)


The different reachability problems for ground rewrite systems are decidable[OY86], [DEGI89]. We prove these results using ground tree transducers of [DATI85] and wellknown algorithms on recognizable tree languages in order to obtain efficient algorithms. We introduce and study derivation proofs to describe the sequences of rules used to reduce a term t in a term t' for a given ground rewrite system S and sketch how compute a derivation proof in linear time. Moreover, we study the same problem for recognizable tree languages.


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  1. [BR69]
    Brainerd, W.S, Tree generating regular systems, Inf. and control, 14 (1969), pp217–231.Google Scholar
  2. [CO90]
    Coquidé, J.L., Ph.D, Lille, to appear. (1990).Google Scholar
  3. [COU89]
    Courcelle, B.,On recognizable sets and tree automata, Resolution of Equations in Algebraic Structures, Academic Press, M.Nivat & H. Ait-Kaci edts, (1989).Google Scholar
  4. [DADE89]
    Dauchet, M., Deruyver, A., "VALERIANN":Compilation of Ground Term Rewriting Systems and Applications, Rewriting Technics and Applications, (1989), Lec. Notes Comp. Sci., 355(Dershowitz ed.).Google Scholar
  5. [DHTL87]
    Dauchet, M., Heuillard, P., Lescanne, P., Tison, S., Decidability of the Confluence of Ground Term Rewriting Systems, 2nd Symposium on Logic in Computer Science, New-York, IEEE Computer Society Press (1987)Google Scholar
  6. [DATI85]
    Dauchet, M., Tison, S., Decidability of Confluence in Ground Term Rewriting Systems, Fondations of Computation Theory, Cottbus, Lec. Notes Comp. Sci., 199, (1985)Google Scholar
  7. [DATI90]
    Dauchet, M., Tison, S., The theory of Ground Rewrite System is Decidable, IEEE Symposium on Logic in Computer Science, to appear, (1990)Google Scholar
  8. [DEGI89]
    Deruyver, A., Gilleron, R., Compilation of Term Rewriting Systems, CAAP 89, Lec. Notes. Comp. Sci., (Diaz ed), 354, (1989)Google Scholar
  9. [DEJO89]
    Dershowitz, N., Jouannaud, J.P., Rewrite systems, Handbook of Theoretical Computer Science, J.V.Leeuwen editor, North-Holland, to appear.(1989).Google Scholar
  10. [EN75]
    Engelfriet, J., Bottom-up and Top-down Tree Transformations, a Comparison, Math. Systems Theory, 9, (1975)Google Scholar
  11. [FUVA89]
    Fülöp, Z., Vàgvölgyi, S., Ground Term Rewriting rules for the Word Problem of Ground Term Equations, submitted paper, (1989).Google Scholar
  12. [GEST84]
    Gecseg, F., Steinby, M., Tree automata, Akademiai Kiado, (1984).Google Scholar
  13. [GI90]
    Gilleron, R., Ph.D, Lille, to appear (1990).Google Scholar
  14. [HUOP80]
    Huet, G., Oppen, D.C., Equations and Rewrite Rules: A survey, in R.V. Book, ed., New York, Academic Press, Formal Language Theory: Perspectives and Open Problems, (1980).Google Scholar
  15. [NEOP80]
    Nelson, G., Oppen, D.C., Fast Decision Procedures Based on Congruence Closure, JACM, 27, (1980).Google Scholar
  16. [OY86]
    Oyamaguchi, M., The reachability Problem for Quasi-ground Term Rewriting Systems, Journal of Information Processing, 9-4, (1986).Google Scholar
  17. [TI89]
    Tison, S., The Fair Termination is decidable for Ground Systems, Rewriting Technics and Applications, Chapel Hill, Lec. Notes Comp. Sci., 355 (Dershowitz ed.), (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. L. Coquidé
    • 1
  • R. Gilleron
    • 2
  1. 1.L.I.F.L(CNRS URA 369)University of Lille-Flandres-Artois UFR IEEAVilleneuve d'Ascq cedexFrance
  2. 2.department informatiqueL.I.F.L(CNRS URA 369), IUT AVilleneuve d'Ascq cedexFrance

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