Advertisement

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)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  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

Personalised recommendations