Skip to main content
Log in

A note on special thue systems with a single defining relation

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

It is shown that a Thue system of the formT 1 = {(w,e)} is Church-Rosser if and only if there is a Thue systemT 2 that is Church-Rosser and is equivalent toT 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Avenhaus and K. Madlener. String matching and algorithmic problems in free groups,Revista Columbiana de Matematicas 14, 1–16 (1980).

    Google Scholar 

  2. J. Berstel. Congruences plus que parfaites et languages algebrique,Seminaire d'Informatique Theorique (1976–77), Institut de Programmation, 123–147.

  3. R. Book. Confluent and other types of Thue systems,J. Assoc. Comput. Mach. 29 (1982), to appear.

  4. R. Book and C. O'Dunlaing. Testing for the Church-Rosser property,Theoret. Comp. Sci. 16, 223–229 (1981).

    Google Scholar 

  5. Y. Cochet and M. Nivat. Une generalization des ensembles de Dyck,Israel J. Math. 9, 389–395 (1971).

    Google Scholar 

  6. G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems,J. Assoc. Comput. Mach. 27, 797–821 (1980).

    Google Scholar 

  7. M. Jantzen. On a special monoid with a single defining relation,Theoret. Comp. Sci. 16, 61–73 (1981).

    Google Scholar 

  8. D. Kunth, J. Morris, and V. Pratt. Fast pattern matching in strings,SIAM J. Computing 6, 323–350 (1977).

    Google Scholar 

  9. R. Lyndon and M. Schutzenberger. The equationa M =b N c P in a free group,Michigan Math. J. 9, 289–298 (1962).

    Google Scholar 

  10. M. H. A. Newman. On theories with a combinatorial definition of “equivalence,”Annals Math. 43, 223–243 (1942).

    Google Scholar 

  11. M. Nivat (with M. Benois). Congruences parfaites et quasi-parfaites, Seminaire Dubriel, 25e Annee (1971–72), 7-01-09.

  12. M. O'Donnell.Computing in Systems Described by Equations, Lecture Notes in Computer Science 58 (1977), Springer-Verlag.

  13. C. O'Dunlaing. Finite and infinite regular Thue systems, Ph.D. dissertation, University of California at Santa Barbara, 1981.

  14. B. Rosen. Tree manipulating systems and the Church-Rosser systems,J. Assoc. Comput. Mach. 20 (1973), 160–187.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by the National Science Foundation under Grants MCS80-11979 and MCS81-16327

Rights and permissions

Reprints and permissions

About this article

Cite this article

Book, R.V. A note on special thue systems with a single defining relation. Math. Systems Theory 16, 57–60 (1983). https://doi.org/10.1007/BF01744568

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01744568

Keywords

Navigation