Skip to main content

Thue systems and the Church-Rosser property

  • Invited Lectures
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1984 (MFCS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 176))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adjan, S., Defining Relations and Algorithmic Problems for Groups and Semigroups, Proc. Steklov Inst. Math. 85, (1966) (English version published by the American Mathematical Society, 1967.)

    Google Scholar 

  2. Avenhaus, J., Book, R., and Sqier, C., On Expressing Communtativity Monoids, R.A.I.R.O. Informatique Théorique, to appear.

    Google Scholar 

  3. Avenhaus, J., and Madlener, K., Algorithmische Probleme bei Einrelatorgruppen und ihre Komplexität, Arch. math. Logic 19, (1978), 3–12.

    Google Scholar 

  4. Avenhaus, J., and Madlener, K., String Matching and Algorithmic Problems in Free Groups, Revista Columbiana de Mathematicas 14, 1–16 (1980).

    Google Scholar 

  5. Berstel, J., Congruences plus que parfaites et langages algébriques, Séminaire d'Informatique Théorique, Institute de Programmation, (1976–77), 123–147.

    Google Scholar 

  6. Boasson, L., Dérivations et réductions dans les grammaires algébriques, Automata, Languages, and Programming, Lecture Notes in Computer Science, Vol. 85, Springer-Verlag (1980), 109–118.

    Google Scholar 

  7. Book, R., Confluent and Other Types of Thue Systems, J. Assoc. for Comput. Mach. 29, (1982), 171–182.

    Google Scholar 

  8. Book, R., The Power of the Church-Rosser Property in String-Rewriting Systems, Proc. 6th Conf. on Automated Deduction, Lecture Notes in Computer Science, Vol. 85, Springer-Verlag (1982) 360–368.

    Google Scholar 

  9. Book, R., When is a Monoid a Group? The Church-Rosser Case is Tractable, Theoret. Comp. Sci. 18, (1982), 325–331.

    Google Scholar 

  10. Book, R., A Note On Special Thue Systems with a Single Defining Relation, Math. Syst. Theory, 16, (1983), 57–60.

    Google Scholar 

  11. Book, R., Decidable Sentences of Church-Rosser Congruences, Theoret. Comput. Sci. 24 (1983) 301–312.

    Google Scholar 

  12. Book, R., Thue Systems and the Church-Rosser Property: Replacement Systems, Specification of Formel Languages, and Presentations of Monoids, in Combinatorics on Words, J.L. Cummings (Ed.), Academic Press Canada (1983) 1–38.

    Google Scholar 

  13. Book, R., Homogenous Thue Systems and the Church-Rosser Property, Discrete Math. 48 (1984) 137–145.

    Google Scholar 

  14. Book, R., Jantzen, M., Monien, B., ÖDúnlaing, C., and Wrathall, C., On the Complexity of Word Problems in Certain Thue Systems, Math. Found. of Comput. Sci., Lecture Notes in Computer Science 118, Springer-Verlag (1981), 216–223.

    Google Scholar 

  15. Book, R., Jantzen, M., and Wrathall, C., Monadic Thue Systems, Theoret. Comput. Sci. 19, (1982), 231–251.

    Google Scholar 

  16. Book, R., and ÖDúnlaing, C., Thue Congruences and the Church-Rosser Property, Semigroup Forum 22, (1981), 367–379.

    Google Scholar 

  17. Book, R., and ÖDúnlaing, C., Testing for the Church-Rosser Property, Theoret. Comput. Sci. 16, (1981), 223–229.

    Google Scholar 

  18. Butzbach, P., Une famille de congruences de Thue pour lesquelles le Probléme de l'équivalence est décidable. Application à l'équivalence des grammaires séparés, in Nivat, M., (ed.) Automata, Languages, and Programming, North Holland (1973), 3–12.

    Google Scholar 

  19. Church, A., and Rosser, J.B., Some Properties of Conversion, Trans. Amer. Math. Soc. 39 (1936) 472–482.

    Google Scholar 

  20. Cochet, Y., Sur l'algěbricité des classes de certains congruences définies sur le monoide libre, Thése 3ème cycle, Rennes, 1971.

    Google Scholar 

  21. Cochet, Y., Church-Rosser Congruences on Free Semigroups, Colloq. Math. Sco. Janos Bolyai: Algebric Theory of Semigroups 20, (1976), 51–60.

    Google Scholar 

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

    Google Scholar 

  23. Dershowitz, N., Orderings for Term-Rewriting Systems, Theoret. Comput. Sci. 17 (1982) 279–301.

    Google Scholar 

  24. Dershowitz, N., and Manna, Z., Proving Termination with Multiset Orderings, Commun. Assoc. Comput. Mach. 22 (1979) 465–476.

    Google Scholar 

  25. Frougny, C., Une famille de langages algébriques congruential: les langages a nonterminaux séparés, Thése 3éme cycle, Rennes (1980).

    Google Scholar 

  26. Greendlinger, M., Dehn's Algorithm for the Word Problem, Comm. on Pure and Applied Math. 13 (1960) 67–83.

    Google Scholar 

  27. Hindley, R., An Abstract Form of the Church-Rosser Theorem I, J. of Symbolic Logic 34 (1969) 545–560.

    Google Scholar 

  28. Hindley, R., An Abstract Form of the Church-Rosser Theorem II: Applications, J. of Symbolic Logic 39 (1974) 1–21.

    Google Scholar 

  29. Huet, G., Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, J. Assoc. Comput. Mach. 27, (1980), 797–821.

    Google Scholar 

  30. Huet, G., and Oppen, D., Equations and Rewrite Rules, in R. Book, Ed., Formal Language Theory: Perspectives and Open Problems, Academic Press, (1980), 349–405.

    Google Scholar 

  31. Huet, G., A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm, J. Comput. Syst. Sci. 23 (1981) 11–21.

    Google Scholar 

  32. Jantzen, M., On a Special Monoid with a Single Defining Relation, Theoretical Computer Science 16, (1981), 61–73.

    Google Scholar 

  33. Jantzen, M., Semi-Thue Systems and Generalized Church-Rosser Properties, Proc. Fêtes des mots, Rouen, June (1982) 60–75.

    Google Scholar 

  34. Kapur, D., and Narendan, P., The Knuth-Bendic Completion Procedure and Thue Systems, Proc. 3rd Conf. on Found. of Software Techn. and Theoret. Comput. Sci., Bangalore, India, (1983) 363–385.

    Google Scholar 

  35. Kasincev, E.V., On the Word Problem for Special Semigroups, Math. USSR Izvestija, 13 (1979) 663–676

    Google Scholar 

  36. Knuth, D., and Bendix, P., Simple Word Problems in Universal Algebras, in J. Leech, Ed., Computational Problems in Abstract Algebra, Pergamon Press, (1970), 263–297.

    Google Scholar 

  37. Lallement, G., On Monoids Presented by a Single Relation, J. Algebra 32, (1974), 370–388.

    Google Scholar 

  38. Lallement, G., Semigroups and Combinatorial Applications, Wiley, 1979.

    Google Scholar 

  39. Lankford, D.S., A Unification Algorithm for Abelian Group Theory, Report MTP-1, Math. Dept., Louisiana Techn. Univ., Jan (1979).

    Google Scholar 

  40. Lankford, D.S., and Ballantine, A.M., Decision Procedures for Simple Equational Theories with Commutative Axioms: Complete Sets of Commutative Reductions, Report ATP-35, Depts. of Math. and Comp. Sci., Univ. of Texas at Austin, March (1977)

    Google Scholar 

  41. Markov, A., On the Impossibility of Certain Algorithms in the Theory of Associative Systems, Dokl. Akad. Nauk 55, (1947), 587–290; II, 58 (1947), 353–356 (in Russian).

    Google Scholar 

  42. A. Markov, Impossibility of Algorithms for Recognizing some Properties of Associative Systems, Dokl. Akad. Nauk SSSR 77 (1951) 953–956. A. Mostowski, Review of (41), J. Symbolic Logic 17 (1952) 151–152.

    Google Scholar 

  43. Metivier, Y., About the Rewriting Systems Produced by the Knuth-Bendix Completion Algorithm, Info. Proc. Letters 16 (1983) 31–34.

    Google Scholar 

  44. Muller, D.E., and Schupp, P.E., Groups, the Theory of Ends, and Context-free Languages, J. Comput. Syst. Sci. 26 (1983) 295–310.

    Google Scholar 

  45. Musser, D.R., On froving Inductive Properties of Abstract Data Types, 7th ACM Symp. on Principles of Programming Languages, Jan (1980) 154–162.

    Google Scholar 

  46. Narendran, P., The Undecidability of Preperfectness of Thue Systems, Abstracts, Amer. Math. Soc. 82T-68-435, 3, Oct. (1982), 546.

    Google Scholar 

  47. Narendran, P., and McNaughton, R., Church-Rosser Languages, in preparation.

    Google Scholar 

  48. Nelson, C.G., and Oppen, D.C., Fast Decision Algorithms Based on Congruence Closure, J. Assoc. Comput. Mach, to appear.

    Google Scholar 

  49. Newman, M.H.A., On Theories with a Combinatorial Definition of "Equivalence", Ann. Math. 43, (1943), 223–243.

    Google Scholar 

  50. Nivat, M. (with Benois, M.), Congruences Parfaites, Seminaire Dubreil, 25e Année, 1971–72, 7-01-09.

    Google Scholar 

  51. ÖDonnell, M., Computing in Systems Described by Equations, Lectures Notes in Computer Science 58 (1977).

    Google Scholar 

  52. ÖDúnlaing, C., Finite and Infinite Regular Thue Systems, Ph.D. dissertation, University of California at Santa Barbara, 1981.

    Google Scholar 

  53. ÖDúnlaing, C., Infinite Regular Thue Systems, Theoret. Comput. Sci. 25, (1983), 171–192.

    Google Scholar 

  54. ÖDúnlaing, C., Undecidable Questions of Thue Systems, Theoret. Comput. Sci. 23, (1983) 339–346.

    Google Scholar 

  55. Post, E., Recursive Unsolvability of a Problem of Thue, J. Symb. Logic 12, (1947), 1–11.

    Google Scholar 

  56. Potts, D., Remarks on an Example of Jantzen, Theoret. Comput. Sci., to appear.

    Google Scholar 

  57. Rosen, B., Tree-Manipulating systems and Church-Rosser Theorems, J. Assoc. Comput. Mach. 20, (1973), 160–187.

    Google Scholar 

  58. Senizergues, G., A New Class of C.F.L. for Which the Equivalence Problem is Decidable, Info. Proc. Letters 13, (1981), 30–34.

    Google Scholar 

  59. Squier, C., The Group of Units of a Monoid with a Church-Rosser Presentation, in preparation.

    Google Scholar 

  60. Squier, C., and Book, R. Almost All One-Rule Thue Systems Have Decidable Word Problems, in preparation.

    Google Scholar 

  61. Squier, C., and Wrathall, C., The Freiheitssatz for One-Relation Monoids, Proc. Amer. Math. Soc., to appear.

    Google Scholar 

  62. Steckel, M.E., Unification Algorithms for Artificial Intelligence Languages, Ph. D. Thesis, Carnegie-Mellon Univ. (1976).

    Google Scholar 

  63. Thue, A., Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln, Skr. Vid: Kristiania, I Mat. Naturv. Klasse 10, (1914), 34 pp.

    Google Scholar 

  64. Yasuhara, A., Some Non-Recursive Classes of Thue Systems with Solvable Word Problem, Zeitschr. f. Math. Logik und Grundlagen d. Math. 20 (1974) 121–132.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. P. Chytil V. Koubek

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jantzen, M. (1984). Thue systems and the Church-Rosser property. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030291

Download citation

  • DOI: https://doi.org/10.1007/BFb0030291

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13372-8

  • Online ISBN: 978-3-540-38929-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics