The unification problem for one relation Thue Systems

  • Christopher Lynch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1476)


We give an algorithm for the unification problem for a generalization of Thue Systems with one relation. The word problem is a special case. We show that in many cases this is a decision procedure with at most an exponential time bound. We conjecture that this is always a decision procedure.


Normal Form Word Problem General Unifier Decision Procedure Ground Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Adian. Definining relations and algorithmic problems for groups and semigroups. Trudy Matem. in-ta im. Steklova AN SSSR, 85, 1996 (Russian).Google Scholar
  2. 2.
    S. Adian. Transformations of words in a semigroup presented by a system of defining relations. Algebra i logika, 15(6),611–621, 1976 (Russian).MathSciNetGoogle Scholar
  3. 3.
    S. Adian, and G. Oganesian. On the word and divisibility problems in semigroups with a single defining relation. Izv. An. SSSR Ser. Matem., 42(2),219–225, 1978 (Russian).Google Scholar
  4. 4.
    J. Bouwsma. Semigroups Presented by a Single Relation. PhD dissertation at Pennsylvania State University, 1993.Google Scholar
  5. 5.
    C. Kirchner. Computing unification algorithms. In Proceedings of the First Symposium on Logic in Computer Science, Boston, 200–216, 1990.Google Scholar
  6. 6.
    G. Lallement. The word problem for Thue rewriting systems. In Spring School in Rewriting, ed. H. Comon and J. P. Jouannaud, Lecture Notes in Computer Science, 1994.Google Scholar
  7. 7.
    C. Lynch. Goal Directed Completion using SOUR Graphs. In Proceedings of the Eighth International Conference on Rewriting Techniques and Applications (RTA), Sitges, Spain, June 2–4, 1997.Google Scholar
  8. 8.
    W. Magnus. Das IdentitÄtsproblem für Gruppen mit einer definierenden Relation. Math Ann., 106,295–307, 1932.zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Y. Matisaevich. Simple examples of unsolvable associative calculi. Dokl. Akad. Nauk. SSSR, 173,1264–1266, 1967.MathSciNetGoogle Scholar
  10. 10.
    R. McNaughton. Well-behaved derivations in one-rule Semi-Thue Systems. Tech. Rep 95-15, Dept. of Computer Science, Rensselaer Polytechnic Unstitute, Troy, NY, Nov. 1995.Google Scholar
  11. 11.
    W. Savitch. How to make arbitrary grammars look like context-free grammars. SIAM Journal on Computing, 2(3),174–182, September 1973.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Christopher Lynch
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA

Personalised recommendations