Abstract
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.
This work was supported by NSF grant number CCR-9712388 and partially done while visiting INRIA Lorraine and CRIN.
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References
S. Adian. Definining relations and algorithmic problems for groups and semigroups. Trudy Matem. in-ta im. Steklova AN SSSR, 85, 1996 (Russian).
S. Adian. Transformations of words in a semigroup presented by a system of defining relations. Algebra i logika, 15(6),611–621, 1976 (Russian).
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).
J. Bouwsma. Semigroups Presented by a Single Relation. PhD dissertation at Pennsylvania State University, 1993.
C. Kirchner. Computing unification algorithms. In Proceedings of the First Symposium on Logic in Computer Science, Boston, 200–216, 1990.
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.
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.
W. Magnus. Das IdentitÄtsproblem für Gruppen mit einer definierenden Relation. Math Ann., 106,295–307, 1932.
Y. Matisaevich. Simple examples of unsolvable associative calculi. Dokl. Akad. Nauk. SSSR, 173,1264–1266, 1967.
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.
W. Savitch. How to make arbitrary grammars look like context-free grammars. SIAM Journal on Computing, 2(3),174–182, September 1973.
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© 1998 Springer-Verlag Berlin Heidelberg
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Lynch, C. (1998). The unification problem for one relation Thue Systems. In: Calmet, J., Plaza, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 1998. Lecture Notes in Computer Science, vol 1476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055913
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DOI: https://doi.org/10.1007/BFb0055913
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