Abstract
We consider the problem of naming the variables of a term so that it becomes equivalent to a given term when left distributivity is assumed, and describe an algorithm for solving this question using conjugacy in a free group. The correctness of the algorithm is reduced to a conjecture involving some particular words. A skew version of the conjecture is established.
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References
R. H. Crowell & R. H. Fox Knot Theory, Blaisdell Publ. Comp., (1963)
P. Dehornoy, Free distributive groupoids, Journal of Pure and Applied Algebra, 61 (1989) 123–146.
-Problème de mots dans les gerbes libres, Theor. Comp. Sc., 94 (1992) 199–213.
-, A canonical ordering for tree distributive magmas, Proc. of the AMS, to appear.
-, Braid Groups and Left Distributive Operations, preprint (1992).
G. Huet & D. Oppen, Equations and Rewrite Rules: a survey, in R. Book, ed., Formal Languages: Perspectives and Open Problems, Academic Press (1980).
R. Laver, The left distributive law and the freeness of an algebra of elementary embeddings, Advances in Mathematics, 91–2 (1992) 209–231.
-, A division algorithm for the free left distributive algebra, Proc. Helsinki 1990 ASL Meeting to appear.
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© 1993 Springer-Verlag Berlin Heidelberg
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Dehornoy, P. (1993). The naming problem for left distributivity. In: Abdulrab, H., Pécuchet, JP. (eds) Word Equations and Related Topics. IWWERT 1991. Lecture Notes in Computer Science, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56730-5_31
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DOI: https://doi.org/10.1007/3-540-56730-5_31
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Online ISBN: 978-3-540-47636-8
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