Thue system

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An associative calculus, named after A. Thue, who first formulated the problem of recognizing equality of words in associative systems (the Thue problem, see [1]). If in a given Thue system the only admissible substitutions are taken to be substitutions of right-hand sides of relations into the left-hand sides (that is, the reverse substitutions are excluded), then one obtains a Thue semi-system (or semi-Thue system, or system of substitutions). These systems in fact coincide with local canonical Post systems. Every Thue system can be regarded as a Thue semi-system, but the converse is false.


[1] A. Thue, "Probleme über Veränderungen von Zeichenreihen nach gegebener Regeln" Kra. Vidensk. Selsk. Skrifter. , 10 (1914)
[2] A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russian)
How to Cite This Entry:
Thue system. S.I. Adyan (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098