# Thue system

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Thue_system&oldid=18164

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098