EQUATIONS IN FREE INVERSE MONOIDS-Reference-Cited by-同舟云学术

EQUATIONS IN FREE INVERSE MONOIDS

Published:2007-06 Issue:04 Volume:17 Page:761-795
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

DEIS TIMOTHY¹,MEAKIN JOHN²,SÉNIZERGUES G.³

Affiliation:

1. Department of Mathematics, University of Wisconsin, Platteville, WI 53818, USA

2. Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA

3. Department of Computer Science, Bordeaux 1 University, 351, Cours de la Libération F-33405 Talence Cedex, France

Abstract

It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding system of equations in the associated free group in an obvious way, but solutions to systems of equations in free groups do not necessarily lift to solutions in free inverse monoids. In this paper, we show that the problem of determining whether a solution to a finite system of equations in a free group can be extended to a solution of the corresponding system in the associated free inverse monoid is decidable. We are able to use this to solve the consistency problem for certain classes of single-variable equations in free inverse monoids.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196707003755

Reference26 articles.

1. One-variable equations in free groups

2. Unification of Concept Terms in Description Logics

3. CONJUGACY IN FREE INVERSE MONOIDS

4. PRODUCTS OF COMMUTATORS AND PRODUCTS OF SQUARES IN A FREE GROUP

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