On the membership of invertible diagonal and scalar matrices

Bell

doi:10.1016/j.tcs.2006.11.011

On the membership of invertible diagonal and scalar matrices

Bell

Authors

Paul Bell p.c.bell@keele.ac.uk

Abstract

In this paper, we consider decidability questions that are related to the membership problem in matrix semigroups. In particular, we consider the membership of a given invertible diagonal matrix in a matrix semigroup and then a scalar matrix, which has a separate geometric interpretation. Both problems have been open for any dimensions and are shown to be undecidable in dimension 4 with integral matrices by a reduction of the Post Correspondence Problem (PCP). Although the idea of PCP reduction is standard for such problems, we suggest a new coding technique to cover the case of diagonal matrices.

Acceptance Date	Nov 19, 2006
Publication Date	Mar 6, 2007
Journal	Theoretical Computer Science
Print ISSN	0304-3975
Publisher	Elsevier
Pages	37 - 45
DOI	https://doi.org/10.1016/j.tcs.2006.11.011
Publisher URL	https://www.sciencedirect.com/science/article/pii/S030439750600870X?via%3Dihub