Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X and Potapov, I (2007) On the membership of invertible diagonal and scalar matrices. Theoretical Computer Science, 372 (1). 37 - 45.

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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.

Item Type: Article
Additional Information: The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 25 Jul 2022 12:32
Last Modified: 25 Jul 2022 12:32
URI: https://eprints.keele.ac.uk/id/eprint/11104

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