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Bell, PC and Potapov, I (2007) On the membership of invertible diagonal and scalar matrices. Theoretical Computer Science, 372 (1). 37 - 45. ISSN 0304-3975
On_the_Membership_of_Invertible_Diagonal_Matrices.pdf - Accepted Version
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1-s2.0-S030439750600870X-main.pdf - Published Version
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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 |
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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 |