Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X and Potapov, I (2008) On undecidability bounds for matrix decision problems. Theoretical Computer Science, 391 (1-2). 3 - 13.

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Abstract

In this paper we consider several reachability problems such as vector reachability, membership in matrix semigroups and reachability problems in piecewise linear maps. Since all of these questions are undecidable in general, we work on lowering the bounds for undecidability. In particular, we show an elementary proof of undecidability of the reachability problem for a set of 5 two-dimensional affine transformations. Then, using a modified version of a standard technique, we also prove that the vector reachability problem is undecidable for two (rational) matrices in dimension 11. The above result can be used to show that the system of piecewise linear functions of dimension 12 with only two intervals has an undecidable set-to-point reachability problem. We also show that the “zero in the upper right corner” problem is undecidable for two integral matrices of dimension 18 lowering the bound from 23.

Item Type: Article
Additional Information: The final version of this article and all information related to it, including copyrights, can be found on the publisher website. The Journal also allows for Open Archive, which allows download of the published version after 4 years. Information can be found at; https://www.elsevier.com/open-access/open-archive
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 17 Jul 2022 09:37
Last Modified: 17 Jul 2022 09:37
URI: https://eprints.keele.ac.uk/id/eprint/11103

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