A1 Refereed original research article in a scientific journal
Undecidability in matrices over Laurent polynomials\
Authors: Halava V, Harju T
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2004
Journal:: Advances in Applied Mathematics
Journal name in source: ADVANCES IN APPLIED MATHEMATICS
Journal acronym: ADV APPL MATH
Volume: 33
Issue: 4
First page : 747
Last page: 752
Number of pages: 6
ISSN: 0196-8858
DOI: https://doi.org/10.1016/j.aam.2004.04.002
Abstract
We show that it is undecidable for finite sets S of upper triangular (4 x 4)-matrices over Z[x, x(-1)] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer weighted finite automata by matrices over Laurent polynomials. (C) 2004 Elsevier Inc. All rights reserved.
We show that it is undecidable for finite sets S of upper triangular (4 x 4)-matrices over Z[x, x(-1)] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer weighted finite automata by matrices over Laurent polynomials. (C) 2004 Elsevier Inc. All rights reserved.
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