A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Undecidability in matrices over Laurent polynomials\
Tekijät: Halava V, Harju T
Kustantaja: ACADEMIC PRESS INC ELSEVIER SCIENCE
Julkaisuvuosi: 2004
Lehti: Advances in Applied Mathematics
Tietokannassa oleva lehden nimi: ADVANCES IN APPLIED MATHEMATICS
Lehden akronyymi: ADV APPL MATH
Vuosikerta: 33
Numero: 4
Aloitussivu: 747
Lopetussivu: 752
Sivujen määrä: 6
ISSN: 0196-8858
DOI: https://doi.org/10.1016/j.aam.2004.04.002
Tiivistelmä
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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