A1 Refereed original research article in a scientific journal
On the undecidability of freeness of matrix semigroups
Authors: Cassaigne J, Harju T, Karhumaki J
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Publication year: 1999
Journal:International Journal of Algebra and Computation
Journal name in sourceINTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Journal acronym: INT J ALGEBR COMPUT
Volume: 9
Issue: 3-4
First page : 295
Last page: 305
Number of pages: 11
ISSN: 0218-1967
DOI: https://doi.org/10.1142/S0218196799000199
Abstract
We slightly improve the result of Klarner, Birget and Satterfield, showing that the freeness of finitely presented multiplicative semigroups of 3 x 3 matrices over N is undecidable even for triangular matrices. This is achieved by proving a new variant of Post correspondence problem. We also consider the freeness problem for 2 x 2 matrices. On the one hand, we show that it cannot le proved undecidable using the above methods which work in higher dimensions, and, on the other hand, we give some evidence that its decidability, if so, is also a challenging problem.
We slightly improve the result of Klarner, Birget and Satterfield, showing that the freeness of finitely presented multiplicative semigroups of 3 x 3 matrices over N is undecidable even for triangular matrices. This is achieved by proving a new variant of Post correspondence problem. We also consider the freeness problem for 2 x 2 matrices. On the one hand, we show that it cannot le proved undecidable using the above methods which work in higher dimensions, and, on the other hand, we give some evidence that its decidability, if so, is also a challenging problem.
UTU Research Portal