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On the undecidability of freeness of matrix semigroups
Tekijät: Cassaigne J, Harju T, Karhumaki J
Kustantaja: WORLD SCIENTIFIC PUBL CO PTE LTD
Julkaisuvuosi: 1999
Lehti:International Journal of Algebra and Computation
Tietokannassa oleva lehden nimiINTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Lehden akronyymi: INT J ALGEBR COMPUT
Vuosikerta: 9
Numero: 3-4
Aloitussivu: 295
Lopetussivu: 305
Sivujen määrä: 11
ISSN: 0218-1967
DOI: https://doi.org/10.1142/S0218196799000199
Tiivistelmä
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.
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