On the undecidability of freeness of matrix semigroups



: Cassaigne J, Harju T, Karhumaki J

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: 1999

International Journal of Algebra and Computation

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

: INT J ALGEBR COMPUT

: 9

: 3-4

: 295

: 305

: 11

: 0218-1967

DOI: https://doi.org/10.1142/S0218196799000199


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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