Given two matrices, do they generate the free semigroup? The problem is open even for 2 × 2 integer matrices.

A related result states that it is undecidable whether a finitely many 3 × 3 integer matrices generate a free semigroup.

-- JeffreyShallit - 13 Jul 2011

Topic revision: r1 - 2011-07-13 - JeffreyShallit
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