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Article Dans Une Revue RAIRO - Theoretical Informatics and Applications (RAIRO: ITA) Année : 2005

Some decision problems on integer matrices

Résumé

Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs to a given finitely generated semigroup.

Dates et versions

hal-00158281 , version 1 (28-06-2007)

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Christian Choffrut, Juhani Karhumaki. Some decision problems on integer matrices. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2005, 39, pp.125-131. ⟨10.1051/ita:2005007⟩. ⟨hal-00158281⟩
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