# Some decision problems on integer matrices

Christian Choffrut; Juhani Karhumäki

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

- Volume: 39, Issue: 1, page 125-131
- ISSN: 0988-3754

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topChoffrut, Christian, and Karhumäki, Juhani. "Some decision problems on integer matrices." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 125-131. <http://eudml.org/doc/244723>.

@article{Choffrut2005,

abstract = {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.},

author = {Choffrut, Christian, Karhumäki, Juhani},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {integer matrices; decision problems; semigroups of matrices; finitely generated semigroups; recursive decidability},

language = {eng},

number = {1},

pages = {125-131},

publisher = {EDP-Sciences},

title = {Some decision problems on integer matrices},

url = {http://eudml.org/doc/244723},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Choffrut, Christian

AU - Karhumäki, Juhani

TI - Some decision problems on integer matrices

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 1

SP - 125

EP - 131

AB - 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.

LA - eng

KW - integer matrices; decision problems; semigroups of matrices; finitely generated semigroups; recursive decidability

UR - http://eudml.org/doc/244723

ER -

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