Extended finite automata and decision problems for matrix semigroups

Özlem Salehi; Ahmet Celal Cem Say

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arXiv · 1807.05516

Extended finite automata and decision problems for matrix semigroups

Özlem Salehi·Ahmet Celal Cem Say

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Abstract

We make a connection between the subgroup membership and identity problems for matrix groups and extended finite automata. We provide an alternative proof for the decidability of the subgroup membership problem for $ 2 \times 2 $ integer matrices. We show that the emptiness problem for extended finite automata over $ 4 \times 4 $ integer matrix semigroups is undecidable. We prove that the decidability of the universe problem for extended finite automata is a sufficient condition for the decidability of the subgroup membership and identity problems.

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Özlem Salehi, Ahmet Celal Cem Say. 2018-07-15. Extended finite automata and decision problems for matrix semigroups. https://arxiv.org/abs/1807.05516

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