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Corpus ID: 67855628

Decidability of the Mortality Problem: from multiplicative matrix equations to linear recurrence sequences and beyond

@article{Bell2019DecidabilityOT,
title={Decidability of the Mortality Problem: from multiplicative matrix equations to linear recurrence sequences and beyond},
author={Paul Bell and I. Potapov and Pavel Semukhin},
journal={ArXiv},
year={2019},
volume={abs/1902.10188}
}

We consider the following variant of the Mortality Problem: given $k\times k$ matrices $A_1, A_2, \dots,A_{t}$, does there exist nonnegative integers $m_1, m_2, \dots,m_t$ such that the product $A_1^{m_1} A_2^{m_2} \cdots A_{t}^{m_{t}}$ is equal to the zero matrix? It is known that this problem is decidable when $t \leq 2$ for matrices over algebraic numbers but becomes undecidable for sufficiently large $t$ and $k$ even for integral matrices.
In this paper, we prove the first decidability… CONTINUE READING