On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond

@inproceedings{Bell2019OnTM,
title={On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond},
author={Paul Bell and I. Potapov and Pavel Semukhin},
booktitle={MFCS},
year={2019}
}

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