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Bell, Pavel Semukhin","submitted_at":"2019-02-26T20:03:52Z","abstract_excerpt":"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.\n  In this paper, we prove the first decidability results for $t>2$. 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