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}
}
• Published 2019
• Computer Science, Mathematics
• ArXiv
• 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

#### References

SHOWING 1-10 OF 48 REFERENCES
Solvability of Matrix-Exponential Equations
• Mathematics, Computer Science
• 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• 2016
• 2
• PDF
Membership Problem in GL(2, Z) Extended by Singular Matrices
• Mathematics, Computer Science
• MFCS
• 2017
• 10
• PDF
The orbit problem is decidable
• Mathematics, Computer Science
• STOC '80
• 1980
• 31
Products of matrices and recursively enumerable sets
• J. Honkala
• Mathematics, Computer Science
• J. Comput. Syst. Sci.
• 2015
• 4
Multiplicative equations over commuting matrices
• Mathematics, Computer Science
• SODA '96
• 1996
• 66