@article{Ouaknine2016SolvabilityOM,
title={Solvability of Matrix-Exponential Equations},
author={J. Ouaknine and A. Pouly and J. S. Pinto and J. Worrell},
journal={2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
year={2016},
pages={1-9}
}

2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

We consider a continuous analogue of (Babai et al. 1996)’s and (Cai et al. 2000)’s problem of solving multiplicative matrix equations. Given k + 1 square matrices A1,…, Ak, C, all of the same dimension, whose entries are real algebraic, we examine the problem of deciding whether there exist non-negative reals t1, …, tk such that\begin{equation*} \prod\limits_{i = 1}^k {\exp ({A_i}{t_i})} = C. \end{equation*}We show that this problem is undecidable in general, but decidable under the assumption… CONTINUE READING