Solvability of Matrix-Exponential Equations

@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}
}
  • J. Ouaknine, A. Pouly, +1 author J. Worrell
  • Published 2016
  • Mathematics, Computer Science
  • 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
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