On Reachability Problems for Low-Dimensional Matrix Semigroups
Computational Complexity
2019-04-30 v3 Formal Languages and Automata Theory
Abstract
We consider the Membership and the Half-Space Reachability problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for finitely generated sub-semigroups of the Heisenberg group over rational numbers. Furthermore, we prove two decidability results for the Half-Space Reachability Problem. Namely, we show that this problem is decidable for sub-semigroups of and of the Heisenberg group over rational numbers.
Keywords
Cite
@article{arxiv.1902.09597,
title = {On Reachability Problems for Low-Dimensional Matrix Semigroups},
author = {Thomas Colcombet and Joël Ouaknine and Pavel Semukhin and James Worrell},
journal= {arXiv preprint arXiv:1902.09597},
year = {2019}
}
Comments
Full version of the paper submitted to ICALP 2019