Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set
Computational Complexity
2022-08-08 v2
Abstract
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for every orbit of a rational matrix to escape a compact semialgebraic set defined over rational data. Our bound is doubly exponential in the ambient dimension, singly exponential in the degrees of the polynomials used to define the semialgebraic set, and singly exponential in the bitsize of the coefficients of these polynomials and the bitsize of the matrix entries. We show that our bound is tight by providing a matching lower bound.
Cite
@article{arxiv.2207.01550,
title = {Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set},
author = {Julian D'Costa and Engel Lefaucheux and Eike Neumann and Joël Ouaknine and James Worrell},
journal= {arXiv preprint arXiv:2207.01550},
year = {2022}
}