It is undecidable whether the growth rate of a given bilinear system is 1 - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Linear Algebra and its Applications Year : 2022

It is undecidable whether the growth rate of a given bilinear system is 1

Abstract

We show that there exists no algorithm that decides for any bilinear system (B, v) if the growth rate of (B, v) is 1. This answers a question of Bui who showed that if the coefficients are positive the growth rate is computable (i.e., there is an algorithm that outputs the sequence of digits of the growth rate of (B, v)). Our proof is based on a reduction of the computation of the joint spectral radius of a set of matrices to the computation of the growth rate of a bilinear system. We also use our reduction to deduce that there exists no algorithm that approximates the growth rate of a bilinear system with relative accuracy ε in time polynomial in the size of the system and of ε. Our two results hold even if all the coefficients are nonnegative rationals.
Fichier principal
Vignette du fichier
2201.07630.pdf (166.27 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

lirmm-03973834 , version 1 (04-02-2023)

Identifiers

Cite

Matthieu Rosenfeld. It is undecidable whether the growth rate of a given bilinear system is 1. Linear Algebra and its Applications, 2022, 651, pp.131-143. ⟨10.1016/j.laa.2022.06.022⟩. ⟨lirmm-03973834⟩
25 View
8 Download

Altmetric

Share

Gmail Facebook X LinkedIn More