DeepAI

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

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.

05/19/2020

### Growth of bilinear maps

For a bilinear map *:ℝ^d×ℝ^d→ℝ^d of nonnegative coefficients and a vecto...
03/19/2020

### On Bilinear Time Domain Identification

The Loewner framework (LF) in combination with Volterra series (VS) offe...
01/15/2014

### A Bilinear Programming Approach for Multiagent Planning

Multiagent planning and coordination problems are common and known to be...
10/31/2019

### The missing link between the output and the H_2-norm of bilinear systems

In this paper, we prove several new results that give new insights to bi...
02/04/2021

### Decoding Reed-Solomon codes by solving a bilinear system with a Gröbner basis approach

Decoding a Reed-Solomon code can be modeled by a bilinear system which c...
06/24/2021

### Guessing Based on Compressed Side Information

A source sequence is to be guessed with some fidelity based on a rate-li...
06/16/2020

### On the Complexity of Solving Generic Over-determined Bilinear Systems

In this paper, we study the complexity of solving generic over-determine...