A linear bound on the k-rendezvous time for primitive sets of NZ matrices

03/25/2019
by   Umer Azfar, et al.
0

A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries (the k-RT). We prove that this value is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata. We then report numerical results comparing our upper bound on the k-RT with heuristic approximation methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/17/2018

The Synchronizing Probability Function for Primitive Sets of Matrices

Motivated by recent results relating synchronizing automata and primitiv...
research
12/07/2017

Sets of Stochastic Matrices with Converging Products: Bounds and Complexity

An SIA matrix is a stochastic matrix whose sequence of powers converges ...
research
07/09/2019

A method for computing the Perron-Frobenius root for primitive matrices

For a nonnegative matrix, the eigenvalue with the maximum magnitude or P...
research
07/07/2022

Constructions and restrictions for balanced splittable Hadamard matrices

A Hadamard matrix is balanced splittable if some subset of its rows has ...
research
05/17/2018

On randomized generation of slowly synchronizing automata

Motivated by the randomized generation of slowly synchronizing automata,...
research
01/22/2019

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete

Checking whether two pushdown automata with restricted silent actions ar...
research
08/16/2021

Approximating the Permanent with Deep Rejection Sampling

We present a randomized approximation scheme for the permanent of a matr...

Please sign up or login with your details

Forgot password? Click here to reset