English

Left-eigenvectors are certificates of the Orbit Problem

Logic in Computer Science 2018-03-28 v1

Abstract

This paper investigates the connexion between the Kannan-Lipton Orbit Problem and the polynomial invariant generator algorithm PILA based on eigenvectors computation. Namely, we reduce the problem of generating linear and polynomial certificates of non-reachability for the Orbit Problem for linear transformations with rational coefficients to the generalized eigenvector problem. Also, we prove the existence of such certificates for any transformation with integer coefficients, which is not the case with rational coefficients.

Cite

@article{arxiv.1803.09511,
  title  = {Left-eigenvectors are certificates of the Orbit Problem},
  author = {Steven de Oliveira and Virgile Prevosto and Peter Habermehl and Saddek Bensalem},
  journal= {arXiv preprint arXiv:1803.09511},
  year   = {2018}
}

Comments

12 pages + references, submutted to ICALP 2018

R2 v1 2026-06-23T01:04:58.824Z