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arXiv · 1803.09511

Left-eigenvectors are certificates of the Orbit Problem

Steven de Oliveira·Virgile Prevosto·Peter Habermehl·Saddek Bensalem
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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.

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Steven de Oliveira, Virgile Prevosto, Peter Habermehl, Saddek Bensalem. 2018-03-26. Left-eigenvectors are certificates of the Orbit Problem. https://arxiv.org/abs/1803.09511

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