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On Matrix Powering in Low Dimensions

Authors Esther Galby, Joël Ouaknine, James Worrell

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Esther Galby
Joël Ouaknine
James Worrell

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Esther Galby, Joël Ouaknine, and James Worrell. On Matrix Powering in Low Dimensions. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 329-340, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.STACS.2015.329

Abstract

We investigate the Matrix Powering Positivity Problem, PosMatPow: given an m X m square integer matrix M, a linear function f: Z^{m X m} -> Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(M^n) \geq 0. We show that for fixed dimensions m of 2 and 3, this problem is decidable in polynomial time.

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Keywords
  • matrix powering
  • complexity
  • Baker's theorem

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