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arXiv · 1908.09051

A walk on max-plus algebra

Sennosuke Watanabe·Akiko Fukuda·Etsuo Segawa·Iwao Sato
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Abstract

Max-plus algebra is a kind of idempotent semiring over $\mathbb{R}_{\max}:=\mathbb{R}\cup\{-\infty\}$ with two operations $\oplus := \max$ and $\otimes := +$.In this paper, we introduce a new model of a walk on one dimensional lattice on $\mathbb{Z}$, as an analogue of the quantum walk, over the max-plus algebra and we call it max-plus walk. In the conventional quantum walk, the summation of the $\ell^2$-norm of the states over all the positions is a conserved quantity. In contrast, the summation of eigenvalues of state decision matrices is a conserved quantity in the max-plus walk.Moreover, spectral analysis on the total time evolution operator is also given.

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Sennosuke Watanabe, Akiko Fukuda, Etsuo Segawa, Iwao Sato. 2019-08-29. A walk on max-plus algebra. https://arxiv.org/abs/1908.09051

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