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• W2969439350 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." @default.
• W2969439350 created "2019-08-29" @default.
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• W2969439350 date "2019-08-23" @default.
• W2969439350 modified "2023-09-27" @default.
• W2969439350 title "A walk on max-plus algebra" @default.
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