TY - JOUR
T1 - A walk on max-plus algebra
AU - Watanabe, Sennosuke
AU - Fukuda, Akiko
AU - Segawa, Etsuo
AU - Sato, Iwao
PY - 2020/8/1
Y1 - 2020/8/1
N2 - Max-plus algebra is a kind of idempotent semiring over Rmax:=R∪{−∞} with two operations ⊕:=max and ⊗:=+. In this paper, we introduce a new model of a walk on one dimensional lattice on 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 ℓ2-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.
AB - Max-plus algebra is a kind of idempotent semiring over Rmax:=R∪{−∞} with two operations ⊕:=max and ⊗:=+. In this paper, we introduce a new model of a walk on one dimensional lattice on 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 ℓ2-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.
KW - Directed graph
KW - Max-plus algebra
KW - Quantum walk
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U2 - 10.1016/j.laa.2020.03.025
DO - 10.1016/j.laa.2020.03.025
M3 - Article
AN - SCOPUS:85082165633
VL - 598
SP - 29
EP - 48
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -