點燈遊戲計算與性質之研究 On sigma-game and sigma+-game

Date
2018
Authors
何昌翰
Ho, Chang-Han
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Abstract
無中文摘要
Lights out is a portable electronic game launched in 1995. Now it is divided into sigma-game and sigma^+-game in many literatures. In this thesis, the main purpose is to simplify the calculation of sigma-game and sigma^+-game. It was going to solve a set of equations to check whether the configuration is solvable and get its solution, but it must solve (mn)^2 variables. Lights-chasing is a method to decrease the numbers of variables to mn variables. Since traditional light-chasing method is not efficient and convenient, we give a new interpretation for light-chasing by Fibonacci polynomial and find its property, and then calculate their period in sigma-game and sigma^+-game in m x n grids respectively.
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Keywords
Fibonacci polynomail, lights out, Fibonacci polynomail, lights out
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