郭君逸Guo, Jun-Yi何昌翰Ho, Chang-Han2019-09-052018-07-312019-09-052018http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G060540007S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101582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.Fibonacci polynomaillights outFibonacci polynomaillights out