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1、1、IntroductionLights,whicharepopularinaveryinterestinggameontheInternetinrecentyears,aredefinedasfollows:Inannxngridboard,everysquarehavetwostates:white(open)andblack(closed).Whenyouclickonanyoneofthesesquareswiththemouse,theboxandallitsadjacentboxeschangestates.Namely,thebl
2、ackboxesbecomethewhiteboxes.Attheedgeoftheboard,theboxcan'thavethefouradjacentboxes.Therefore,weonlyconsiderthoseexistedboxes.usingthemethodofalgebraandmathematicalmodelingtogivethemathematicalmodeling,basedonthelinearequationsoffinitefield,ZhouHaogaveallthesolutionsfortheca
3、seof5.Furthermore,heusedthe"Classification"methodofalgebratogivetheintuitivedescriptionoffourequivalenceclassesofthegamesothattheplayerscanimmediatelydeterminewhichtypethe“mess”is.Ofcourse,beforeZhouHao,scholarsaddedthecontrolvectorforaproblemofPRGgameonasimilarlightandanaly
4、zedandprovedtheproblembyamathematicalmodel.Afterthat,researchersmadegeneralpromotionforacontrolproblemintheRPGgameandgiveamorecomprehensivesolution.Furthermore,someforeignscholarsusedthedynamicprogrammingmethodstoproveavarietyofmatrixreconstructionproblemsandalsoprovedsomeco
5、mplexresultsonreconstructingneighborhoodbinarymatrix.ThemathematicalknowledgethatZhouHaousetobuildthemodelonthecontrolstateissuesoflightsisrelativelycomplicated.Afterthat,scholarsmadegeneralpromotionfortheZhouHao'smathematicalmodelinordertobeaccepted.However,ifthecontrolvari
6、ableislarger,solvingtheeffectivematrix“Q”andthecombination“»+必=兀］Q}+x2-Q2+•••+xr(2rnismorecomplicated.IfswisetousetheprogramormathematicalSoftwaresuchasMathematic.2、Thelightissuewhenn=9Fortheabovedefinedrulesofthegame,westudythefollowingtwoissues:Whenn=9,theboard'sinitialsta
7、teisamess:partoftheboxesiswhiteandpartoftheboxesisblack.Ifyoucontinuetoclickonit,whetherthereisawaytomakethemesseventuallybecomecompletelywhiteorcompletelyblack.Suchlightissuesarecontrolissues・Becauselightonlyhaveopenedorclosedstates,wecanmakethedefinitionsuchasbinaryvectort
8、ostudytheissue,andultimatelytranslateitintotheexisteneeoflinearequationsona
