布尔代数和布尔代数上的自动机

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1、AbstractBooleanalgebraiSallimportantmathematicaltoolusedinthe蠡eldofinformationscience+Itcontortsabundantcontentandiswl＆lyapplied．Inthisthesis．wefirstcompilesomeutilizablepartsofBooleanalgebratheory,whichare德efundamentalobjects：thestructureofBooleanalgebra，theBooleanfunctions，theBoolean

2、equations，andtheBooleanmatrices。ThenWestudythesystemoffixed．pointBooleanequations．Somenewresultsarederivedasfollowing：1．Wedeterminethegeneralrepmductlvesolutionsofthesystemoffixed-pointBooleanequationsandpresentthenecessaryandsufficientconditionsforittohaveasingularsolution[theorem2．1～

3、2．2]．2+W毫provethat，when．eachcolumnofAisorthogonal，thesystemoffixed-pointBooleanequations一1—1A

4、i

5、=l；

6、{l{＼xn)Lx》hasthesamesetoforthogonalsolutionsandoforthonormalsolutionsasthelinearBooleanequationa{lx}+t·‘+娃础善#=0·Thenwereducethetotalnumberoforthonormalsolutionsofthesystemoffixed-pointBo

7、oleanequation删=Ⅳ[theorem2．3～2．41。AutomatatheoryisallimportantbranchofcomputersciencetheoryItiswidelyappliedinmanyfields，suchascommunication，detection，biology,neurology,psychology,intelfigence，economy,andsociology．讯leresearchonitiscloselyrelatedtothedevelopmentofcomputersottwareandhardw

8、al'e。Inthisthesis，westudythenon-invertiblelinearfiniteautonomousautomataandderivethefollowingnewresults：1．Aformulaisgiventocountthenumberofthenodesofevery＼●●；；，；J●nh卜呼＼、，；；；；●●／■；％，j弋levelinadown-orientedtreeofaDautonomousautomaton．Thenanecessaryandsufficientconditionispresentedformegr

9、aphofartautonomousautomatontobeallexact-equibranchdown-orientedtree[theorem3．2～3．3J．2．SomenecessaryandSUfficientconditionsarepresentedforanautonomousautomatontobeacircle-treeautonomousautomaton[theorem3．7～3．8J．3．111egraphstructureofsomenon-invertibleautonomousautomataiSdiscussedinregul

10、arspace，orthogonalspace，andorthonormalspacerespectively．Somenewresultsarederived[theorem3．10～3．1a]．BOOleanringhasmuchdistinctiredifferencefromdomaininthatBooleanringhaszerodivisors．Thedifferencegivesrisetogreatdifficultinresearchinglinearcharacteristic．臃explorethegraphstructureofthea