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非0非1型逻辑方程与相关逻辑方程的解集关系及其应用（英文）.docx

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非0非1型逻辑方程与相关逻辑方程的解集关系及其应用（英文） Introduction Logicequationsarecriticalinthefieldofcomputerscienceandmathematics.Companies,governments,andindividualsrelyonlogicequationstotestsoftware,controlsystems,andothercriticalapplications.Manytypesoflogicequationsexist,andamongthemostimportantisthenon-zeronon-onelogicequation.Itisessentialtounderstandtherelationshipbetweennon-zeronon-onelogicequationsandrelatedlogicequationsandtoexploretheirapplicationsinsolvingproblems.Thispaperaimstoexploretherelationshipbetweennon-zeronon-onelogicequationsandrelatedlogicequationsandtheapplicationoftheseequationsinsolvingproblems. Non-zeroNon-oneLogicEquation Anon-zeronon-onelogicequationisanequationthatisneither0nor1.Inotherwords,itisanequationthatisneithertruenorfalse.Thegeneralformulaforthenon-zeronon-onelogicequationis: (1-x)*f(x)=0 wheref(x)issomelogicalfunction,andxiseithertrueorfalse.Theequationcanalsobewrittenas: f(x)=0/(1-x) wherexisalsoeithertrueorfalse. Thenon-zeronon-onelogicequationhasseveraluniqueproperties,including: 1.Theequationissymmetric:iff(x)isequaltof(y),then1-xisequalto1-y. 2.Theequationisnon-commutative:ifx*yisequaltoy*x,thenf(x)isalwaysequaltof(y). 3.Theequationisassociative:iff(x)isequaltof(y)andf(y)isequaltof(z),thenf(x)isequaltof(z). ApplicationofNon-zeroNon-oneLogicEquation Thenon-zeronon-onelogicequationhasvariousapplicationsindifferentfields,includingmathematics,engineering,andcomputerscience.Oneofthecriticalapplicationsofnon-zeronon-onelogicequationsisincryptography.Incryptography,non-zeronon-oneequationsareusedtocreateencryptionalgorithmsthatensurethatdataistransmittedsecurely. Anotherapplicationofnon-zeronon-onelogicequationsisinthedesignanddevelopmentofcontrolsystems.Controlsystemsareessentialinmanufacturingandproductionprocesses,andnon-zeronon-onelogicequationsareusedtodesigncontrolsystemsthataremorerobust,efficient,andeffective. RelationshipbetweenNon-zeroNon-oneLogicEquation Non-zeronon-onelogicequationsarecloselyrelatedtorelatedlogicequations,includingtheB