(V,R)-language,(V,R)-semigroup,interconnection nework,graph theory

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1、(V,R)-Œ+!(V,R)-Šó!pëä†ãØÚóˆ«ëÏpëä(V,R)-semigroup,(V,R)-language,interconnectionKãëÏpëänetworkandgraphtheory(劗–¯Ì•“°§IK•HaizhongShiJJIIJIÜ“‰ŒÆêƆÚOÆCollegeofMathematicsandStatistics11•
23•NorthwestNormalUniversityˆ£¶w«'4òÑÚówwwJJJjjjˆ«ëÏpëäKãëÏpëä(劕—ÄVg•¯K–

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23•ˆ£¶w«'4òÑÚóReportContentˆ«ëÏpëäKãëÏpëä(劕—BasicConcepts•Problems–¯Ì••AnswerstoProblemsIK••ConclusionJJIIJI~Thank-you13•
23•ˆ£¶w«'4òÑÄÄÄVVVggg2014c§“°§²L29cg•JÑü‡Vgµ(V,R)-Œ+Ú(V,R)-Šó(V,R)-ŒŒŒ+++V´˜‡i1L§FV´VþgdŒ+§R´FV˜‡f8§ÚóKFRF´Fþ

3、˜‡nŽ§-I=FRF§=(II)[ˆ«ëÏpëäVVVRVVIRRRKãëÏpëä1FV´FVþReesÓ{§K¡ûŒ+FV=IR•(V,R)-Œ+.FVƒ•¡(劕i§ïÄi

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5、Ü.—(V,R)-ŠŠŠóóóé?ÛŠóL§Ñki1LV§¦LF.é/ªŠóLkz0dÄN–¯Ì•VXµáŠ(Šó§þe©k'Šó§þe©Ã'Šó9KŠó.AOIK•/§R´F˜‡f8§FFRF¡•(V,R)-Šó.VVVVJJIIFVFVRFV=ff2FVjf(IR)2FV=IR;f(IR)6=

6、0g:JI14•
23•[[[{{{üüüãããÚÚÚ[[[îîî‚‚‚kkk•••ãã㈣G=(V;E)´äkº:8VÚ>8E[{üã£Ã•>Œ±k‚¤¶D=(V;A)´äkº:8VÚl8A[î‚k•ã(ò1>Œ¶w«±k‚).3dÄ:þ§k‡ã§‘ÅãVg.'4pppëëëäääòÑpëä´AÏ[{üã½[î‚k•ã.BasicConceptsIn2014,afterconsideringfor29years,HaizhongShiproposedtwoconcepts:(V;R)semigroupand(V;R)lan

7、guage.Úó(V,R)-semigroupˆ«ëÏpëäKãëÏpëäVisanalphabet,FVisafreesemigrouponV.LetRbeasubsetofFV,then(åŠFRFisanideaofF.LetI=FRF§=(II)[1beaRees—VVVRVVIRRRFVcongruenceofFV,thenthesemigroupFV=IRiscalledasa(V;R)semigroup.TheelementofFVisalsocalledasword,andthestudyofthecombin

8、atorial–¯Ì•propertiesofwordiscalledasthecombinationofword.IK•(V,R)-languageJJIIForanylanguageL,thereisanalphabetVsuchthatLF.Ac-VcordingtoChomsky,formallanguageLcanclassifiedintofourtypes:phraseJIstructurelanguage,contextsensitivelanguage,contextfreelanguageandregu-15•
23•larlang

9、uage.Especially,LetRbeasubsetofF,thenFFRFiscalledVVVVˆ£as(V,R)-Language;furthermore,wehave,¶w«FVFVRFV=ff2FVjf(IR)2FV=IR;f(IR)6=0g:'4òÑÚóˆ«ëÏpëäPseudosimplegraphandpseudostrictdigraphKãëÏpëä(åŠG=(V;E)isapseudosimplegraph(mayhaveloopsbutdoesnothave—twoofitsedgesjoin

10、thesamepairofvertices)withvertexsetVande