保持独立语言和关联码的映射-论文.pdf

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1、第27卷第2期纺织高校基础科学学报Vo1．27，No．22014年6月BASICSCIENCESJOURNALoFTEXTILEUNIVERSITIESJun．，2o14ArticleID：1006—8341(2014)02—0202-04MappingspreservesomeindependentlanguagesandintercodeLIULi，XUYing—wu(1．CollegeofMathematicsandComputerScience，YananUniversity，Yanan，Shaanxi716000，China；2．SchoolofScience，XianPolyt

2、echnicUniversity，Xian710048，China)Abstract：LetXbethefreemonoidonafinitealphabetX，thehomomorphismsfromXintoxisstudied．Someconditionswhichpreservepc—independentlanguages，pb—independentlan—guages，intercodeandP—languagesaregot．Thisworkisusefulforhomomorphismswhichpre—servelanguages．Keywords：homomorphi

3、sm；一independentlanguages；pb—independentlanguages；intercodeCLCnumber：O15Documentcode：A1IntroductionandpreliminariesLetXbeanonemptyfinitesetofletters，whichiscalledanalphabet．AnyfinitestringoverXiscalledaword．Thewordthatcontainsnoletteriscalledtheemptyword，denotedby1．ThesetofallwordsisdenotedhyX，whic

4、hisafreemonoidwithconcatenation．LetX==：X＼{1}．Foranyword训inX+，1etlg(w)bethenumberoflettersthatoccurinwandlg(1)一0．Anynon-emptysubsetofX+iscalledalanguage．AlanguagePiscalledaprefixcodeifPnPX：==[．AlanguageLiscalledacomma—freecodeifLnXLX===(2『．AmappinghfromXintoXsuchthath(xy)一(z)()forallx，yEXisahomomor

5、phism．Leth：XXbeahomomorphismand~CbeafamilyoflanguagesoverX．If(A)∈~-foreveryAEthenwesaythathpreservesJ-orhis~-preserving．Ifhisinjective，thatisif()一()implies—，thenhisamono—morphism[．Inthefollowingwereviewsomeresultswhichwillbeusedintherestofthepaper．Letw，∈X，thefollowingaresomeusefulpartialordersdefi

6、nedonXIs]．(1)叫≤ifandonlyif一wforsome≥1；Receiveddate：2013—10-14Foundationitem：SupportedbyNationalNaturalScienceFoundationofChina(11226038)；SpecializedResearchFundofEducationDepartmentofShaanxiProvincialGovermment(11JKO499)Correspondingauthor：XUYing-wu(1965一)，male，anativeofXian。Shaanxiprovince。associ

7、ateprofessorofXianPoly—technicUniversity．E-mail：xuyingwul13@163．corn第2期Mappingspreservesomeindependentlanguagesandintercode203(2)叫≤6ifandonlyif一forsomex，yEX．Definition1E]AlanguageLXiscalledanindependentlanguagewi