PDF-SIAMJ.COMPUT.Vol.9,No.1,February19801980SocietyforIndustrialandApplied

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REPRESENTATIONSOFLANGUAGES115Indeedacloseinspectionoftheoriginalproof6revealsthatitdoesnotholdwhenwerepresentdeterministiccontextfreelanguagesbydeterministicpushdownautomataandpushdownautomatawitha

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SIAMJ.COMPUT.Vol.9,No.1,February19801980SocietyforIndustrialandApplied: Transcript

REPRESENTATIONSOFLANGUAGES115Indeedacloseinspectionoftheoriginalproof6revealsthatitdoesnotholdwhenwerepresentdeterministiccontextfreelanguagesbydeterministicpushdownautomataandpushdownautomatawitha. Abstract. 1.Introductionandmotivations.Thelast12yearshavewitnessedmanycontributionstotheinpaintingproblemindigitalimages,i.e.,theproblemofrecoveringentireregions 1144F.CAO,Y.GOUSSEAU,S.MASNOU,ANDP.PER Abstract.Withdiscretizedparticlevelocityspace,amulti-scaleuniedgas-kineticschemeforentireKnudsennumberowshasbeenconstructedbasedonthekineticmodelinone-dimensionalcase[J.Comput.Phys.,vol.229(2010),pp SPHERICALSPLINEAPPROXIMATIONDuetothisspecialrepresentation,manypropertiesofSBBpolynomialsareanal-ogoustothoseofclassicalplanarBernstein ReceivedbytheeditorsMarch17,2005;acceptedforpublication(inrevisedform)July6,2006;publishedelectronicallyJanuary12,2007.http://www.siam.org/journals/sinum/45-1/62708.html J.QIAN,Y.-T.ZHANG,ANDH.-K.ZHAO A.J.RADCLIFFE,A.D.SCOTT,ANDE.L.WILMERofauthorshavegivenapproximationalgorithms:KececiogluandSanko[23]gavea2-approximationalgorithm,BafnaandPevzner[2]gavea1.75-approximationalgorithm,Christie[8]gavea1 228B.K.NATARAJANthenumberofnonzerosreportedisatmost18Opt(e/2)IIA+1122In(lib12/),whereOpt(e/2)istheoptimumnumberofnonzeroentriesaterrore/2,AisthematrixobtainedbynormalizingeachcolumnofAwithrespecttothe HOWFASTARENONSYMMETRICMATRIXITERATIONS?779TABLEIterativemethodsfornonsymmetricsystemsAxb.(Thedifferencesamongthesealgorithmsareslightinsomecases.)Theterminologyap-proximatelyfollowsElman[6]andGutknech 1002U.FEIGE,RRAGHAVAN,D.PELEG,ANDE.UPFAL"Xi"Xj,"andgivesthewronganswerwithsomeprobability.Eachleafislabeledwithapermutationrepresentingthesortedorderfortheinput(forsortingandmerging)oranindexin[1,N](f ThisworkissupportedbyNSFunderGrantCCF-0702662. J.Comput.Sci.&Technol.,Month200X,Vol.21,No.X Figure1:Left:typesofgeometricerrors.Middle:apolygonsoupthatexhibitsamixtureofgeometricerrors.Right:atopologi MARKOVDECISIONPROBLEMS,STATE-ACTIONFREQUENCIES787visitstOstatex.Belowweshowthatthepathwiselimitsofthese"conditionalfrequen-cies"arethemorebasicquantity,inthattheydeterminetheexpectedstateactionfrequen 4J.Bonin,AConstructionofIntertwines,SIAMJ.DiscreteMath.24(2010)1742-1752.(ii)1(F)=M(F[T1[S02)forF2Z0(M1)and2(F)=M(F[T2[S01)forF2Z0(M2).Proof.Werstnoteausefulinequality:foranyi2f1;2gandFi2Z(Mi),(3 12 q=N+p Thisisthecorrespondingauthor Authors'addresses:LiliSu,CSAIL,EECS,MIT,32VassarSt,Cambridge,MA,02139,USA,lilisu@mit.edu;JiamingXu,TheFuquaSchoolofBusiness,DukeUniversity,100FuquaDrive,Durha Figure2.ExhaustivesearchscorerangeThescoresforBFS(inFigure3)arealsosteadilyincreasing,andthealgorithmperformsquitewell,butonlyscoresabouthalfoftheoptimalscorespossible,becauseitrunsoutoftime.Theperfor Research ProgrammesResearch AreasL ro has xp rtis across multipl disciplin s from d p th or tical comput r sci nc and formal m thods through to participatory d sign human-comput r int raction th

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