Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank

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(1)Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank Olivier Carton, Chloé Rispal. To cite this version: Olivier Carton, Chloé Rispal. Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank. 6th Latin American Theoretical INformatics (LATIN’04), Apr 2004, Buenos Aires, Argentina, Argentina. pp.292-301. �hal-00619905�. HAL Id: hal-00619905 https://hal-upec-upem.archives-ouvertes.fr/hal-00619905 Submitted on 3 Oct 2011. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(10) HZRTB0X à å ä <>EgXZXFJGðã[LT=@HZBW<>=@LTBEOC!JGC8P|B/CZ=>LgX/ïN HZRTB ä <]EGXKXSJOð ä J à LjH8EOåT<>B JGC8P|=@LQEO<]XFEGL[P HZRTB ä <>EgXZX!JGð ä J à LjHKEGåT<@B0X ä EOHIHZB/CZBP&<>=>LTB/EGC'JGC8P|B CK=@L gX/í ì ÿ * fX [þ %@7ý N

(11) ý Z * Gý g >9u)a

(12) ÿ zþ þcý Z

(13) ý z R * z. b I:PAJZI>EAC éê û Ký * >9Wþ * 3>U ( ;Tý Zý þ ;[ýÿ | L

(14) ý Z Zy ý Rf[ÿoþ ný g0ý + N

(15) ý % % =- Z¡Dl EA¢.

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(17) åjæ

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(20) å Mà HÆP|JABX¦LTJOH`åNB <>JGL ÌHZJ EOL[P.HZR[BJGC8P|B CK=@L M åQB/<@JgL gXHKJ å à HP|JAB/X0LTJGHåQB/<@JgL HZ!J

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(24) !/ ½CKB/XZYQB ä HK=@?gB <>æ / 4ð½JGCFXIJgá¦B =>LgHKB gB 1C 0jí !R à XÀHZRTBâSJgCKP[X JO8ð &('*)R[En?GBWECKEGLTóÆ<>JzâSB/CSHKR[EOLJgCFB à EO<HK2J 0jí 3 4 )ØTÞqÚÀ$× ) % # 'xØ # Ú 576ÌÚ4ÙQ$Û # ÚS& × %IÞI$× '*)"Ù.Ú4ÙQ(Û 'Ù[ÞZ(× + # C à 9æ B/8 CZBEGL[PøDFEOCZHZJgL é û ìRQEn?GB=>LjHZCKJAP à[ä BPCKEOHZ=>JGL[EG<(Bè|YTCKB/XKXZ=@JgL[X*EOLQP E à HKJGáÈzH8E`ð½JgC âSJgCKPTX=>L[P|B èABP åAæ ä J à LjH8EOåT<>B`X ä EzHIHKB CKB/Pø<@=>LTBEOCWJGC8P|B CK=>L gX/í !RTB æ RQEn?GBYTCZJz?gB/P HZR[EOH EÌXZBHÆJGðâFJGC8PTX¦=]X¦CKEOHZ=>JGL[EG<'=ð0EOLQP JgLT<>æ =ð0=@HÆ=>XÆCZB ä J gLT= /EOå[<@BÓBèAHZB/L[P|=>L çW<>B B L[B X HZRTB/JGCKB á5í $JgCZB'Y[CZB ä =]XIB/<@ægïzHZRTB/æRQEn?GB*P|B ã[LTB/P&EWâ'RTJG<>B*RT=>B C8EOC ä RAæJOðxC8EzHZ=>JGLQEO<TXZBHKXé ëOì í TJGC B/E ä RX à å[XZBH JGðC8EzHK=@JgL[EO<(JGYNB C8EzHZ=>JGLQX ïAHKRTB æ ä JgL[XI=]P|B/C'HZRTB ä <]EGXKX!JOð ä JgCZCKB/XZYQJgL[P|=> L CKEOHZ=>JGL[EG<<]EOL à E GB/XWEGL[PøPTBã[LTB¦HKCKEGL[XZ=HK=@JgL[XWJOð!E à HKJGáÈzH8E ä EOY|H à CK=@L ÓHKRTBÆXZEGá¦B<]EOLTö à E GB/X/í L&HZRTBð½JG<><>Jzâ'=@L XIB ä HK=@JgLïGHKRTB ä R[EOC8E ä HZB CK= /EzHK=@JgL¦JOð(C8EzHK=@JgL[EO<XIB HKXSJOð(âFJGC8PTXÀJOð ã[LT=@HZB0C8EOLTóÆ=]X!LTJGHZ=@ã[B/Pxí. : CFE ;KXM?OFPAQTKNV I <DHTJZI:S?S}O0PRQWS. !RTBC8EzHK=@JgL[EO<"XZBHKXJOðÀã[LT=@HZB¦CKEGLTó ä EGL åQB¦Jgå|HKEG=@LTBPð½CKJGá ã[LT=@HZB¦XZBHKXJGð4ã[LT=@HZBâSJgCKP[X à XI=>LWHKRTB à LT=>JGL]ïnHZR[B ä JgL ä EOHZB LQEzHZ=>JGL=@ïOHZRTB XIHKEGC?>AïnHKRTB'JGá¦BjE=HKB C8EzHZ=>JGL EOL[PHZR[B å[E ä óAâ!EOC8PTXÀJgá¦BgE=@HZB/CKEOHZ=>JGL *í BH @ EOL[P.A åNBWHqâSJ`XZBHKX!JGðâFJGC8PTX/ïAâSB0P|B ã[LTB.

(25) @ ] A @ =A @ n @ .@ @ -. d @ ` A ¢ ?2 , = , d @l d A ¢ 1 % ,X1 d l ,N1 d @ ¢ 1 3 M ,X1 ,X1 d @ ¢ 13 @ , 1 , 1 d @ ¢ . (JPTBã[LTB CKEOHZ=>JGL[EG<[XIB HKXÀJOðxâSJgCKP[X=@LQP|Bè|B/PÆåjæ¦EO<><[<>=>LTB/EGC4JGC8P|B CK=>LgX/ïnHZRTCKB B áJgCZB JGYNB CZö EzHZ=>JGLQXFEGCZBLTB/B/P|BP AHKRTBWJGC8P|=@LQEO<=HKB C8EzHK=@JgL &ïAHZRTBWå[E ä óAâFEGCKPTXÀJGC8P|=>L[EO<=@HZB C8EzHK=@JgL. EOL[P&HZRTB0=@HZB/CKEOHZ=>JGL¥ð½JGC*EG<@<<>=>LTB/EGC ä J à LgH8EOåT<>B0X ä EzHZHZB CKB/P&JGC8P|B CK=>LgX Ní .

(26).

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