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Attribute grammars and automatic complexity analysis

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(1)Attribute grammars and automatic complexity analysis Marni Mishna. To cite this version: Marni Mishna. Attribute grammars and automatic complexity analysis. [Research Report] RR-4021, INRIA. 2000. �inria-00072620�. HAL Id: inria-00072620 https://hal.inria.fr/inria-00072620 Submitted on 24 May 2006. 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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(239) PMK Y]KMLQP+KMZ'h b L€A'LQV LQ‚S@ˆi]LNZ.V L€KMR+YMLQZ > @UZ~^]@UV¨ f@U@BKJV > @ h]P3Z Z L€^MLQONLQV LQ@UZWSKMiˆZ5Y]A'ZfV > @‚˜WrO€YM@WrTUTUP b i]LŠKMR'V P'V > @TBWrZ @SŽ =-> LQZfLQZfV > @ZWSA'@

(240) WrZ8V > @

(241) WrV V b L€^]YMV @ ‰ P b Y]KMLQP+KMZBŽ eh]W b V L€WrO]TUPMA~h]P+KM@BK3V8i]@UZ.TU@BKSVfLQZ8@BKMTBWShMZYMOŠWXV @Uiƒ LNV > V > @ ab P+i P+h]@ b WXV P b ‰ P b h b PMiYMTUV ZfWSKMiƒW

(242) Z.@UON@UTUV.LN‚3@ WrV V b L€^]YMV @-L€K~V > @PSV > @ b TBWrZ @UZBŽ => @ ‰ YMOQO7TUP+A~h„P+KM@BK3V8LQV @ b WrV.LNPMK7š`A WShMZ8V PW3K~LQV @ b WXV LQ‚S@-P+h„@ b WrV P b Ž eZ8L€K V > @ TBWrZ @

(243) P ‰ WrV.V b L€^]YMV @

(244) R b W3A~A~W b ZzšSP+KMOQ\ˆZ5Y]^3dh b PSR b WSA'Z-P ‰ Z5Y]^MZ V b YMTUVY b @UZ-TBWSKo^]@

(245) TBWrOQOQ@UiJ -LQV > L€K™W'TUP+A h]P+KM@BK3V i]@UZ TU@BK3VBŽ . . . . ™]ŽA‡„Ž GŽ y  €£7|+Œ£]xB£w y]w€©  '=->. '@ WSK]WrOQ\+Z.LNZ

(246) P ‰ i]LA@ b @BK3V L€WrV LQP+KoLQOQO€YMZ V b WrV.@UZ

(247) V > @'LŠKMTUO€YMZ LQP+K P ‰ \— p L€K™WrV.V b L€^]YMV @

(248) R b W3A~A~W b ZzŽ fP+KMZ.LNi]@ bb @UR+YMO€W b WrOQRS@B^ b WrLQT-@U]h b @UZ Z LQP+KMZfTUP+A h]PSZ @Ui P ‰ TUP+KMZ.V5WSK3V ZËmFWSKMiunWSKMi ~YMZ L€KMRV > @Vd fP

(249) ^ML€K]W b \ P+h„@ b WrV LQP+KMZ  WSKMix,WSKMiuV > @

(250) Y]K]W b \~P+h„@ b WrV LQP+Kˆ@U]h]PMKM@BKSV L€WrV.LNPMK7š]V > WrVfLQZBš  .]Ž =-> @

(251) R b WSA A~W b P ‰ V > LQZ.

(252) 4 =U   4

(253) 

(254)  ‡ . Z @UV-P ‰ @U]h b @UZ Z LQP+KMZ  ˆ -LQV > e-V.P+A'Z. 0.LQZ@BWrZ.LNOQ\ui]@UZ T b LŠ^„@Ui2. Z/f/. š?š. 8. {. 8. m(Qnf( p(u{q( >l(.  .  l*&* \*  . > 8. 8. l* )*. ..    . -= > @ ‰ PSOQOQP˜ LŠKMRˆh b PSR b W3A 4RR š]WrZfLQV- fP+YMOQi™^]@

(255) @BK3V @ b @UiuL€K3V P \— p'š]LQZW'h b PSR b W3A i]@UZ.T b L€^MLŠKMRˆi]L‘@ b @BKSV.LŠW˜ V LQP+K7Ž => @

(256) TUPSZ V-P ‰ W ‰ Y]KMTUV.LNPMKuLQZ-V > @KMY]A'^]@ b P ‰ WrV PMA'ZfRS@BKM@ b WrV @Ui™^3\ˆV > @WrOQRSP b LQV > A¤š+V > YMZ-V > @

(257) TUP+Y]KSV.@ b Z W b @

(258) PMKM@ ‰ P b @BWrT > WXV P+A'LQT

(259) Z V b YMTUV5Y b @SŽ. R   ˆH  ‰   4RR3J1 != Ž,7 < != X ˆ * Œ 1 1

(260) -= Ž ‰ R @ ŽT‰B .=> SŒ $ 1  $M1 ' 7 @> wŒ  B  RRJ1  $ B  RR3J1 '  X @ ŽT‰B    Š 1 Œ $ 1  $M1  7 @> wŒ   Š 1 Œ  B 4RRP1  Y$E1  Y$  Š 1 Œ J1  $ B  RRJ1 '   YX @ ŽT‰B P1 != ‰ $ 1 . 7  Š 1 Œ  B 4RRP1  Y$ 1" YX  7 1DX   1 7 1 ŽT‰ X  1 Žo‰ 7 1 ŽT‰ X 1B X Š 1* Œ/LŽ 1 => wŒ $   Š 1 Œ $ 1 -= ‰ $  1 ŽT‰ $  1 $ 7M X =-> @-WrV V b L€^]YMV @8R b WSA~A~W b ‚S@ b Z LQP+K > WrZ$P+KM@-KMP+K3Z.LnmU@WrV V b L€^]YMV @ 0 šz > PSZ @f‚˜WXOŠYM@LNZ$V > @KMY]A'^]@ b > @BK¤V > @

(261) @U`h b @UZ Z LQP+KuLQZi]L‘ @ b @BKSV L€WrV.@UiŽ 

(262) &!  % 8 nf(Šnf(Qnf( 

(263) &!|{%( 

(264) ^!B>G%( 

(265) G!$% 

(266) ^!{% 8 

(267) &! % n  

(268) &! % > 8 ‡  

(269) &! % Z LhmU@1!  % 

(270) &! % Z LhmU@1!  % 8 D  

(271) &! % Z LhmU@1!  % Œ 4N'1 b @ ‰ @ b ZV P'V > @

(272) Z V b YMTUVY b @

(273) Z LhmU@SŽ. =-> @ b @UZYMONV.LŠKMRˆRS@BKM@ b WXV L€KMR ‰ Y]KMTUV LQP+Ku@U_]Y]WrV LQP+KˆZ.@UV-TBWSK™^„@jA~W3KMLŠh]YMO€WrV.@UiŽ.

(274)  ‰ 5 Q Ž * Š 7

(275) 9-< -= G @ Žo‰B   N'1 Žo‰

(276)  1‰(Š => SŒ

(277)  1‰(Š. , N1 ŽT‰ $ ‰ 1 $ $ @ Žo‰B  = > SŒ $A< -=?$ < -=L Y$  Š 1 Œ $ < !=I$ < != $E@ ŽT‰B P1 $E< -=L . $ "

(278)  1‰(Š $ ‰  1!

(279) G 1‰VŠ $ $ Šo > 

(280)  1‰(Š $O1;

(281)  1‰VŠ H7. 5 -* Q 7

(282) 9  0 #< != K

(283) GL ‰ ,  $  $  $F@ Žo‰B   $  0  < -=L Y$  0  < -=L  Y$ @ Žo‰B $  0  < -=L  Œ  N1 < -=L Y$  0 #< !=  Œ 4N'1#< !=  $ @ Žo‰B  $  0  < -=L  Œ  N1 < -=L   H7 5 1!S  Œ7

(284) *-QR'1S Œ  Q Ž * Š $E*!Q$  >* ‹ 1>>1 B $ VV  $  0-WW$EN YX. P ‰ WXV P+A'Z.

(285) šk.  

(286) . MR4J2 8 ›zP+KM@f!4/ % 8 /h!4/ % 8  /A9!4/ %—8  / # ]h!4/ %—8\mU@ b P!4/nE% -PMKM@f!4/7n%  -! 47 / n%  h!4/7n% # ]h!4/ %    A9!,4/7n% # `h!  / %   @f!4/7n% # ]h! / %a/ @f! Œ/ % 8  ]/ ! 4/ % 8  /jmU@ b PU!Œ/ % 8 œ.

(287) *-QR LŠ ‰VŠ 1  ! Œ(‰ > 1P1!S Œ $ / 7 5  T Š 7 ;

(288) *-QR LŠ ‰VŠ 1  ! Œ(‰ > 1P1!S Œ $  7 5 * Q 7 ; ˜@U+VBšV >. u@ RS@BKM@ b WrV L€KMR ‰ Y]KMTUV LQP+KMZ ‰ P b V > @u@U`h b @UZ.Z LQP+K‡WSKMi V > u@ TBY]A'YMO€WrV LQ‚S@™Z.LnmU@JW b @uLQZ PSO€WrV.@Uiš-WSKMi1V > @ WrZ \]A~hMV P3V LQT

(289) ‚˜WrO€YM@P ‰ V > @

(290) TUPM@6ƒTULQ@BK3V ZLQZ@U+V b WrTUV @Ui2 5  T Š 1

(291) -= 7

(292) Œo‹wŒ . oŠ $E< !=,#N  7 * Q  1

(293) -= 7

(294) Œ/o‹wŒ b* Q,$ < -= V!W N  7  5  TŠ ˆ(‰ 1(R 7

(295) "1!S   *2>1     oŠ  1

(296) -=I$ N,$A 7 * Q  ˆ(‰ 1(R 7

(297) "1!S   *2>1   b* Q  1

(298) -=I$ N,$A 7  Q B 1 &*Q  ˆ(‰ 1(R   oŠ2 ˆ-‰ 1 R,$

(299) J RJL 6 $  YXO1"*2>(R' YX . .   .  

(300)          .       .                          .      .     .      . D–qSmXl+D]n#"-™XlSl+m   ). =-> @

(301) ‚rW b L€WSKMTU@LQZ

(302) WrOQZ P~TUP+A h]YMV5WS^MOQ@ ;! Y]KMOQL€‹r@'L€K \— p%a2. 5 -* QR LŠ ‰VŠ 14 !Œ(‰ >'1P1!S  R"* ˆŠL‰VŠ 7

(303) 21!S  "*2>1   1  *2> R3 Q B 13#R"* ˆ/ŠL‰VŠ . Œ $ .  Œ/o‹wŒ * Q . .  .   . !   . 1pq! % . . 7.  $ < -= V $ -W#N  Y$.N,$fL 7 ˆH‰ 1(R 4 -Š 1ˆ-‰ 1 R $D#*Q  ˆ(‰ 14R 4 o Š2 ˆH‰ 1(R &%$U

(304) J"R JL 6 $ '  YX. 4m D–m-‡ Xl rl+m-‡„nSn  

(305) !¨n D–m % ™]Ž lŽ ©  yx.¸vU©   \— p b @BA~WrL€KMZV > @~A'P b @'K]WrV5Y b WXO -WB\ˆV Pˆ@U`h b @UZ ZZ.P+A'@jh b PSR b WSA A'L€KMR h b L€A'LQV LQ‚S@UZ Z5YMT > WrZi]L b @UTUV

(306) Z.V b YMTUV5Y b @Fi]@UZ TU@BK3VWSKMiJi]@UTUO€W b WXV LQP+KMZ

(307) -LQV > A'P b @FV > WSK¤P+KM@L€K]h]YMVBŽœ‘VLQZKMPSV

(308) WrZZ V b WXLNR > V¨ ‰ P b -W b i' -LQV > WrV V b LŠ^]YMV.@R b WSA~A~W b Z$V Pi]@U‚S@UOQP+huW!TUP b b @UZh]P+KMi]L€KMR~Z > P b V > WSKMiƒKMP3V5WrV LQP+K7š3TUP+KMZ @U_]YM@BKSV OQ\ˆV > @ R b W3A~A~W b Z-A'YMZ V^„@jA~W3KMLŠh]YMO€WrV.@Ui ^3\uV > @YMZ @ b Ž =-> @UZ.@jA~WSKML€h]YMO€WrV LQP+KMZW b @WrOQ -WB\MZh„PSZ Z L€^MOQ@Sš7Z L€KMTU@'Z L€A'L¡ O€W b A~WSKML€h]YMO€WrV LQP+KMZ

(309) W b @i]P+KM@LŠK3V @ b K]WXONOQ\u -LQV > L€KˆV > @L€A~hMOQ@BA'@BK3V5WrV LQP+K¤P ‰

(310) \ — p'!Ž ”-Pr f@U‚S@ b š ‰ P b PSV > @ b V¨\`h„@UZ @U]h b @UZ Z LQP+KMZV > @WrV V b L€^]YMV @

(311) i]@UZ T b L€hMV LQP+KoTBWSKu^„@jA'YMT > Z.LŠA hMON@ b šWSKMiuV > @

(312) RS@BKM@ b WXO A'@UV > PMiuZ L€A~hMOQ@ b Ž =-> LQZ[LŠA hMON@BAC@BKSV5WXV LQP+K'P ‰ WrV V b LŠ^]YMV.@8R b W3A~A~W b Z TUP+KMZ LQi]@ b Z$@BWrT > WrV.V b L€^]YMV @ rZ V b YMTUV5Y b @$TUP+A'^ML€K]WrV LQP+K7š3@U‚S@BK V > P+YMR > LŠK¤V > @ \ — p A'PMi]@UO W'R3LN‚3@BK ‰ Y]KMTUV LQP+K™A~Wz\~PMKMON\ > Wz‚S@P+KM@ b @UOQ@U‚˜WSK3V-Z V b YMTUV5Y b @

(313) L€K]h]YMVV¨\]h]@SŽ => LNZ TBWSK!ON@BWXi~V PA'YMOQV LQ‚˜W b LŠWXV @ ‰ Y]KMTUV LQP+KMZ > LQT > KM@U@Ui'V P

(314) ^]@-A~WSKMY]WrOQOQ\ b @UiYMTU@Ui'V P

(315) ^]@fZ P3ON‚3@UijWSKMi~A~WSKML€h]YMO€WrV @UiŽ =-> @Jh b L€KMTULŠhMOQ@Sš'WSKMi‡Z.LNRMKML–žTBW3KSVBš

(316) Wri]‚rWSK3V5WrRS@oV P†V > @†YMZ @oP ‰ WrV V b LŠ^]YMV.@™R b W3A~A~W b Z LNZuV > @ WXi]i]LNV.LNPMK]WrO L€K ‰ P b A~WrV LQP+K7Ž 8W b L€WSKMTU@~WSKMi ‰ Y b V > @ b A'P+AC@BKSV ZTBWSKu^]@'@UMV b WrTUV @Ui ‰b P+A V > @@U_]Y]WrV LQP+KMZBšY]KMONL€‹r@'V > @ \ — p TUP+Y]K3V @ b h]W b V ZBŽ (' &". =. #). +*.

(317) 4 =U   4

(318) 

(319)  ‡ . š.  

(320)  

(321)    

(322)   

(323)  !" # $ %& '%)(*+(,-./ 

(324)  021 

(325) 3 4  5

(326) 6'

(327)  879.:7;<:1 

(328)  =/6'.

(329) =.:7>@?.BA87/ '  

(330) =<:1  81 5

(331) 6'

(332)   

(333) 87C.DE

(334) 87F<G 

(335)     

(336) HID.J

(337)  K

(338) 3&L: 

(339)  % L "MH 

(340) :N %&O'MP L L  N

(341) 3&?.QA  .  

(342) HIR<0

(343)  K

(344) 3&L: 

(345)  % L "MH 

(346) :N %&SL  T K

(347) 3&?.BA.  . '%U(V+(V-WX

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