lecnotessep031 - ‡ lc ¬ a a a a ‡ ‡ a ‡ ‡‡‡ a‡‡...

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Unformatted text preview: ‡ lc ¬ a a a a ‡ ‡ a ‡ ‡‡‡ a‡‡ ‡a‡ aa‡ ‡‡a a‡a ‡aa aaa ¼»º D¹ D¹ ¨¹ ‡j fh e e™ `bl”Y © Dg j t W ‘Y k ¸ j  “ “ ‘ “ f d t W S “S ‚YS q ‘ e ™ h RjQYY hy e ™  ™ ‘Sy ™ x ™  t h h W  Q v €–Qfg€U¥o†f·6€yr¨¥sQ¥”¶UT”U‹f–™TD¥%w€U”¥`·f¥¶¥shU•f4‚‰¥@sQ¥¤%¢i¥g)m ‡Q ‘ fYQ “Sh eQS ‘ e ‘ jj t ™ ‚ µ ´§ ³ ² jQS q ™ t h h z Q k “ e ™ ¥Usjr”`fUg €Ul@syf–™bU€–QfTd l¨ ”p6§ o¥ @”l2¢g€–Q¤{±of¢Dg s™­Tg@Tff¥%2fg‚%i”‹€ifw”¥‚U¥TD¥if–™¤svg”‚%r–tstr‚{p”–S`”sY•rstb— ‘¬ ™ x eQ e ™ ‚ h W ™ ‚ x h Q W hS e Q V ‚jj  QY  S ‚ h W  q ‘ t S Q W ‘ f Q f j ‘ ‚y ‘y t ‡ ‡ U–q)±`U2sfX”¥4hdp—|±j ‚… ¯¬¥—hdd†b¥{€X”¥4hd‚„X††d— QY ‚ ‘ ¡ QQj d~ t ‚ VY x ¡ ° } ® x ¬ „ ° — Yh ~ t ‚ VY x ¡ ° } j „ ° ¬¯g­¬ ‚… gr@U–S`p€jp–S•6sY•«s™­Tg@Tff¥%2fuUT@T#‚w”¥«g`upX¥sh™Ÿ x h ® ™  YQ “ ‘Q ‘ ‘ ‚y ‘y ‘¬ ™ x eQ e ™ ‚ h W ™ ‚ e “S RQ e  Q V ‚jj  ™ y Q f q t ‡ ‘ ‚y ‘y ™ th h W e “S RQ e n W eQS ‚ R V hy Q W ™ @–S•6–Y` ¥@sQ¥¤%Xˆ”T`T«2 €UT•u%«¥`y ¨ § ª ©¨ § ¥ ¤ g‡ fa ¥ i€g‡ a ¦£ ™ ‘Sy ™ x n ™ S “S ¥shU•f4‚‹¤gdgfUp€j‘ Q kh W  ™ ‘SjQ ‚ ¢ hS YQ fj ™ Q “S S “S QSh ™ ‘ f Q f Sj ‘ ¡ ‡j e ™ ‚ h W YQ f t eQS t R V h lD¥¥shUw@2X”…`pwDg†fU˜gfUr”g%st–trbpyw”sY)…`D¥%…`pl–h€Ug`€y–‘•y q ‘ fh “j hS ‘ h q Q f QY xQ W ™ ‘ ‘ ‚S ‘ ‘ ‚y ‘y ‘j  W Q V hj ‘ ‚ W hS eQQ ™ ‘ f Q s™rlUi”2–™#¥‚{‚U4h•%¢–h”’S”2–™’Sf•6–Y`†€ywfdw sestiU@@¨–tstr†œŸ ž  –£ £ ¦© (" " “ ›  – ¡§ – & $"£ ¡ ˜ ¦©£  ¦ §£ ¦ ” ¦© (" " “ ‘  ‘ l@§o¥•¤¡%3yœ)¦€‰€†š'%¥‰X™f¥‹)D0"@g))—–•¤¡%3yBo0£’ ‡n ‘Y R Y „’S”gDr¥4hx j ‘ ‚y ‘y “S RQ e eQ e ™ ‚ h W Y x j e ™ ‚ h W YQ f t Q ‘j t ‘S ™Q ™ h R Q Ž e Sj Œ ”–S•6–Y`7”T`T7@TD¥%#4huff¥%X@{lsh@–‰Up¥s”2`DT•#j r¥6„ Š d “S RQ e ™ h j ™ ‘S ‘YSjQY h ™ “ ‘ 3UT@T¥pf¥shU•sy”Uw@”‹U–Srf Š dj e ™ ‚ h W YQ f t Q ‘j ™ fh ™ v SjQ z ‡ @fD@{lshu`s‰wrl¤r„€{bfc “S RQ e nYY ‘ WY — ‡ ”T`U¥””’S”bbe j ‘ ‚y ‘y ™ t h h W e “S RQ „ 6’S`”sY•g€–Q¤D#ˆUT@db‡ ‡ ƒ ™ t R tYQ †g€¨–t¥”@¥k … ‡~ f tQ W j VQ ‘ h fS SjY } ™ ‘ ‘ ‚S ‘ Q V hj R ‚ ‘ ‚ W h •dl–h@Db@U–S{„w”f4ƒ'¥shU–SU2s™‚w‰€e–tfUS ~ | } j ‘ ‚y ‘ | ™ t h h z S ‚ h W jSy x ‘j  W Q V hj S v h t hS q ‘ h q QY Q f n e h r0zd6’S`”sY{¢g€–Q2p{¥%gy6psyU¥fdiwpl#¤–hu”us™¥¥r”gbpXof¤m khj h ™ h V h x fQY e ™ — ƒQ ‘Yy lUi3g`”Tfd˜¥%–W”•TP e a ae d c a YQ W VQS RQ gfb`%X@UT@¤P VY “ ‘ P YQQ ˆ ‡Y „ ƒYQY ‚SyQ g6gf”’ST6`@‰…@†…@@UfU€3x v it sqpi wfuDr)h FEC H 98 GFECA 98 5  1 ( & $"  ¡£ ¦© © § ¦¡£¡ D%¨I@#%%%%DB@#764§320¡)'%#!¦¤¨¤¥¤¢ e¬ „lc j “q ‚ ™Y D q ‘j ‚ j ‘ ‚y ‘y Q ‘ ‘S R h Q f h e f ¥¥fU¥±)–™Uf6’S`”sY•u@–‰sVUTu{T¦lh Œ ‡ ¡ ° „ ‘ ‘ ‚y ‘y Sj ‘j  ” ‡ ‘ ‚y ‘y t ‘jj h {††r€jb–S•6–Y`w@sQU¥y†€’Sf•6–Y`usQsWw”%R SjQ W Q “S Sy ‚YSj ™ hy hS ‘ e ™ ‚ h W YQ f t q ‘ khY R ™Q “ f nYS t ‚ h “j Q ™ h q ‘ “S Sj ‘ „€Dr”šf”Uwf¥`uU)€jif¥%š`pl–h‚s™¤lU@rX”UXsef¥Ur¥±s™”)w6–Y)¡ jjQS q f x q j ‚ t€Ug¦`4Qis™w‘fb–S‘ S ™Q V t R ‘ hS t ‚y ‘ e ‘ jQ v V S “S ™ ‘Sy ™ x n ‘Y R Q “S S ‚h W ‘ ‘ S “ f h @`sQ–V‹”r’S`…„Td–S@g‹blDU ¥shU•f4‚‹„–SU¥f±”rT¥%gd–Ssjbgfr¤P “B|W !% ({ 4 §fƒ#z#iƒ‚)~ © 0e} € ¨( 0 ( " ¦¨ "!( g ¨  '    1 ¦  &%1 ¦  ¦ |  "¤ ¨"w " g x v $ ¡ " ¡ fTR"™§ˆƒR‚)##iU$¢§%¦ Tv©¨gg#3~3t&3}¢gzV{2A3tXrzyw¤lf¤)‘ u ets q ¤#xr~ o ¹ º Rp©o V} ¤ ~ © ¹ `y§ º ¹ } £ n §mmm ¨§ g‡ fa ¥ ª © ¥‡ a ¥ ƒ £ ¨§ ¦ § £ ¦ –” 5   © D0"@¥)­B6§odl j hQ ‘j t W ™hjQ ky`s‰U‚sQgD¥U¥@”Y x h j ‘ ‚y ‘y “S RQ e “ ‘ f h e Q f ™y S “ ff xh ™ ‘SjQ ‚ ¢ hS vy  W SQ q jS fh ¥‹”–S•6sY•'e ”T`!U–SrITˆp™g@«lfrUFg™¥shUw@f7UI6f¢`¥6•sQt lb° ‡QS t R V h ¬ ˜ ° ‘ ‘ Qy ™Q “ d ˜ ° ‘ h t V t W hY R ‘ “ m ‡ e ™ “S QYh ¥U`–Qfi•y …9rsjb–S±•f@š9 s™w€jgr€j‘ @–QUfsj…x¥fU‚”¥V h ™ Q ‘j xh ‘ ‚y ‘y  j  f‚@–‰U)¥r’S`”sY•rf“ £ RiXt@wg€jrTU¥TIv@D#¤¢Dg £ ¥shU•f4‚«g€–Q2%W ‘ hjQ nf ‘ S ‚ RS ‚ h d e YQ W V ‚ ™ e ™ ™ ‘Sy ™ x ™ t h h  V t WhY R ‘ “S hS S ‚ R d ‡ eY ¬ ˜ ° ‘ ™ ‘S ‘ ‘ ‘ V x V t WhY R Q “S — ¡  Xsj‘ @–Qf¥”u€jU ”uT™ )3”¥f—“˜™±€j'¥shUg@s‰isVs™{gh `sQ¥”‹”±q)€ – ‡ eQj ‚ jQS q xh YQ W V ‚ ™ Qy ‚ eQY hS nYS hS ~ySQ e h “SQ r@Uf@”l2gr@D#¤±•f@”i”‹”UU{€”`«T”•V nQ vj t |y ˆ Q ‘ ‚ •dj R  V “ q ‚ ™Y } j ‘S ‘Y ‚Q “ j ‚ ‘Yk Qj ‚ jYQQ ‘ q ™Qt ‘YSy t `wD–‚{oˆ˜s™†#@f¥‚¥fgf”g±D ˜`€yUwsj”@¨f¥sh”gl…wD¨”@`s™¥@lg@sy”U•@sQ˜” “¨ 0w ¦&(! ¸ %    1 ( 0%%w ‡ ( &%1 ~ … } „ " ¦ R"u(§f’r1‘§%¦ T‰#TR"#ƒTˆi§$#3p†¸ †© —e9ƒR‚¨ 1v3h&€#TR"§yTxv©¨ut)hr7gd#igqp#ih¥fed$7b¨ a§XV"§R(UTR"0FQ PHFgf† % ¦  ¦ ( 0%%w (  ¦s" "&"  (   c% g¨ ¨( c ¦ ` YW  0 S& 0  I G ¡ §£ © 0‡¥s”@¥%T•snstg€U2`”g%rsj6’Sf•6–Y` 6fU…gu`s‰wufUrTpz t ‘S ™Q ™ h R Q t ‘S ™QSh R ‘ j ‘ ‚y ‘y “y ‚j xh Q ‘j Q “S S ‚ ‡j ‚y y  th h W e “S RQ e n W eQS ‚ R Vhy Q W ™y j ™ ‘Sy ™ x ™ th h W t QY xQYQ “ `6’S‘`”sY‘•#™g@sQ¥¤%r#”T`u¤X@U¥•pDXg`)f–h”f4‚ug@sQ¥¤%stg˜”¥4h`U@m ‡~j R 6fg‹V “¥fgf”g±DEUjfpr”–S`”sY•‹œUT@T·s™‰`¥@usQ–WU”%±U¥df–h”l@s‰–V”T¥†`”wf4‚¯x} q ‚ ™Y Q ‚ ¬ j ‘ ‚y ‘y e “S RQ e ‘ ™Q kQ t ‘jj h R QY  j ™ ‘S ‘ ‘S R h YQ “SY ~ ¼ ¹ ³ » ¹ ³ º ¹} ² ~ ¼ ¹ ³ » ¹ ³ º ¹} ² ~ ¼ ¹ ³ » ¹ ³ º ¹} ¤ ~ ¹} £ B @ 8 4 '&%10( '&%  "    ¦¤ Sy ‚Y j ™hy e ™ jQ ™h t Qv CA9765#32#)#$#!¦ ©¨§¥•f”UwSf¥` Dgr@f¥rstgu¥g)m ž  – £  £ ©  © ¦ § £ ¦ –”  ‘§ ¡   ˜ " ˜ " o§o¥œ‹™%"@¥)­)@‰€4§l¶€§ ¤‰£ j ‚… Dgb‚d†f–™”lf”`”’S¥š¥‚@U”X·UT@d…%¢l†%›r ® e ™ j „ ° — q ‘S ™YQ t xh QQYS e “S RQ „ ƒ ¡ ¡ –  Input {0,1}^n Output in {0,1} c lc ¬ c e§ º¼ ¹ a» ¹ ºX ¹ ¤ Y § © ¨ f§ ‡ a ¥ db aY º EX 7¤ ¼ ¹ º ¹ Y `¤ ¼ ¹ » ¹ º ¹ h t — X ™ ‘SSh ™ t ‘jj h w€jb˜‡ º¼ ¹ º£¹ ¥shUg”gf‚sQsWw”%R YQ “Sh ™ — ‡~ hS ™ t R ‘ Q ‘Y Rf e ty ‘ ‘ n “ f ‘ S “ } `”gd)•t2¥`€y–‘sVysVUUP€–Qstg@€j…’Su¤r)sjšlf0m{‡ ‡ ¤ ~ ¹ } £ `”S ‡ ¤ ¼ ¹ º ¹ –x‘ ™Q“ ¼ ƒr€e–‘¥o{€j¥shUg`€y–‘sVus™rl–hst¥4h†š‡ ‡ ¤ D¹ a ¤ ¨¹ Q —‡¤d D•¨¹ €jp2g@sys‘sVb™ … tk ‘ ™ ‘S t R ‘ q ‘ f t x Q “ m § º ‘ ¼ ¹º ‘ S™ tR ‘ Q ‡‡‡‡ ‡a‡‡ a‡a‡ aaa‡ ‡‡‡a aa‡a ‡‡aa aaaa ¼»º D¹ D¹ ¨¹ sQg•r¡ tR VQ Yh R“0ec fˆWTˆr% £ #%¦ T1 0" ¨( V "w    "  T S¤" s T " c g ¦ c ¨ 0w ¦&(! % "¨ B¤"!% '"& "w ( " %  4 0( ¦ ¦ ' ‡  rg7$s 0#Tk~U3ig Xtg 93R"32(##™1†3¥t##)h9tF#T z#A"“V¦~#)'i‰E†#( ©¨¦ £ 1Ai§(T¦ ™'))'US“ £ 1A†#T¦ ™'))'E)©¨XB £ 4 3r"iFQ QD0"@4§)š  %   0 { ¦ " ¦& R %  ( 0 { ¦ " ¦& { ( ¦ '&  ¦ P ¦   ¦ ¡ “ F  ¦ % " ¦ "  } ) 6 ¤     1 % F ¦  ¦ ( 0%% )I¦3h&¥1 ‰ƒR‚¨ ig¥©¨¦ ~ £ b8H§( £ #%¦ 3zT†1 yG3t&3¢#TR"§yTw 1% gzV{2‘igP©¨¦ ~ £ }d) xhrg )~ © EA C0e} € ¤ ~ © A §4¸} € 9~ £ r87r7gP†¸ » 5s 3} € "¤ " t "&" c S DB @ B@ 1 } ) 6 "  ~ 4 1 2~ £ }b0P1 ¦ Vh€ %1 ƒRT¨ §( 7ru¤ 3Tec 3Tw { hr§¦ §Rh& z#TT3 4¨ gf† )t B¨¦   &¦ " ‚¦ ¤  g { "  " "  " ¦ g ¨  %  (0 " ¤  %  " H § £ © ‡~S ‘h R  hS R } QS ‚ R Vhy hS eY “  •62s™¥%#‹”4‚‹U¥•”6gD#d–S‘ j@¥¥‹†€j‘U±fgysQ¥s”glk±6y¥€Q4hx˜`yf`D(–™X¥sq†fu–h”f4‚†„–SU¥fu–n@¥skU–SU2™ d Qv V “S e ™ t W ‘Y “  Y Q ™Q ‚ ' ‘ “ ‘ “ j  “ ™ ‘Sy ™ x n ‘Y R tQ ‘ ‘ ‚S ~ © `y§ º o § ‡ § º ¨o @my§ º ¦} !&~ © `yy§ º o ”§ º ©¨o @y§ º %¦} £ $ m µ ¦§mmm ¦ ¦§m m £ ¤ ¦ § m m m ¦ § a ¦ § m m m ©e § " ¨ © g‡ fa ¥ ƒ © ym º o ¦ º ©¨o m º ¦ ¥ #¤ ~ }£ o ! 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This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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