Exercises

# Exercises - h"qyz aia` aygnd ircnl dhlewtd zia ilibxz sqe`...

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h"qyz aia` aygnd ircnl dhlewtd zia ilibxz sqe` - zeiaeyigd zxez hxqdn letil dqpn dpi` xy` ,divwpet dze` z` zaygnd M 0 h"n zniiw M h"n lkl ik egiked .1 .(hxqa xzeia il`nyd `za `vnp y`xd xy`k dl`ny zkll oeiqp ici lr) :zzl yxcip .dpeknd zlert ly wiiecn inzixebl` xe`z miavndn cg` lk ly ciwtzd hext jez , M = ( Q,q 0 ,F, Γ , Σ ,[,δ ) diriayk dpeknd xe`z . Q -a .dlah zervn`a ievx , δ divwpetd hext . M = ( Q,q 0 ,F, Γ , Σ ,[,δ ) ,M 0 = ( Q 0 ,q 0 0 ,F 0 , Γ 0 , Σ 0 ,[,δ 0 ) eidi :fnx . Γ -a epi`y \$ oniq miiwy egipde , δ 0 xe`zl δ -a eynzyd .zepezp zeivwpet zeaygnd bpixeih zepekn xicbdl eyxciz ef dl`ya .2 :zzl yi sirq lka .dpeknd zlert ly wiiecn inzixebl` xe`z miavndn cg` lk ly ciwtzd hext jez , M = ( Q,q 0 ,F, Γ , Σ ,[,δ ) diriayk dpeknd xe`z . Q -a .dlah zervn`a ievx , δ divwpetd hext . f ( x ) = x 1 divwpetd z` zaygnd (ihxcphqd lcena) h"n eazk (1) epnn dxiqgne ,(miliaen miqt` lelkl ieyr xy`) ix`pia aizka mly xtqn zlawn dpeknd xzen hltl .dwixd dlind zeidl jixv hltd ,0 e` dwixd dlind `ed dpeknl hlwd m` .1 .miliaen miqt` lelkl . f ( x ) = 2 x 1 mr ,mcewd sirqd enk (2) zktedd divwpetd z` zaygnd (mihxq dnk liknd lcena e` ,ihxcphqd lcena) h"n eazk (3) .ix`pia beviia xtqnl ix`pe` beviia xtqn . f (11111) = 101 :`nbecl zktedd divwpetd z` zaygnd (mihxq dnk liknd lcena e` ,ihxcphqd lcena) h"n eazk (4) .ix`pe` beviia xtqnl ix`pia beviia xtqn . f (0100) = 1111 :`nbecl hxt zeivwpet aeyigl libxd h"n lcenl ddf lcen `ed zeivwpet aeyigl dcinrd liba h"n lcen .3 :mi`ad miiepiyl .zxver `l mlerl dpeknd okle ,miiteq miavn oi` dpeknl wx zrvan M d`lde t -d aeyigd crvn xy`k t -d aeyigd crva zcnrp M dpekny xicbp ( Left e` Right xzei rvaz `l mlerle) Stay zfefz .zcnrp dpeknd xy`k y`xl l`nyn z`vnpy y dlind `ed dpeknd hlt x hlw xear ly rpkyn ilelin xe`z zervn`a ewnp - ok m` .ihxcphqd lcenl lewy df lcen m`d eraw . wiiecna egiked - `l m` .zeni`zn zeivleniq 1

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lkl .h"n ly ihxcphqd lcend zxcbda edylk izcewp iepiy x`ezn mi`ad mitirqdn cg` lka .4 ewnp - ok m` .ihxcphqd lcenl lewy iepiydn lawznd h"nd lcen m`d eraw ,cxtpa sirq . wiiecna egiked - `l m` .zeni`zn zeivleniq ly rpkyn ilelin xe`z zervn`a .miielz-izla mpid mitirqd :dxrd :l`ny oeeikl iteqpi` hxq mr h"n (1) hrnl ,(oini oeeikl iteqpi`-ivg hxq zlra h"n ly) iqiqad lcenl ezxcbda ddf df lcen :mi`ad miiepiyd .(oini oeeikl mewna) l`ny oeeikl iteqpi` `ed hxqd ipnid dvwl cenv oinil l`nyn meyx x hlwd :`id x hlw lr zizlgzdd divxebitpewd dxwad avne ,hxqa xzeia ipnid `zl riavn y`xd , [ ipniq seqpi` el`nyle hxqd ly . q 0 `ed ,(hxqd ly ipnid dvwl cr) dxivrd zra y`xl ynn oininy zfexgnk xcben hltd .oinil l`nyn z`xwp `idyk :sv y`x zlra h"n (2) ly xzeia ipni d ezl riavn y`xd aeyigd zligzay jkl hxt ,iqiqad lcenl ddf df lcen .(wix hlwd m` ,oey`xd [ -l e`) hlwd . ( [x,q 0 ,[[[. .. ) `id x hlw lr zizlgzdd divxebitpewd (3) :drez y`x mr h"n (4) .dvixd zligza hxqd lr y`xd mwenn okide hlwd mwenn okid reci `l , x hlw lr dvixa dvwa riten `l `edy dxwna) el`nyle epinilyk hxqa edylk mewna zetivxa aezk hlwd hlwd lr llk riavn epi` y`xdy okzie) hxqa edylk `z lr riavn y`xde ,
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## This note was uploaded on 03/12/2011 for the course CS 236343 taught by Professor Bensasson during the Winter '11 term at Technion.

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Exercises - h"qyz aia` aygnd ircnl dhlewtd zia ilibxz sqe`...

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