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Problems 9.6 and 9.7 page 209.SSEnd K9ZmT A B@BDS Homework 5 - Jeff AbsherSSEnd/d A8x @mzqk@ Default TextP@@@i@@Default Text Style@@@pE A@x`aAnD}AA"x@@@PP@@@  IPAmT A H@ASSEnd q{oB PP  ZHZOZG  Z ZIYmZLZP:ZNZW AxpA@PX AxpA@P\[u^_`abZJZKZQb(Ru(S%M;(e(f(c(h(j]  # #AyU@@ Default FrameQ A@IQXAAP@DFrameH@@Default Frame Style$@@ Default TextIAAAAc@ @YAfAdAe@ A]@ 0PAm /@ASSEndU@@Default Drop CapQ A@IQXA AP @FDropCapIAxH@@Default Drop Cap Style$@@ Default TextI&AAAyA@!AfAdAe@ X@Dzb%@@ ) ,Bqd@d@FStory ,BWm -PAm ,@ASSEnd 'Ayd@d@FStoryAYAAm 8$q Hyd@d@Story[ HY9A9Amk0mAo@ Note Initials`P@Y@x`al2 :1@Engineering NumberingI8@ OX+@Outline (Not Indented)P@@@i@"@ Left Justified Outline Numbering@@@pE A@A+@D  O @@@QP mrW@@ Default TableQH@@RB0PAAP @ SuperTableH@@Default Table Style Ay@. A@_X@@Default Right ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!qyX@@ Default CellQAA@@@R@0@AAP@CCellH@@Default Table Cell Style$@ @ Table TextI3AAAA@7Ay[AyX@@Default ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!`AyX@@Default Left ColumnQ@H@@@QH0@AAP@CCellX$@@ Default Texty@!1b@Default Headingsa; 'y:qAu *yd@Q $@StoryYAAm 'yd@d@Story_m SmCHHBvSSEnd 'Ayd@d@FStoryAYAAmaSm@D@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE)@@ap@PT@@apE)@@ap@PT@@apE)@@apE(@@ap@P T@@apB)SSEnd9RSm8@D@@ap@PT@@apF.0@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@PT@@a?pE.@@a?p@PT@@apE.@@ap@PT@@apE.@@ap@PT@@apE.@@ap@P QSSEndo,kA @ Note Date`P@Y@x`al2 .A:@Legal NumberingI@ OX+@Outline (Indented)P@@@i@(@&Traditional Indented Outline Numbering@@@pE A@CfD?" @@@QP ,q@Default OutlineI@ OPZa  ' ; # PAm@ASSEnd SmCHHBSSEndTSm@D@@@Px@PT@@@PxE.@@@Px@PT@@@PxE.@@@Px@PT@@@PxE.@@@Px@PT@@@PxE.@@@Px@PT@@@P?xE.@@@P?x@PT@@@PxE.@@@Px@PT@@@PxE.@@@Px@PT@@@QpE.@@@Qp@P QSSEndGoA @ Body Singlep@i@P@@@pE A@Am@D= Xw+@DTitleP@@@i@P@@@pEAm@DdB}q*A # @@@  f\Uw @ Number Listp@i@P@@@pE A@Am@D  ! @@@QP  {U  c '  ZB @GBullet 1p@i@P@@@pE A@Am@D  " @@@RH wOf @ Table Textp@i@P@@@pE A@Am@Db|r}# U[Df @ Heading 3P@@@i@P@@@pEAm@D B}t> # @@@   A CDc  b ZB( @GBullet 2p@i@P@@@pE A@Am@D  " @@@RH c PD[2U @ Heading 2P@ @@ i@P@@@pEAm@D B}t> # @@@   q C2 c (S2 @First Line Indentp@i@P@@@pE A@Am@D-# c P2[(D @ Heading 1P@ @@ i@P@@@pEAm@D B}t> # @@@       &APKmT*\A@B,9.6 for each E between 0 and d describe an @ @ @ EalgR for sequential consistency in which reads take time d - E and writes take time E.SSEnd&*A PRmT A@ASSEnd*J.A&PKmT A@B Sequential @ @ @ Consistancy:SSEnd.b9A*PKmT A@B1) the @ @ @ permuation is legal for every objectSSEnd9~=A.PRmT A@BZ2) for all non-overlapping actions at the same node, order must be preserved at that node.SSEnd=AA9PRmT A@ASSEndAbEA=PKmT A@B(Assume underlying gives totally ordered @ @ @ bdcast.SSEndERAAPRmT A@ASSEndRaVAEP KmT A@BGiven Theory 9.7, t(read) + @ @ @ t(write)F >= dSSEndV{ZARP KmT A@B,So we have to find the best case, and it is @ @ @ theorhetically possible.SSEndZAVP RmT A@ASSEnd^zbAP KmT> A@DX Local read R@ @ @ GalgX for R@ @ @ procXF p(i)SSEndb@A^P KmT A@BWhen @ @ @ read(x):SSEndfEjBHKmT A@AJRead( @ @ @ copy[x])SSEndjnAfPRmT A@ASSEndnArAjPKmT A@BWhen @ @ @ write(x):SSEndrDAnPKmT A@AL@ @ @ tbc-send(x,D v)SSEndzr~APKmT A@BWhen @ @ @ tbc-recv(x,v) from @ @ @ p(j)@ @ @ B:SSEnd~AAzPKmT A@AL@ @ @ Copy[x]:=C vSSEnd#A~PKmT A@AISSEndHKmT A@B89.7 show that if u == 0 then local read and local write @ @ @ Falgs are possible for @ @ @ linearizability.SSEndjPRmT A@BF2) Consider the following implementation of distributed shared memory:SSEnd%E0J mT A@ASSEnd AZI RmT A@ASSEndSAI RmT A@B/Assume that local operations take 0-length timeSSEnd2AI RmT A@BAssume a clockSSEnd AI RmT A@ASSEnd ^AI RmT A@ASSEnd5AI RmT A@BAssume d is knownSSEndbI@ KmT A@AL@ @ @ Waitfor@ @ @ C(E @ @ @ nolocalblock@ @ @ timer@ @ @ E(@ @ @ copy[x]@ @ @ E)@ @ @ B)SSEndAIKmT A@AL@ @ @ localBlock@ @ @ GtimerE @ @ @ (copy[x],E @ @ @ Ed-E)SSEnddAI RmT A@B?Make the local copy of x block local writes until clock expiresSSEndzAIYmT A@ASSEndFArI@KmT A@AJWrite @ @ @ copy(x,v)SSEnd"IKmT? )A@B What this @ @ @ Ealg* does is it allows writes, but then waits @ @ @ I Jd-ED  length of time after any local writes before reading the local copy of x. It also dispatches all remote updates of X before it reads the local copy.SSEndPfAI KmT A@AJ Dispatch any @ @ @ tbc-recvs(x)SSEndAIYmT A@ASSEnd  I RmT A@ASSEnd x#A0KmT A@B,U is part of the message delay in the range @ @ @ G[d-u, d] and u <= dSSEnd#W0 A8RmT A@B2So if U == 0 then the message delay is fixed at d.SSEnd0B#A:KmTifDA@BsWith a fixed & predictable message delay you can perform local reads and local writes and keep the requirements of @ @ @ linearizability@ @ @ C." Like the above algorithm, with a @ @ @ tbc, when writing you merely block for d- length of time before allowing a read on that register then process queued writes. All external writes that have occurred on that register will be queued up by that time, and get processed before the local processor can read the register.SSEnd {W qB_ PP  qPBA@q rAHAmT A@Bonly to @ @ @ Fpi+1- mod n. Messages are delivered in FIFO order.SSEnd{PYmT A@BXThere are n processors p0, p1, ..., p n-1 arranged in a ring, where pi can send messagesSSEnd!ARmT A@ASSEndqAHAmT A@B(sends the message "pi: write v to x" to @ @ @ Fpi+1 mod n. ThenSSEnd AYmT A@ASSEndAHAmT*\A@B if pi receives message @ @ @ F"pj: write v to x" for @ @ @ CiP not equal to j, pi writes v to its local copy of x and forwards the message to @ @ @ Fpi+1 mod n. SSEndAHAmT*\A@Bz if pi receives a message "pi: write v to x", pi writes the message to its local copy of x, and discards the message. SSEnd AYmT A@ASSEndAHAmT A@BIs this @ @ @ EDSM/ implementation sequentially consistent? Is it @ @ @ linearizable? Is it causally consistent?SSEndAHAmT*\A@BEach processor keeps a copy of all shared variables. To read a variable, the processor just reads the copy in its local memory. To @ @ @ `write value v to variable x, piSSEnd1 ARmT A@B YES, No, NO.SSEnd !ARmT A@ASSEnd) ARmT A@B[All write events are seen by all members in the same order. (this should be trivial to see)SSEnd)`RAKmT? )A@Read events may be out of order, and given the definition of happens-before it is possible to have a read operation that is an early read and therefore that read could trigger an operation that violates consistency. Here is an example of an execution that violates all that in a ring @ @ @ A->B->C->A:SSEndR)0) cKm@BDWSSEndmWQ``T@iaAIQXD` CP @ SuperTableL[eR Cbs[( __@RW @ @ SuperTable_8_; y([R` @@Tabley[P@BffI]B.@D` `D g)Wi!A@BQJ0PEgWH@DTableJ_a @ c W g4uw`iaA@Bp0@Eu`H@BRowZ.P u7gv`iaA@Bp0@EvgH@BRowHB.Pv6F ui A@PP`EuH@CCellLy$  y- _Rv @@Story_Wzzwz wyBASSEnd 7u`iaA@Bp0@EvH@BRowHB.P5 i H@PP`EH@CCellL$  /ys_R,@@StoryyWw wBBSSEnd 7`iaA@Bp0@EH@BRowHB.P5 i H@PP`EH@CCellL$  /s_R,@@StoryWw wBCSSEnd 7m`iaA@Bp0@EH@BRowHB.P1e i H@PEH@CCellL+  /s_R @@StoryWw wBASSEnd 7`iaA@Bp0@EH@BRowHB.P1 i H@PEH@CCellL+  /s_R @@StoryWw wBBSSEnd 7`iaA@Bp0@EH@BRowHB.P1 i H@PEH@CCellL+  /s_R @@StoryWw wBCSSEnd 7`iaA@Bp0@EH@BRowHB.P5 i H@PP`EH@CCellL$  /s_R @@StoryWw wBASSEnd 7`iaA@Bp0@EH@BRowHB.P5 i H@PP`EH@CCellL$  /s_R @@StoryWw wBBSSEndZC 7`iaA@Bp0@EH@BRowH B.P5 i H@PP`EH@CCellL$  /s_R @@StoryWw wBCSSEnd 7`iaA@Bp0@EH@BRowH B.P1 i H@PEH@CCellL+  /s_R @@StoryWw wBASSEnd 7`iaA@Bp0@EH@BRowH B.P1 i H@PEH@CCellL+  /s_R @@StoryWw wBBSSEnd 7`iaA@Bp0@EH@BRowH B.P1 i H@PEH@CCellL+  /s_R @@StoryWw wBCSSEnd. gi H@PEH@CCellL+! /s_R @@StoryWw% w@ @ @ EProcSSEnd3sgi H@PEH@CCellL+  /s_R @@StoryWw wCommandSSEnd3sgi H@PEH@CCellL+  /s_R,@@StoryWw% w@ @ @ EMesgSSEnd0rsgi H@PEH@CCellL+  /s_R @@StoryWw w registersSSEnd9Ksui H@PP`EFH@CCellL$ @ /Is_R,@@StoryIWw wX=5, y=5SSEndF9Kvsui H@PP`EKH@CCellLI$ @ I/Ns_RF,@@StoryNWJJwJ! wI Set (x = 0)SSEndK9Fsui H@PP`EeFH@CCellLN$ @ N/hIs_RK,@@StoryhIWOOwO wNFX = 0SSEnde5si H@PEmKH@CCellLh+ @ h/pNs_Re,@@StorypNWiiwi6 wh Set (y = @ @ @ Read(x))SSEndm2rsi H@PE}eH@CCellLp+ @ p/hs_Rm @@StoryhWqqwq! wp X = 5, y =5SSEnd}9si H@PP`EmH@CCellL$ @ /ps_R} @@StorypWw wX=?, y=?SSEnd9si H@PP`E}H@CCellL$ @ /s_R,@@StoryWw wX=?, y=?SSEnd5si H@PEH@CCellL+ @ /s_R @@StoryWw wDX=0SSEnd2rsi H@PEH@CCellL+ @ /s_R @@StoryWw wX=0, y=?SSEnd2rsi H@PEH@CCellL+ @ /s_R @@StoryWw wX=?, y=?SSEnd9si H@PP`EH@CCellL$ @ /s_R @@StoryWw wX=5, y=5SSEnd9si H@PP`EH@CCellL$ @ /s_R @@StoryWw wX=0, y=5SSEnd5mesi H@PEH@CCellL+ @ /s_R @@StoryWw wDy=5SSEnd9si H@PP`EH@CCellL$ @ /s_R @@StoryWw wDy=5SSEnd9si H@PP`EH@CCellL$ @ /s_R @@StoryWw wDx=0SSEnd9si H@PP`EH@CCellL$ @ /s_R @@StoryWw wX=0, y=?SSEnd5si H@PEH@CCellL+ @ /s_R @@StoryWw wDy=5SSEnd2rsi H@PEH@CCellL+ @ /s_R @@StoryWw wX=0, y=5SSEnd2rsi H@PEH@CCellL+ @ .s_R @@StoryPACw wX=0, y=5SSEnd2rsi H@PEH@CCellL+ @ /.s_R @@Story.Ww wX=0, y=5SSEnd 72 `iaA@Bp0@EH@BRowH B.P 7)9`iaA@Bp0@E)H@BRowHB.P )5w+%`iaA@Bp0@E+H@BRowHB.P+5 )i H@PP`E2)H@CCellL.$  ./5s_R+ @@Story5W//w/ w.BCSSEnd25 i H@PP`E9+H@CCellL5$  5/<.s_R2 @@Story<.W66w6 w5BASSEnd95 i H@PP`E?2H@CCellL<$  </B5s_R9 @@StoryB5W==w= w<BBSSEnd?9  si H@PP`ED9H@CCellLB$ @ B/G<s_R? @@StoryG<WCCwC wBX=0, y=5SSEndD9si H@PP`EI?H@CCellLG$ @ G/LBs_RD @@StoryLBWHHwH wGX=0, y=5SSEndI9%!s)i H@PP`EDH@CCellLL$ @ L/Gs_RI @@StoryGWMMwM wLX=0, y=5SSEnd7rsui A@PP`EIH@CCellL$ @ )Ls_R @@StoryL w:si A@PP`EH@CCellL$ @ )s_R @@Story w:}si A@PP`EH@CCellL$ @ /s_R,@@StoryW::w6r}si H@PP`EH@CCellL$ @ /s_R,@@StoryWw:si A@PP`EH@CCellL$ @ /s_R,@@StoryWw:si A@PP`EH@CCellL$ @ /s_R,@@StoryWw6rsi H@PP`EH@CCellL$ @ /s_R @@StoryW--w GwSSEnd GwSSEnd:si A@PP`EH@CCellL$ @ )s_R @@Story w:si A@PP`EH@CCellL$ @ /s_R,@@StoryWVVw6rsi H@PP`EH@CCellL$ @ /s_R,@@StoryW//w:si A@PP`EH@CCellL$ @ /s_R,@@StoryW99w7rsi A@PP`EH@CCellL$ @ /s_R,@@StoryW..w:si A@PP`EH@CCellL$ @ )Cs_R @@EStoryC w7rsi A@PP`EH@CCellHB$ @ )s_R @@Story w GwSSEnd: 2si A@PP`E H@CCellL$ @ / @s_R,@@Story @WWWw :?si A@PP`E H@CCellL $ @  )s_R  @@Story w 6r?si H@PP`E H@CCellL$ @ ) s_R  @@Story  w:9si A@PP`E H@CCellL$ @ /s_R,@@StoryW88w:Dsi A@PP`EH@CCellL$ @ )s_R @@Story w6rDsi H@PP`EH@CCellL$ @ ) s_R @@Story  w:!+s)i A@PP`E!H@CCellL $ @  /$s_R,@@Story$W??w!:Is)i A@PP`E%H@CCellL$$ @ $)( s_R! @@Story(  w%3rIs)i H@PP`z!H@CCellL($ @ ($r$s_R% @@DStoryr$ w- GwSSEnd. GwSSEnd/ GwSSEnd0BRAKmT? )A@BSo in the above table, the @ @ @ GSet(x"D =0) A OHappens beforeA O the @ @ @ set(y=E @ @ @ read(x))/ because they happen at the same node/processor., and yet consistency is violated because the @ @ @ read(x)V returns an incorrect value. Therefore at least causal consistency is not maintained. SSEnd8 GwSSEnd9 GwSSEnd: GwSSEnd? Gw SSEndB"Q0mT A@ASSEndQbJ BA!KmT? )A@BIs it @ @ @ linearizable?S No, in the above situation, there is no way to reorder the operations to maintain @ @ @ consistancy that respects the order of operations that was performed by A. Since the only 2 operations were by A, they cannot be reordered, yet they return incorrect values.SSEndV GwSSEndW GwSSEndJ !Q QA#RmT A@ASSEndQ R J A#HAmT A@BIs it sequentially @ @ @ consistant@ @ @ C, yes, it is similar to @ @ @ Ealg 9.1 from page 201SSEndR $uQ #J` AmT A@ASSEndV rR HBA@W  W t{BV PP  X  v` V _ rR HBA@{`  X s_ H$@P@P P P DiEa H@H@@P@@P@@PPpPP`@p@P P wV=f DQGAOALQPQHATANAYAZAVAUAWAXA\A[A^A_A`AaAbAIAJAKAQARASAM dAeAfAcAgAhAiAjP AH dP@QH pcPa cpccpcPaH pcPaUUH cpcP@QHdP@QTT cpcP@QTT cpcP@QH dP@QUUH cpcP@QHdP@P@@Times New RomanHWH@ MS Sans Serif H @ WingdingsH @ Arial Black H@Arial hWHGH@ ]AAQrys@@George P. Burdell832882267FA iaA@H@@P@@P@@PPpPP'@%C:\lotus\smasters\wordpro\default.mwpH@p@P P pAJFaxBADX'@@D od@@@@@@@ULetter?DfaxX?????B'd@PB@@@ENe00:@CFax @winspoolP@E1-9999XPDUVerD@P@Original Version @IBM_USERW=3=`@@ASMHV=f QA A Q QAA AAAAAAAAAAAAAAAAAAAA !A"A#A A$A%A&A'(A)A*A+A,A-A.A/A0A1A2A3A4A5A6A7A8A9A:A;@ A A A QAAQ>A?AAAB@@IBM_USER1023587414A DYƤ1:.P@@CHH@sh PIHBJN   KnI II}I!IIIIII<IIIII I*IiIWI{IIEINIIIoIIIIII>II,I5IGIPIYIbIkIxIIIIIIIIIIIPI II$I0I<IHIIIHLQIIkI I( IIIIIIII1II%IIIII IN IFI_II=IIxI9IIIIIIIIII I'I I0IvIcI IqI I IVIIIIIIII[III@II IIkI IoIiIIIpII}III!IZIII'IiI I"IYI I I I $IP%IKI I"%II%IxIII I I$IIII#IIIIINI.IIu I!I&IIo#I I #IIUIv$I$II$I I#It"III"I$!I"+YƤ1}Qv1XA<U]1!@Ec1AFe1H@a @F2"@U&/2! ?0/2*G${R02UE72#E{23FKM5@EV=    7  V={ CYg(Z @@@PPPPPPA@PPBAHHII IIxIIDIOIII IIIIIIt I I I!Ig ITII IIa I=ITIII Ij II{IIIIIIIeIJIIIIIIII I" I!I6 II Id II#I"I!I1 IIITI]IfI3%I%I&Im&I&I]'I'I'I(I~(I)I()I)I)I?*If*I*I*Iu+I+I+I,I-I5-I]-I-I-I.IB.I.IK/I/IE0Il0I0I1I=2Id2I2I 3Ik3I5I5I5I5IY6I6I7I~7I7I8IG9Io9I%:I ;ID;Im;I;I_=I=I=I>I\>I> IW I>Im I>I>I2?Ip?I?I?I@I@@Iw@I@I@IAIIAIhAIAIAIBI6BIuBIBIBICICCI|CICICIDINDIDIDIDI EIWEIvEIEIEIEI6FIUFIFIFIGI#GIbGIGIGIGI0HIiHIHIHIHI,IIYIIIIIIII+JIbJIJXGV=ARHAAA AA AA AHHHHHAAHHD AAAHHAu@@@@@@@H@@@@@A@@@@@@@@APKA@HAJI%KIfKIKIKILI;LIdLILILILI     > r_` `^L L   Lg#' %  & )*H          (!#1      "&!!!/}  }{}>o!o!o!o." !!1! !" */! ! !' u!u!u!uNe" e!  e!e)   +| | |} 06R M M  P3ka a   eDUIJ  K) qj j  j,x `a g#F &  '   )m i i m  X =           <z q rsz z } MiscellaneousMiscellaneousFileProtectionHeaderLWPStreamTypePreviewWordProData   xx0͓Ɠ ۓCMHdr