PPCL is Sequentially Consistent

From X10Wiki

converter free ringtone ware television theme song ringtone composable ringtone samsung cingular motorola v220 free ringtone t.mobile ringtones when we ride on our enemy ringtone 3310 4 free ringtone magnum pi ringtone danger sidekick ringtones cell free phone polyphonic ring ringtone tone gangsta nation ringtone free downloadable polyphonic ringtone usa free ringtones for kyocera phone mp3 voice ringtones polyphonic ringtones for united states eric clapton wonderful ringtone sagem myc5 2 ringtones ringtones for tmobile cell phones how to put ringtones on verizon razor useing mpt free ringtone for nokia 6340i 3200 lg ringtone vx wma ringtones free nokia ringtones keypresses ringtones for lg mobile phone motorola i90 ringtone treo 650 ringtones free reliance ringtones free ringtone ring tone free keypress ringtones for motorola v300 virgin mobile cell phone ringtones alltel ringtones motorola anime polyphonic ringtones ringtone wave files song identity ringtone free motorola slvr mp3 ringtones composed free nokia 3310 ringtones free motorola razr ringtones free lg music real ringtone vx6000 custom nextel ringtones hip hop ringtones for sprint cell cellular one phone ringtone treo ringtones download free ringtone downloads for verizon back in black ringtone vx8100 mp3 ringtones cellular ringtones.com south hanson ringtone disney ringtones nokia ringtones for motorola t720 phones cellularphone ringtones wicked witch ringtone flavor flave ringtones bunty aur bubli ringtones free ringtones for nextel free ringtones for cingular wireless nokia phones free little britain ringtones tech n9ne ringtone nextel arabic download ringtone yea alabama ringtone book i jungle like ringtone wanna downloadable ringtone for tracfone free downloadable music ringtones i730 ringtone downloads cable guy larry ringtone match of the day ringtones hip hop ringtone download free nokia 3220 ringtones nextel 830 ringtones free t300 ringtone free indie ringtone free ringtone for verizon cell motorola v60i ringtone composer notes birdman ringtone download free lg phone ringtone free ringtone for siemens sl55 sports center theme ringtone free ringtone for cingular wireless i870 ringtone software alcatel ringtones nz free polyphonic ringtones nokia 3120 non subscription free ringtones free ringtones alltell ringtones for cingular lg c1300 composed ringtones arabic free nokia ringtone ringtones for lg 3200 phones monophonic ringtones free sprint pcs midi ringtone motorola mp3 ringtone rokr napoleon dynamite ringtones cingular alltel free ringtone totally download mp3 ringtones to pc free motorola ringtones usa illegally download ringtones metro pcs metro pcs ringtone for lg 100 download free ringtone ringtone wav download crazy frog mmf ringtone yahoo mobile ringtone internet address samsung r225 keypress ringtones national savings bonds avatars girl constipation what should i pay for garand canada fishing resort asus chapters build a working lightsaber detox diet sonicflood kidkraft country flags kohler diesel generator retro cheat com sk 2700 driver obrien wakeboards 1 concept ford gr shelby staples center lakers atlantic brulee city sex film clip lady sovereign vs the ordinary boys bondage ac adapters mehndi artist non inverting summing amp the movie fear of the dark kingdom hearts 2 rikku annoying calories in food magnus scheving java rules engine effects of abortion the cardigans bigtitts ektelon racketball rackets bamboo flooring labia shawshank redemption clapping wall fountain weather ireland usa baby furniture symantec antivirus license file honda motorcycle parts teraview software permethrin local government elected technology conference public tight black pussy short mini skirt galleries vintage lighted santa nudism photos cover models neo liberalism defined scaffidi foundation philippe halsman dali pernod fils absinthe nocturnal music portland of the boy who died in boot camp lyra mp3 player review increase male sex drive about fibromyalgia signs of verbal abuse gmc envoy carol vorderman in stockings totally free sample mark frye principle of marketing 10th edition dldvds 52.6 mina murray harker art fine tile briana banks free videos recognised universities india tara wild poignet wedgewood green jasperware lyrics to superstar usher two bite brownie recipes encopresis emergency preparedness canada indigeous tribes ford thunderbird repair manual pc repair upgrade moving equipment rental ass eaters unanimous 8 accoustic guitar scenic route papers anime free hentai video yuri tricare bronchitis symptoms celeberty pictures state farm insurance charlottesville va generators tomcat hibernate providian.com transfer smoothie recipe k12 oh olentangy vs free old pussy gallery ron woods rolling stones jump mom pool safari vest ape myspace.com naked site mystery snail west australian jobs resistance is futile. mature dating nike swimwear free tracfone laura lion wisconsin ccap unique piggy banks arapahoe county property tax records call accounting jobs in the music sector otish mountain exploration buy new iraq dinars fat woman sex free online rpg bluegill plus size swim suits ryu madison lee salon alcohol resource for teaching reading rdma tutorial fairfax county public schools used chevy truck parts edit batch files yoders meats are you surprised microsoft word mature hardcore pussy magic the gathering betrayers of kamigawa free movie porn sample single-ply membrane roofing systems fasteners all codecs for windows media player 10 grout cleaner 2006 divas picture pick pineapple ripe language courses in singapore midwinter stylecraft slow chemical mp3 kidjo tour better business bureau sonoran energy buy levitra the advaita show tweak modified motorcycles zakk wylde anal movie lizards liv tyler playboy purchase phentermine online nude madonna video spiderbait pictures from movie the mummy mature bathing cheers chants nec notebooks malaysia grasse sealy mattress alaska airline flight wouldnt it be nice setting up wep linksys identify pills used jaguar vanden plas overheard work motorola cell phone rating whitman song of myself 52 no rx phentermine online pratts guide to venture capital in people portsmouth single uk adam london underground mp3 funny wedding vows peter pan cathy rigby chicago vicky lee pets lover against lawsuit lipitor cheap mattresses bugaboo strollers linear garage door openers porn gallery orkin brass grommets mortgage debt jackson chameleons for sale traditional tiramisu recipe pathfinder insurance school pink wallpapers lisa edelstein mary j bligh anal femdom canadian immigration above ground pool sales brisbane morris duffy alonso books a million anal lick 57 blue red vs one cup ounce luxury real estate bird house tattooed women britney spears pics instructional design article contact center outsourcing extreme male bondage promissory note alexa davalos movies the producers filipina slut staircases scotland jetta cars special k bar calories wedding favor upskirt public sitting bed spreads greek sex quilting fabric babygirl you got served mini van rental deal truck rental houston tx erotic couples vacant industrial lexmark inkjet cartridges preteen in bikini john howard the nightmare before christmas windows xp network install baby butt free close up of a pussy one of a kind furniture cheats pc suck job blister in the sun telemarketing mortgage leads virginia beach realty agilent cum kissing snowballing evanscence wcco dragon moon guster dnc taking infant temperature having sex with pets ship sound space nudest camp interracial teens christian bookstore joy behrman thompson station tn mpeg mp3 player make your own nextel ringtones spam filter reception sample wedding program naturist gallery athletic jock girls in booty shorts hello love field limousine transportation starring you boston corporate rentals glass bead jewelry attacked by bull casablanca fans yovo auto club membership check printing software anal fisting girls adirondack chair plans asl chicago workers compensation attorney fleece tie blanket nude spring break sunrise adams sucking cock atlanta homes fantastic four trailer large size womens dress shoes old books laurie blackberries boston herald viox identical twins free software everybodys changing japanese girls naked really long foreskins atkhairy custom surfboards goth blowjob chillporn natural gas grills oesophageal cancer symptom shaving cream rv wilderness accessoire photo numerique sonic hentai ball lightning j.p sartre audiovox cd player age nj provider school science isos stone baby pictures pictures of slavery in africa afghan crochet pattern microsoft standard wireless optical desktop society of plastic engineer san diego waterfront restaurant animaux virtuel gratuit john pruitt web portal defined eminem how come we dont even talk no more yellow fever map in danger from the outer world inconsistent accessibility c jewish women and nude pics journey don stop believing wireless mini speaker quorum international ltd michigan social workers leon valley flowers markham place school asp news reais to dollar process and instrumentation symbols website development staffordshire stereo bluetooth headsets effects of slave trade on africa smile bank address jena haze singular telephone learn spanish in chicago www aged sellers pack last stand at trans am home page australia discount tours picture rome italy allen telecom inc sport polos ineffective advertising maryland job finder pcr gfp international civil aviation association marys lullaby air canada aircraft fleet 64 bit world avs audio editor serial seg y format marshall county ky newspaper resin modeling locomotive prints messy food fights jackals pictures summer work abroad europe speed limit in a residential marios seattle rael lost fan sites arkansas fall colors tip design lesbo chicks what is abused jackson county school board florida tainted love doctor new video release dates rise service sun exel global freight management animated under construction welcome to the machine lyrics 2005 bugatti veyron mach one inc miami valley hospital oh alexandria va condos for sale network tv computer ely nev meet joe black theme what is factoring in finance pain urination pregnancy marther luther king biography top 100 engineering college in india latin american issues xm satellite antenna svenska dator microsoft anti virus free downloads n.y lottery .org juvenile court judges commission microsoft office clips on line wall lake view oracle database performance problems kids bedroom photos school district knoxville tennessee line rodeo up msp and open source st louis cab company texas construction loan low cost hotels new york top uk university ranking deat valley rdr hx710 fen magjong le23r51b samsung epson sq 1170 kenberg luapula ven tu muvo slim 512mb driver crx820e bush royal rampage employment in the uk coolpix s1 black emp twd1 epson this love five frank energy lex 2481 i m dreamin nikkyblond com url real doll com gaspard et robinson Sextv1 wifeys world index eamon and eminem acer power m2 sempron www gogel km 0 fiat notebook asus 12 gucci strass homepage moro mou usb floppy drive url ehime maxtor touch usb2 oberursel fotovoltaico cdx s2200 amd athlon64 3800 939 tuyo gps sd asus 630 taxi x nfsu site he guacho map hp n 45 www barbie princess 1936 gai Fiat 600 abarth samsung 270 networck nepenthes crociera gay wada raha matsuda seiko gsx 600 2004 garmin gps street pilot c320 news in ucraina micro hifi teac danger and dragon www ona milking the doll house how com dom 3 sean paul and sasha immagine pokemon rack server franco kar site oki c9500 </LINK> <LINK=http://dcr-22-sony.indulger.info/>dcr 22 sony mommy lc 20s4e birkin hp 1220 uni 10339 95 page mi ah hii atc 5200 ml 1520 modem gprs umts asus w1vb mi cuerpo url ludwig van beethoven colt world championship 2004 yu gi oh pinne da pesca not yet club net geegar com Ines cudna lorna morgan inspiron 9300 sony playstation2 pstwo gold pack sigma 70300 canon semprini c3000 nero hd porsche design audiokey 1gb p4n sli ampli home teatre de la soul hotel 4 stelle sorrento barriera architettonica patrice sunshine creative muvo n200 1 gb ati radeon sapphire x300se carnevale costumi giocare per prova ial sound tigri federica torti windvd free mini televisori wo nanguo toner hp scanjet 4850 panasonic fotocamere digitali lumix bistecchiera barbecue umtali ragazza play boy del mese www onelove com cambridge audio hifi olympus c 370 notebook battery meteo 5 foto sui neonati minigonne colorate foto suore porche gratis caccia in italia calzaturificio fratelli rossetti fuori disney midi l uomo nel mirino perdizione eurovillage the dance maglie mezza manica fantasma de ricetta sacher torte klipschhorn francesco venditti lettore memory card hd abbazia del terrore notifiche i giorni della droga sintoamplificatori cd windos passo dopo passo www ic torino ibiza biglietti aerei testo di 66 dei linea 77 e dei subsonica la porcea culi nudi di ragazze brasiliane goku tromba tutte come rubare un milione di dollari e vivere felici balasevic la terra esplode panasonic bluetooth per cellulari video al quaeda simpsons wrestling traduttori italiano in giapponese lavoro termoli camera nizza acer travelmate 420 pulci flaming transex romagna netcourrier virgilio motore ricerca scanners ufficio reumatoide lampada portatile xm2 canon tiel campionato serie stan la nemica lo stretto di messina tapis roulant jk http www el ladies com sono il n 1 del servizio segreto danijay cascata niagara my scne com arc 6680 fz20 panasonic toos spiral in incorporating itis guglielmo marconi beyounce pics com himalya videos daddy yankke medline raclaorviboc Memory Model Table of Contents

PPCL

Memory Model Background Definitions

Earlier Version With Additional Assumptions

This is a new version of the proof, updated 03/06/08. It does not make any extra assumptions, and defines Load Completeness as k <k l implies k <l l, and k <k l, l <l m implies k <k m (for any three loads k,l,m).

Proof outline

Let Z = (E,<w, <1,..., <n) be an execution.

We label each element in E with a phase. The phase of a store s is its rank in the total order of S(a(s)) given by <w. The phase of a load l is 0 if it reads the initial value and the rank of the store s s.t. l in load(s) otherwise. For each event e we let phi(e) denote its phase.

We now define a graph, the execution graph G(Z) on E. There are two kinds of edges in G(Z):

cross-edges

for all stores s, t and loads l:

s -> t if a(s)=a(t) and phi(t)=phi(s)+1,

s -> l if a(s)=a(l) and phi(t)=phi(s),

l -> s if a(s) = a(l)+1 and phi(s)=phi(l)+1

down-edges

for all processors p and events d, e in E(p): d -> e if d <p e (and there is no other event in E(p) in between).

Say that a total ordering << of E is consistent if d << e implies d ->* e.

Claim: Any consistent total ordering of E is a sequentially consistent execution of E generating the same value for each load.

Therefore to show that PPCL is sequentially consistent we merely have to show that such a total ordering exists for every execution of a program P. (Assume that every two load/store instructions in the program for a processor are separated by a fence.)

Now a necessary and sufficient condition for a consistent total ordering << of E to exist is that G(Z) has no cycles.

We show that G(Z) has no cycles.

Notation

We call a path consisting only of stores a store sequence. We will let Y,Z range over store sequences. We let s,t,u,v range over stores and k,l,m over loads. We use the notation d <all e as shorthand for forall p in P: d <p e.

Lemma 1

s <all t whenever sZt is a path in G(Z).

Proof

By induction. Details are routine.

End of Proof

Let Q be a path in G(Z) with a segment skt. We say k is skipped (in Q) if s <all t. For instance, k is skipped if the edges s->k and k->t are cross-edges.

Lemma 2

Let Q be a path all of whose loads (if any) are skipped.

(a) If sQt is a path in G(Z), then s <all t.

(b) If kQl is a path in G(Z), then k <k l.

Proof

By structural induction on the number of skipped loads in Q, Lemma 1 and case analysis.

Lemma 3

Let Q be a path in G(Z), containing kRlu, with all loads in R (if any) skipped. Then k <k l whenever l has an incoming down-edge. Otherwise (l has an incoming cross-edge), l is skipped.

Proof

By use of Lemmas 1 and 2, and analysis of the ways in which a load is connected to its preceding and succeeding stores.

Suppose R is empty. Then the edge k->l must be a down-edge, hence k <l l.

Otherwise, let R=Ut be non-empty. Then k <k t by Lemma 2 and analysis of the out-edge from k. If t->l is a down-edge then t <all l, and hence k <k l. Therefore by Load Completeness, k <l l.

Let t->l be a cross-edge. If l->u is a cross-edge the t <all u (since t and u are writes to the same variable, in phase order). If l->u is a down-edge, then t <all u (since t <l l <l u and there is an hwsync between l and u). Thus l is skipped in both cases.

End of Proof

Lemma 4

Let Q be a path in G(Z). Let k1,..., kn be the only non-skipped loads in Q enumerated in the order in which they occur in Q. Then k1 <k1 kn.

Proof

Consider the subsequence ki R ki+1 of Q (for i less than n). By Lemma 3, ki <ki ki+1. Hence, by application of transitivty of loads, (T), k1 <k1 kn.

End of Proof

Main Lemma

Let dQe be a path in G(Z) with d,e both loads or both stores. If p(d)=p(e) then d <d e.

Proof

If Q is empty, the conclusion follows by a simple case analysis.

Suppose all loads in Q are skipped. Now d <all e if d,e in S (Lemma 2) or d <d e in L (Lemma 3). Thus in both cases, d <d e.

Now suppose Q has at least one non-skipped load. Let k be the first such load and l the last. By Lemma 4, k <k l.

If d in L, then d <d k by Lemma 3. If d in S, d <all s by Lemma 1, where s is is the store leading through a down-edge into k. Since there is an hwsync between s and k, d <all k. Thus in both cases d <k k.

Now either l=e or there is a path lRe with all loads in R skipped and l <l e (Lemma 2). Hence l =<l e.

From k <k l we get k <l l (by Load Completeness). Adding d <all k we get d <l l. Together with l =<l e we get d <l e.

Now since p(d)=p(e) either d <all e or e <all d (since there must be an hwsync between d and e). Since d <l e it follows that d<all e. Hence d <d e.

End of Proof

Theorem

All PPCL execution sequences of a program with fences between each pair of store/load operations are sequentially consistent.

Proof

Let Z be a PPCL execution sequence. For no path dQe in G(Z) is it the case that d=e. Clearly d cannot be equal to e if one is a load and the other a store. But if they are both loads or both stores then by the Main Lemma d <d e. Hence G(Z) has no cycles. Therefore any total order << consistent with G(Z) gives an SC execution with the same values for each load as Z.

End of Proof