S`QiQ+QH mbBM; i?2 ar22T@GBM2 J2i?Q/
H2DM/`Q _Q/`ő;m2x- G`b JB+?2H E`Bbi2Mb2M M/ /`BM _miH2 .2T`iK2Mi Q7 *QKTmiBM;- Ji?2KiB+b- M/ S?vbB+b- q2bi2`M LQ`rv lMBp2`bBiv Q7 TTHB2/ a+B2M+2b- "2`;2M- LQ`rv
&`i2-HKF`-`m'!?pHXMQ
#bi`+iX JZhh Bb Tm#HBb?@bm#b+`B#2 +QKKmMB+iBQM T`QiQ+QH i?i Bb #2+QKBM; BM+`2bBM;Hv mb2/ 7Q` BMi2`M2i@Q7@i?BM;b UAQhV TTHB+iBQMbX AM 2`HB2` rQ`F r2 ?p2 /2p2HQT2/ 7Q`KH M/ 2t2+mi#H2 KQ/2H Q7 i?2 JZhh T`QiQ+QH mbBM; *QHQm`2/ S2i`B L2ib U*SLbV M/ T2`7Q`K2/ M BMBiBH p2`B}+iBQM Q7 #2?pBQm`H T`QT2`iB2bX AM i?Bb TT2` r2 BMp2biB;i2 i?2 mb2 Q7 i?2 br22T@HBM2 K2i?Q/ 7Q` p2`B}+iBQM Q7 i?2 JZhh *SL KQ/2H BM Q`/2` iQ HH2pBi2 i?2 2z2+i Q7 i?2 bii2 2tTHQbBQM T`Q#H2KX q2 7Q`KmHi2 i?2 #2?pBQm`H T`QT2`iB2b mbBM; *QKTmiiBQM h`22 GQ;B+
U*hGV M/ b?Qr ?Qr iQ 7Q`KmHi2 T`Q;`2bb K2bm`2 7Q` i?2 br22T@HBM2 K2i?Q/ #b2/ QM i?2 KBM T?b2b Q7 i?2 JZhh T`QiQ+QHX hQ T2`7Q`K p2`B}+iBQM Q7 i?2 *hG T`QT2`iB2b- r2 mb2 bQK2 T`QT2`iv@bT2+B}+ H;Q@
`Bi?Kb i?i `2T`2b2Mi }`bi bi2T iQr`/b KQ`2 ;2M2`B+ *hG KQ/2H +?2+FBM; H;Q`Bi?Kb +QKTiB#H2 rBi? i?2 br22T@HBM2 K2i?Q/X
R AMi`Q/m+iBQM
h?2 /2p2HQTK2Mi Q7 /Bbi`B#mi2/ bQ7ir`2 bvbi2Kb Bb +?HH2M;BM;- M/ QM2 Q7 i?2 KBM TT`Q+?2b iQ i+FH2 i?2 +?HH2M;2b Bb iQ #mBH/ M 2t2+mi#H2 KQ/2H Q7 i?2 bvbi2K T`BQ` iQ BKTH2K2MiiBQM M/ /2THQvK2MiX *QHQm`2/ S2i`B L2ib U*SLbV (RR) Bb 7Q`KH KQ/2HHBM; 7Q`KHBbK +QMp2MB2Mi 7Q` bT2+B7vBM; +QKTH2t +QM+m``2Mi M/ /Bbi`B#mi2/ bvbi2KbX *SL hQQHb (N- Rj) Bb bQ7ir`2 iQQH i?i bmTTQ`ib i?2 +QMbi`m+iBQM- bBKmHiBQM U2t2+miBQMV- bii2 bT+2 MHvbBb- M/ T2`@
7Q`KM+2 MHvbBb Q7 *SL KQ/2HbX PM2 Q7 i?2 F2v 7mM+iBQMHBiB2b Q7 *SL hQQHb Bb i?2 #BHBiv iQ T2`7Q`K KQ/2H +?2+FBM; (R) Q7 i?2 KQ/2HH2/ bvbi2KX h?Bb K2Mb i?i QM2 +M ;2M2`i2 i?2 bii2 bT+2 Ub2i Q7 `2+?#H2 bii2bV Q7 bvbi2K BM Q`/2` iQ p2`B7v F2v #2?pBQm`H T`QT2`iB2bX h2KTQ`H HQ;B+b (RN) bm+? b *QKTm@
iiBQM h`22 GQ;B+ U*hGV M/ GBM2` h2KTQ`H GQ;B+ UGhGV `2 rB/2Hv mb2/ iQ 2tT`2bb #2?pBQm`H T`QT2`iB2b Q7 bvbi2KbX
JZhh (k) Bb Tm#HBb?@bm#b+`B#2 K2bb;BM; T`QiQ+QH 7Q` AQh bmBi2/ 7Q` +QM@
bi`BM2/ 2MpB`QMK2Mib bm+? b J+?BM2@iQ@J+?BM2 +QKKmMB+iBQM UJkJV M/
AQh +QMi2tib /2bB;M2/ rBi? i?2 BK Q7 #2BM; HB;?i@r2B;?i M/ 2bv iQ BKTH2K2MiX AM 2`HB2` rQ`F (Re)- r2 ?p2 /2p2HQT2/ 7Q`KH M/ 2t2+mi#H2 bT2+B}+iBQM Q7 JZhh (k) KQiBpi2/ #v i?2 7+i i?i JZhh Bb mMiBH MQr QMHv bT2+B}2/ mb@
BM; M UK#B;mQmbV Mim`H HM;m;2 bT2+B}+iBQMX JZhh +QMiBMb `2HiBp2Hv
+QKTH2t T`QiQ+QH HQ;B+ 7Q` ?M/HBM; +QMM2+iBQMb- bm#b+`BTiBQMb- M/ [mHBiv Q7 b2`pB+2 H2p2Hb `2Hi2/ iQ K2bb;2 /2HBp2`vX Pm` BMBiBH p2`B}+iBQM rb +QM/m+i2/
mbBM; Q`/BM`v 7mHH bii2 bT+2 b bmTTQ`i2/ #v *SL hQQHb M/ Qm` BMBiBH 2t@
T2`BK2Mib +H2`Hv ?B;?HB;?i2/ i?2 T`2b2M+2 Q7 i?2 bii2 2tTHQbBQM T`Q#H2K (3- R3) r?B+? Bb +mb2/ #v i?2 2tTQM2MiBH ;`Qri? BM i?2 MmK#2` Q7 `2+?#H2 bii2b Q7 i?2 bvbi2KX
H`;2 T`i Q7 i?2 KQ/2H +?2+FBM; `2b2`+? ?b BK2/ i /2p2HQTBM; i2+?@
MB[m2b 7Q` HH2pBiBM; i?Bb BM?2`2Mi +QKTH2tBiv T`Q#H2KX q2 +M }M/ b2p2`H /Bz2`2Mi 7KBHB2b Q7 `2/m+iBQM K2i?Q/b i?i ?p2 2K2`;2/ /m`BM; i?2 Hbi v2`b Ubm+? b T`iBH@Q`/2` `2/m+iBQM K2i?Q/b (d) M/ ?b? +QKT+iBQM (Rd)V r?B+? i`v iQ `2/m+2 Q` T`QpB/2 KQ`2 +QKT+i `2T`2b2MiiBQMb Q7 i?2 bii2 bT+2X >Qr2p2`- bBM+2 i?2 KQmMi Q7 K2KQ`v Bb Q7i2M i?2 HBKBiBM; 7+iQ` BM KQ/2H +?2+FBM;- r2 7Q+mb QM i?2 7KBHv Q7 K2i?Q/b i?i +QK#i bii2 2tTHQbBQM #v /2H2iBM; bii2b 7`QK K2KQ`v /m`BM; bii2 bT+2 2tTHQ`iBQMX aT2+B}+HHv- r2 +QMbB/2` i?2 br22T@
HBM2 K2i?Q/ (Ry) r?B+? Bb #b2/ QM i?2 B/2 Q7 2tTHQBiBM; MQiBQM Q7 T`Q;`2bb 2t?B#Bi2/ #v KMv bvbi2KbX q2 7Q+mb QM *hG bBM+2 *SL hQQHb BKTH2K2Mib
*hG@HBF2 i2KTQ`H HQ;B+ +HH2/ aE@*hG (j)X aE@*hG 2ti2M/b *hG BM Q`/2`
iQ iF2 BMiQ ++QmMi #Qi? bii2 M/ i`MbBiBQM BM7Q`KiBQMX
h?2 +QMi`B#miBQM Q7 i?Bb TT2` Bb irQ7QH/, URV i?2 BKTH2K2MiiBQM Q7 i?2 br22T@HBM2 K2i?Q/ mbBM; i?2 aiM/`/ JG UaJGV HM;m;2 iQ;2i?2` rBi? i?2
#BHBiv Q7 T2`7Q`KBM; KQ/2H +?2+FBM; Q7 +2`iBM #2?pBQm`H T`QT2`iB2b bT2+B}2/
mbBM; iBHQ`2/ *hG br22T@HBM2 KQ/2H +?2+FBM; H;Q`Bi?Kb (R9)c M/ UkV i?2 TTHB@
+iBQM Q7 br22T@HBM2 #b2/ *hG KQ/2H +?2+FBM; iQ Qm` *SL KQ/2H Q7 i?2 JZhh AQh T`QiQ+QHX
h?2 `2bi Q7 i?Bb TT2` Bb Q`;MBb2/ b 7QHHQrbX AM a2+iX k r2 BMi`Q/m+2 i?2 br22T@HBM2 K2i?Q/ M/ *hG KQ/2H +?2+FBM;X a2+iBQM j ;Bp2b #`B27 `2pB2r Q7 i?2 *SL KQ/2H Q7 i?2 JZhh T`QiQ+QHX q2 /2b+`B#2 i?2 2tT2`BK2Mib +``B2/
Qmi M/ i?2 bbQ+Bi2/ `2bmHib BM a2+iX 9X 6BMHHv- BM a2+iX 8- r2 bmK mT i?2 +QM+HmbBQMb M/ QmiHBM2 /B`2+iBQMb 7Q` 7mim`2 rQ`FX h?2 `2/2` Bb bbmK2/ iQ #2 7KBHB` rBi? i?2 #bB+ +QM+2Tib Q7 *SLb M/ *hG KQ/2H +?2+FBM; i2+?MB[m2bX
k "+F;`QmM/
AM i?Bb b2+iBQM r2 BMi`Q/m+2 i?2 br22T@HBM2 K2i?Q/ M/ i?2 bbQ+Bi2/ *hG KQ/2H +?2+FBM; H;Q`Bi?Kb- M/ ?Qr r2 ?p2 BKTH2K2Mi2/ M/ BMi2;`i2/ i?2K BMiQ *SL hQQHbX
kXR h?2 ar22T@HBM2 bii2 bT+2 2tTHQ`iBQM K2i?Q/
h?2 br22T@HBM2 K2i?Q/ (9) Bb BK2/ i bvbi2Kb 7Q` r?B+? Bi Bb TQbbB#H2 iQ /2}M2 K2bm`2 Q7 T`Q;`2bb #b2/ QM i?2 bii2b Q7 i?2 bvbi2KX h?2 T`Q;`2bb K2bm`2 Bb Q7i2M bT2+B}+ 7Q` i?2 bvbi2K mM/2` +QMbB/2`iBQM- #mi i?2 F2v T`QT2`iv Q7 KQMQiQMB+ T`Q;`2bb K2bm`2 Bb i?i 7Q` Mv ;Bp2M bii2 b- HH bii2b `2+?#H2 7`QKb?p2 T`Q;`2bb pHm2 r?B+? Bb ;`2i2` i?M Q` 2[mH iQ i?2 T`Q;`2bb pHm2 Q7 bX .2}MBM; T`Q;`2bb K2bm`2 Q7 i?2 bvbi2K KF2b Bi TQbbB#H2 iQ Q`;MBb2
i?2 bii2 bT+2 BMiQ Hv2`b bm+? i?i bii2b i?i b?`2 i?2 bK2 T`Q;`2bb pHm2
#2HQM; iQ i?2 bK2 Hv2`X
h?2 #bB+ B/2 Q7 i?2 br22T@HBM2 K2i?Q/ Bb iQ 2tTHQ`2 i?2 bii2 bT+2 BM H2bi@T`Q;`2bb@}`bi Q`/2`- QM2 Hv2` i iBK2- bm+? i?i QM+2 HH bii2b BM ;Bp2M Hv2` ?p2 #22M T`Q+2bb2/- i?2v `2 `2KQp2/ 7`QK K2KQ`v M/ i?2 2tTHQ`iBQM T`Q+22/b iQ i?2 M2ti Hv2` (Ry)X AM +QMp2MiBQMH bii2 bT+2 2tTHQ`iBQM- i?2 bii2b `2 F2Ti BM K2KQ`v iQ `2+Q;MBb2 H`2/v pBbBi2/ bii2bX >Qr2p2`- bii2b r?B+? ?p2 T`Q;`2bb pHm2 r?B+? Bb bi`B+iHv H2bb i?M i?2 KBMBKH T`Q;`2bb pHm2 Q7 i?Qb2 bii2b 7Q` r?B+? bm++2bbQ`b ?p2 MQi v2i #22M +H+mHi2/ +M M2p2`
#2 `2+?2/ ;BMX Ai Bb i?2`27Q`2 b72 iQ /2H2i2 bm+? bii2b 7`QK K2KQ`v r?B+?
bB;MB}+MiHv `2/m+2b i?2 K2KQ`v mb;2 /m`BM; i?2 bii2 bT+2 2tTHQ`iBQMX AM i?Bb TT2`- r2 +QMbB/2` i?2 p2`bBQM Q7 i?2 br22T@HBM2 H;Q`Bi?K 7Q`KQMQ@
iQMB+ T`Q;`2bb K2bm`2b(Ψ)X KQMQiQMB+ T`Q;`2bb K2bm`2 T`2b2`p2b i?2 `2+?@
#BHBiv `2HiBQM- BX2X- B7 bii2 s′ Bb `2+?#H2 7`QK bii2 s- i?2M Ψ(s)⊑Ψ(s′)X h?2 T`Q;`2bb 2tTHQBi2/ #v i?2 br22T@HBM2 K2i?Q/ 7Q` bvbi2K Bb 7Q`KHBb2/ #v T`QpB/BM; KQMQiQMB+ T`Q;`2bb K2bm`2 b /2}M2/ #2HQr- r?2`2 S /2MQi2b i?2 b2i Q7 bii2b M/ s0∈S /2MQi2b i?2 BMBiBH bii2X
.2}MBiBQM RX UJQMQiQMB+ S`Q;`2bb J2bm`2V KQMQiQMB+ T`Q;`2bb K2@
bm`2 Bb imTH2 P = (O,⊑,Ψ) bm+? i?i O Bb b2i Q7 T`Q;`2bb pHm2b- ⊑ Bb iQiH Q`/2` QM O- M/ Ψ : S → O Bb T`Q;`2bb KTTBM; bm+? i?i
∀s, s′∈reach(s0) :s→∗s′⇒Ψ(s)⊑Ψ(s′)X !
T`Q;`2bb K2bm`2 Bb MQM@KQMQiQMB+ r?2M i?2`2 Bb i H2bi QM2`2;`2bb 2/;2- BX2X- 2/;2b r?2`2 i?2 bQm`+2 bii2 ?b H`;2` T`Q;`2bb pHm2 i?M i?2 /2biB@
MiBQM bii2X ;2M2`HBb2/ p2`bBQM Q7 i?2 br22T@HBM2 K2i?Q/ i?i +M ?M/H2 MQM@KQMQiQMB+ T`Q;`2bb K2bm`2 M/ `2;`2bb 2/;2b HbQ 2tBbib (Rk)- #mi Bb MQi i?2 7Q+mb Q7 Qm` rQ`FX
kXk *hG JQ/2H *?2+FBM; rBi? i?2 ar22T@HBM2 J2i?Q/
*hG (8) Bb M BKTQ`iMi #`M+?BM; i2KTQ`H HQ;B+ i?i Bb bm{+B2MiHv 2tT`2bbBp2 7Q` i?2 7Q`KmHiBQM Q7 M BKTQ`iMi b2i Q7 #2?pBQm`H bvbi2K T`QT2`iB2bX 1p2M i?Qm;? H`;2 b2i Q7 T`QT2`iB2b +M #2 bT2+B}2/ mbBM; i?2 b2KMiB+b Q7 *hG- i?2`2
`2 bQK2 `2bi`B+iBQMb r?2M TTHvBM; i?2K rBi? i?2 br22T@HBM2 K2i?Q/ H;Q`Bi?KX h?2 +?HH2M;2 Q7 +QK#BMBM; *hG KQ/2H +?2+FBM; rBi? i?2 br22T@HBM2 K2i?Q/ Bb i?i +QMp2MiBQMH H;Q`Bi?Kb 7Q` *hG KQ/2H +?2+FBM; T`QT;i2b BM7Q`KiBQM
#+Fr`/b 7`QK bii2 iQ Bib T`2/2+2bbQ`b (e)X h?Bb 7QHHQrb i?2 QTTQbBi2 rQ`F@~Qr i?M i?2 7Q`r`/ T`Q;`2bb@}`bi 2tTHQ`iBQM i?i i?2 br22T@HBM2 K2i?Q/ T2`7Q`KbX AM i?Bb rQ`F- r2 +QMbB/2` bm#b2i Q7 *hG +Qp2`BM; T`QT2`iB2b Q7 i?2 7QHHQrBM;
7Q`Kb- r?2`2 ΦBb bii2 7Q`KmH,
S`QT2`iv @ :Φ dzAMp`BMiHvǴ- K2MBM; i?i i?2 T`QT2`iv ?QH/b B7Φ?QH/b BM HH bii2b i?i `2 `2+?#H2 7`QK i?2 +m``2Mi bii2X
S`QT2`iv @ 16Φ dz>QH/b TQi2MiBHHvǴ Q` dzTQbbB#HvǴ- K2MBM; i?i i?2 T`QT2`iv
?QH/b B7 Bi Bb TQbbB#H2 iQ }M/ bii2 `2+?#H2 7`QK i?2 +m``2Mi bii2 r?2`2 Φ?QH/bX
S`QT2`iv @ :16Φ dzHrvb TQbbB#H2Ǵ- K2MBM; i?i Mv bii2 `2+?#H2 7`QK i?2 +m``2Mi bii2- bii2 biBb7vBM; i?2 T`2/B+i2Φ+M Hrvb #2 `2+?2/X S`QT2`iv @ :6Φ dzHrvb 2p2MimHHvǴ- K2MBM; i?i 7`QK Mv bii2 `2+?@
#H2 7`QK i?2 +m``2Mi bii2- bii2 biBb7vBM; Φ rBHH Hrvb 2p2MimHHv #2
`2+?2/X
q2 bv i?i 7Q`KmH UT`QT2`ivV f ?QH/b BM ;Bp2M KQ/2H M B7 f ?QH/b BM i?2 BMBiBH bii2 b0X
H;Q`Bi?K R bT2+B}2b i?2 br22T@HBM2 H;Q`Bi?KX b K2MiBQM2/ BM i?2 BMi`Q/m+@
iBQM- r2 ?p2 #b2/ i?2 BKTH2K2MiiBQM QM i?2 Q`B;BMH br22T@HBM2 H;Q`Bi?K 7Q`
KQMQiQMB+ T`Q;`2bb K2bm`2bX h?2 H;Q`Bi?K bi`ib rBi? ?b? i#H2 Q7 pBbBi2/
bii2b M/ T`BQ`Biv [m2m2 rBi? i?2 bii2b i?i `2 biBHH iQ #2 T`Q+2bb2/X "Qi?
`2 BMBiBHBx2/ i i?2 #2;BMMBM; rBi? i?2 BMBiBH bii2 b0 UHBM2b k@jVX h?2 T`Q;`2bb K2bm`2ψcBb HbQ BMBiBHBx2/ BM HBM2 9X h?2M- i?2 H;Q`Bi?K 2t2+mi2b HQQT UHBM2b 8@keV r?B+? 2M/b r?2M HH i?2 `2+?#H2 bii2b ?p2 #22M T`Q+2bb2/X 6Q` 2+?
Bi2`iBQM- r2 b2H2+i QM2 Q7 i?2 bii2b rBi? i?2 HQr2bi T`Q;`2bb pHm2 KQM; i?2 mMT`Q+2bb2/ bii2b UHBM2 eVX h?2 +QM/BiBQM BM HBM2 d +?2+Fb B7 i?2 T`Q;`2bb pHm2 Q7 i?2 Hv2` Bb bi`B+iHv H2bb i?M i?2 T`Q;`2bb pHm2 Q7 i?2 b2H2+i2/ bii2c B7 bQ- r2 `2
#Qmi iQ KQp2 BMiQ i?2 M2ti Hv2`X q2 MQr +?2+F i?2 #2?pBQm`H T`QT2`iv 7Q`
i?2 MQ/2b BM i?2 Hv2`- #27Q`2 r2 KQp2 iQ i?2 M2ti QM2 UT`Q+2/m`2 +?2+FS`QT2`iv i HBM2 3VX
hQ KQ/2H +?2+F i?2 :16 M/ :6 T`QT2`iB2b- i?2 H;Q`Bi?K 2tTHQBib i?2 bi`QM;Hv +QMM2+i2/ +QKTQM2Mib Ua**bVX M a** Q7 /B`2+i2/ ;`T? Bb KtBKH bm#b2i Q7 MQ/2b i?i `2 KmimHHv `2+?#H2X "2+mb2 Q7 i?2 KQMQiQMB+Biv Q7 i?2 T`Q;`2bb K2bm`2- 2+? a** QMHv +QMiBMb MQ/2b #2HQM;BM; iQ i?2 bK2 Hv2`
M/ ?2M+2 2+? a** Bb Hrvb +QMiBM2/ BM bBM;H2 Hv2`X h?2`27Q`2- r2 +M +QKTmi2 i?2 a**b 7Q` ;Bp2M Hv2` BKK2/Bi2Hv #27Q`2 r2 /2H2i2 i?2 MQ/2b BM i?2 +m``2Mi Hv2` M/ KQp2 iQ i?2 M2ti QM2X h?2 H;Q`Bi?K +?2+Fb i?2 T`QT2`iv /2T2M/BM; QM i?2 7Q`K Q7 i?2 T`QT2`iv,
S`QT2`iv @ :Φ q2 +?2+F i?i 2p2`v MQ/2 rBi?BM i?2 Hv2` biBb}2bΦ A7 Φ /Q2b MQi ?QH/ BM QM2 Q7 i?2K- r2 `2im`M 7Hb2 M/ #Q`i i?2 2tTHQ`iBQMX S`QT2`iv @ 16Φ A7 i H2bi QM2 bii2 biBb}2b Φ- i?2M i`m2 Bb `2im`M2/ M/ i?2
2t2+miBQM }MBb?2bX h?mb- 7Hb2 rBHH #2 `2im`M2/ B7 i i?2 2M/ Q7 i?2 2tTHQ`iBQM MQi bBM;H2 bii2 biBb7vBM; Φ?b #22M 7QmM/X
S`QT2`iv @ :16Φ 6Q` i?Bb T`QT2`iv- i?2 T`Q+2/m`2 }`bi +QKTmi2b i?2 a**b Q7 i?2 ;Bp2M Gv2`X h?2 T`QT2`iv rBHH MQi #2 biBb}2/ M/ i?2`27Q`2 i?2 T`Q@
+2/m`2 rBHH }MBb? i?2 2t2+miBQM `2im`MBM; 7Hb2- B7 Mv b++ KQM; i?2 b2i Q7 a**b Q7Gv2`Bb i2`KBMH M/Φ/Q2b MQi ?QH/ BM Mv Q7 i?2 bii2b +QMiBM2/
BMb++X
.i,LQ/2b◃>b? i#H2 Q7 pBbBi2/ bii2b +m``2MiHv biQ`2/X lMT`Q+2bb2/◃S`BQ`Biv [m2m2 Q7 mMT`Q+2bb2/ bii2bX Gv2` ◃GBbi Q7 bii2b T`Q+2bb2/ BM i?2 +m``2Mi Hv2`X ψc ◃S`Q;`2bb pHm2 7Q` +m``2Mi Hv2`
Φ ◃S`QT2`iv iQ #2 p2`B}2/X
_2bmHi,h`m2 B7 i?2 T`QT2`iv Bb biBb}2/- 7Hb2 Qi?2`rBb2X
R #2;BM
k LQ/2bXBMb2`iUb0V
j lMT`Q+2bb2/XBMb2`iUb0V
9 ψc 4ψ(s0)
8 r?BH2¬UlMT`Q+2bb2/XBb1KTivUVV/Q
f MQ/2 rBi? HQr2bi T`Q;`2bb K2bm`2 f
e b ←−lMT`Q+2bb2/X;2iJBM1H2K2MiUV
d B7 ψc #ψ(s)i?2M
3 +?2+FS`QT2`ivUGv2`-ΦV
N 7Q`HHb′ ∈ Gv2` /Q
Ry LQ/2bX/2H2i2Ub′V
RR 2M/
Rk Gv2`←− ∅
f lT/i2 T`Q;`2bb K2bm`2 7Q` +m``2Mi Hv2` f
Rj ψc 4ψ(s)
R9 2M/
R8 Gv2`XBMb2`iUbV
f 6Q` 2p2`v bm++2bbQ` bii2 Q7 b f
Re 7Q`HHUi- b′V bm+? i?i b−→i b′ /Q
Rd B7 ¬ULQ/2bX+QMiBMbUb′VVi?2M
R3 LQ/2bXBMb2`iUb′V
RN B7 UψUbV$ψUb′VVi?2M
ky _Bb21t+2TiBQMUǵ_2;`2bb 2/;2 7QmM/ǶV
kR 2Hb2
kk lMT`Q+2bb2/XBMb2`iUb′V
kj 2M/
k9 2M/
k8 2M/
ke 2M/
kd 2M/
H;Q`Bi?K R, ar22T@HBM2 H;Q`Bi?K 7Q` KQMQiQMB+ T`Q;`2bb K2bm`2b
S`QT2`iv @ :6Φ 6Q` i?Bb T`QT2`iv- i?2 T`Q+2/m`2 }`bi +QKTmi2b i?2 a**b Q7 i?2 ;Bp2MGv2`X 6Q` 2+? b++- r2 }`bi `2KQp2 i?2 bii2b i?i biBb7v i?2 T`QT2`ivX A7 i?2 `2bmHiBM; b2i Q7 MQ/2b ?b +v+H2- i?2M i?2 T`QT2`iv Bb pBQ@
Hi2/ M/ i?2`27Q`2 i?2 2t2+miBQM }MBb?2b `2im`MBM; 7Hb2X
6m`i?2` /2iBHb M/ i?2 /2KQMbi`iBQMb Q7 i?2 T`QT2`iB2b :16 M/ :6 +M #2 7QmM/ BM (R9) Ui?2 T`Q+2/m`2 +?2+FS`QT2`iv Bb +HH2/*>1*Ea** BM i?i TT2`VX 7i2` i?2 T`QT2`iv Bb +?2+F2/- r2 `2KQp2 i?2 MQ/2b BMGv2`- `2bi`i Bi M/
mT/i2 i?2 T`Q;`2bb pHm2 ψc UHBM2b N@RjVX h?2M i?2 bii2 Bb //2/ iQ i?2 +m``2Mi Hv2` UHBM2 R8V M/ Bib bm++2bbQ` bii2b `2 +QKTmi2/X 6BMHHv- B7 bm++2bbQ` bii2 UMQ/2V ?b MQi v2i #22M pBbBi2/- Bi Bb //2/ iQ i?2 b2i Q7 mMT`Q+2bb2/ MQ/2b UHBM2 R3VX A7 i?2`2 Bb `2;`2bb 2/;2 i?2 H;Q`Bi?K biQTb M/ M 2``Q` K2bb;2 Bb
`2im`M2/ UHBM2 kyVX
b i?2 +QMiBMmiBQM Q7 i?2 rQ`F T`2b2Mi2/ BM (R9)- r2 ?p2 BKTH2K2Mi2/
H;Q`Bi?K R mbBM; i?2 aiM/`/ JG HM;m;2- M/ BMi2;`i2/ Bi BMiQ *SL hQQHbX h?Bb HHQrb mb MQi QMHv iQ MHvb2 bii2b bT+2b Q7 KQ/2Hb +QMbi`m+i2/ mbBM;
*SL hQQHb iFBM; /pMi;2 Q7 i?2 br22T@HBM2 K2i?Q/- #mi HbQ iQ p2`B7v i?2 7Q`2K2MiBQM2/ #2?pBQm`H T`QT2`iB2bX
j h?2 *SL JZhh JQ/2H
Pm` BK Bb iQ mb2 Qm` BKTH2K2MiiBQM Q7 i?2 *hG@#b2/ br22T@HBM2 KQ/2H +?2+F@
BM; H;Q`Bi?Kb 7`QK i?2 T`2pBQmb b2+iBQM iQ p2`B7v i?2 F2v #2?pBQ`H T`QT2`iB2b Q7 i?2 *SL KQ/2H r2 ?p2 /2p2HQT2/ Q7 i?2 JZhh T`QiQ+QH (Re)X
JZhh TTHB2b iQTB+@#b2/ }Hi2`BM; Q7 K2bb;2b rBi? iQTB+ #2BM; T`i Q7 2+? Tm#HBb?2/ K2bb;2X M JZhh +HB2Mi +M bm#b+`B#2 iQ iQTB+ iQ `2+2Bp2 K2bb;2b- Tm#HBb? QM iQTB+- M/ +HB2Mib +M bm#b+`B#2 iQ b KMv iQTB+b b i?2v
`2 BMi2`2bi2/ BMX b /2b+`B#2/ BM (R8)- M JZhh +HB2Mi +M QT2`i2 b Tm#@
HBb?2` Q` bm#b+`B#2- M/ r2 mb2 i?2 i2`K +HB2Mi iQ ;2M2`HHv `272` iQ Tm#HBb?2`
Q` bm#b+`B#2`X h?2 JZhh #`QF2` (R8) Bb i?2 +Q`2 Q7 Mv Tm#HBb?fbm#b+`B#2 T`Q@
iQ+QH M/ Bb `2bTQMbB#H2 7Q` F22TBM; i`+F Q7 bm#b+`BTiBQMb- `2+2BpBM; M/ }Hi2`BM;
K2bb;2b- /2+B/BM; iQ r?B+? +HB2Mib i?2v rBHH #2 /BbTi+?2/- M/ b2M/BM; i?2K iQ HH bm#b+`B#2/ +HB2MibX PM QM2 ?M/- i?2 #`QF2` mb2b i?2 iQTB+b iQ /2i2`KBM2 r?2i?2` bm#b+`B#BM; +HB2Mi b?QmH/ `2+2Bp2 i?2 K2bb;2 Q` MQiX PM i?2 Qi?2`
?M/- +HB2Mib +M bm#b+`B#2 iQ b2p2`H iQTB+b /2T2M/BM; QM i?2B` BMi2`2biX
jXR AMi2`+iBQM Pp2`pB2r
JZhh /2}M2b }p2 KBM QT2`iBQMb, +QMM2+i- bm#b+`B#2- Tm#HBb?- mMbm#b+`B#2- M/ /Bb+QMM2+iX am+? QT2`iBQMb- 2t+2Ti i?2 +QMM2+i r?B+? Kmbi #2 T2`7Q`K2/
#27Q`2 i?2 Qi?2`b #v i?2 +HB2Mib- `2 BM/2T2M/2Mi Q7 2+? Qi?2` M/ +M #2 i`B;@
;2`2/ BM T`HH2H #v 2Bi?2` i?2 +HB2Mib Q` i?2 #`QF2`X q2 ?p2 /2p2HQT2/ i?2 *SL KQ/2H 7QHHQrBM; KQ/2HHBM; Tii2`M i?i 2Mbm`2b KQ/mH`Biv- M/ i?2`27Q`2 2M@
+TbmHiBQM Q7 #Qi? i?2 T`QiQ+QH HQ;B+ M/ i?2 #2?pBQm` Q7 bm+? QT2`iBQMbX h?2 JZhh T`QiQ+QH /2HBp2`b TTHB+iBQM K2bb;2b ++Q`/BM; iQ i?2 i?`22 ZmHBiv Q7 a2`pB+2 UZQaV H2p2Hb /2}M2/ BM (k)- r?B+? `2 KQiBpi2/ #v i?2 /Bz2`2Mi M22/b i?i AQh TTHB+iBQMb Kv ?p2 BM i2`Kb Q7 `2HB#H2 /2HBp2`v Q7 K2bb;2bX
AM Q`/2` iQ b?Qr ?Qr i?2 +HB2Mib M/ i?2 #`QF2` BMi2`+i- r2 /2b+`B#2 i?2 /Bz2`2Mi +iBQMb i?i +HB2Mib Kv +``v Qmi #v +QMbB/2`BM; M 2tKTH2X 6B;m`2 R b?Qrb b2[m2M+2 /B;`K 7Q` b+2M`BQ r?2`2 irQ +HB2Mib +QMM2+i- T2`7Q`K
Client 1 Broker
1 - CONNECT 2 - CONNACK
Client 2
1 - CONNECT 2 - CONNACK 3 - SUBSCRIBE(topic(1), QoS(1))
3 - SUBACK (topic(1)) 4 - PUBLISH (topic(1), QoS(1))
5 - PUBLISH (topic(1), QoS(1)) 4 - PUBACK(topic(1),QoS(1))
6 - PUBACK(topic(1),QoS(1)) 7 - UNSUBSCRIBE (topic(1)) 7 - UNSBACK(topic(1)) 8 - DISCONNECT
8 - DISCONNECT
6B;X RXJ2bb;2 b2[m2M+2 /B;`K BHHmbi`iBM; i?2 JZhh T?b2bX
bm#b+`B#2- Tm#HBb? M/ mMbm#b+`B#2- M/ }MHHv /Bb+QMM2+i 7`QK i?2 #`QF2`X h?2 T`QiQ+QH BMi2`+iBQM Bb b 7QHHQrb,
RX *HB2Mi RM/ *HB2Mi k`2[m2bi +QMM2+iBQM iQ i?2 "`QF2`X
kX h?2 "`QF2`b2M/b #+F +QMM2+iBQM +FMQrH2/;2K2Mi iQ +QM}`K i?2 2bi#@
HBb?K2Mi Q7 i?2 +QMM2+iBQMX
jX *HB2Mi k bm#b+`B#2b iQ iQTB+ R rBi? ZQa H2p2H R- M/ i?2 "`QF2` +QM}`Kb i?2 bm#b+`BTiBQM rBi? bm#b+`B#2 +FMQrH2/;2K2Mi K2bb;2X
9X *HB2Mi RTm#HBb?2b QM iQTB+ R rBi? ZQa H2p2H RX h?2"`QF2``2bTQM/b rBi?
+Q``2bTQM/BM; Tm#HBb? +FMQrH2/;2K2MiX
8X h?2"`QF2`i`MbKBib i?2 Tm#HBb? K2bb;2 iQ *HB2Mi kr?B+? Bb bm#b+`B#2/ iQ i?2 iQTB+X
eX *HB2Mi k ;2ib i?2 Tm#HBb?2/ K2bb;2- M/ b2M/b Tm#HBb? +FMQrH2/;2K2Mi
#+F b +QM}`KiBQM iQ i?2"`QF2`i?i Bi ?b `2+2Bp2/ i?2 K2bb;2X dX *HB2Mi kmMbm#b+`B#2b iQ iQTB+ R- M/ i?2"`QF2``2bTQM/b rBi? M mMbm#b+`B#2
+FMQrH2/;2K2MiX
3X *HB2Mi RM/ *HB2Mi k/Bb+QMM2+iX
jXk *SL JQ/2H Pp2`pB2r
q2 MQr #`B2~v b?Qr M/ /Bb+mbb i?2 KQ/2H M/ Bib KBM 2H2K2Mib i?i `2 BKTQ`iMi 7Q` i?2 mM/2`biM/BM; Q7 i?2 rQ`F +``B2/ QmiX q2 `272` i?2 `2/2`
iQ (Re) 7Q` /2iBH2/ /2b+`BTiBQM Q7 i?2 JZhh T`QiQ+QH M/ i?2 JZhh *SL KQ/2HX h?2 +QKTH2i2 *SL KQ/2H Q7 i?2 JZhh T`QiQ+QH +QMbBbib Q7 k9 KQ/@
mH2b Q`;MBb2/ BMiQ bBt ?B2``+?B+H H2p2HbX h?2 KQ/2H Bb Q`;MBx2/ 7QHHQrBM;
KQ/2HHBM; Tii2`M i?i 2Mbm`2b KQ/mH`Biv M/ i?2`27Q`2- 2M+TbmHiBQM Q7 i?2 T`QiQ+QH HQ;B+ M/ #2?pBQm` Q7 bm+? QT2`iBQMbX h?Bb Qz2`b /pMi;2b #Qi? 7Q`
`2/#BHBiv M/ mM/2`biM/#BHBiv Q7 i?2 KQ/2H M/ HbQ- 7Q` KFBM; 2bB2` iQ /2i2+i M/ }t 2``Q`b /m`BM; i?2 BM+`2K2MiH p2`B}+iBQMX 6Q` BMbiM+2- i?Bb ?b
HHQr2/ mb iQ KF2 +H2` b2T`iBQM Q7 i?2 /Bz2`2Mi ZQa HQ;B+b rBi?Qmi ?pBM;
Mv M2;iBp2 +QKTH2tBiv BKT+i QM i?2 KQ/2HX
6B;m`2 k b?Qrb i?2 iQT@H2p2H KQ/mH2 Q7 i?2 *SL JZhh KQ/2H r?B+? +QMbBbib Q7 irQ bm#biBimiBQM i`MbBiBQMb U/`rM b `2+iM;H2b rBi? /Qm#H2@HBM2/ #Q`/2`bV
`2T`2b2MiBM; i?2*HB2MibM/ i?2 "`QF2``QH2b Q7 JZhhX am#biBimiBQM i`MbBiBQMb +QMbiBimi2 i?2 #bB+ bvMi+iB+H bi`m+im`BM; K2+?MBbK Q7 *SLb M/ 2+? Q7 i?2 bm#biBimiBQM i`MbBiBQMb ?b M bbQ+Bi2/ KQ/mH2 i?i KQ/2Hb i?2 /2iBH2/ #2@
?pBQm` Q7 i?2 +HB2Mib M/ i?2 #`QF2`- `2bT2+iBp2HvX h?2 MK2 Q7 i?2 Ubm#VKQ/mH2 bbQ+Bi2/ rBi? bm#biBimiBQM i`MbBiBQM Bb r`Bii2M BM i?2 `2+iM;mH` i; TQbB@
iBQM2/ M2ti iQ i?2 i`MbBiBQMX
CtoB
BrokerxMessages []
BtoC
ClientxMessages initMsgQueue()
Broker
Broker Broker Clients
Client Client
1 1`[]
1 1`[(client(1),[]),(client(2),[])]
6B;X kXh?2 iQT@H2p2H KQ/mH2 Q7 i?2 JZhh *SL KQ/2HX
h?2 irQ bm#biBimiBQM i`MbBiBQMb BM 6B;X k `2 +QMM2+i2/ pB /B`2+i2/ `+b iQ i?2 irQ TH+2b*iQ"M/"iQ*X h?2 +HB2Mib M/ i?2 #`QF2` BMi2`+i #v T`Q/m+BM;
M/ +QMbmKBM; iQF2Mb QM i?2 TH+2bX h?2 TH+2b *iQ" M/ "iQ* `2 /2bB;M2/
iQ #2?p2 b [m2m2bX h?2 [m2m2 K2+?MBbK Qz2`b bQK2 /pMi;2b i?i i?2 JZhh bT2+B}+iBQM BKTHB+BiHv BM/B+i2bX h?2 Tm`TQb2 Q7 i?Bb Bb iQ 2Mbm`2 i?2 Q`/2`2/ K2bb;2 /Bbi`B#miBQM b bbmK2/ 7`QK i?2 i`MbTQ`i b2`pB+2 QM iQT Q7 r?B+? JZhh QT2`i2bX
jXj *HB2Mi M/ "`QF2` aii2 JQ/2HHBM;
h?2 +QHQm` b2ib /2}M2/ 7Q` KQ/2HHBM; i?2 +HB2Mi bii2 `2 b?QrM BM 6B;X jX h?2 TH+2 *HB2Mib UiQT@H27i TH+2 BM 6B;X 9V mb2b iQF2M 7Q` 2+? +HB2Mi iQ biQ`2 Bib
`2bT2+iBp2 bii2 /m`BM; i?2 +QKKmMB+iBQMX h?2 aii2+QHQm` b2i Bb M 2MmK2`@
iBQM ivT2 +QMiBMBM; i?2 pHm2b _1.u U7Q` i?2 BMBiBH bii2V- qAh Ur?2M i?2 +HB2Mi Bb rBiBM; iQ #2 +QMM2+i2/V- *PLUr?2M i?2 +HB2Mi Bb +QMM2+i2/V- M/.Aa*
U7Q` r?2M i?2 +HB2Mi ?b /Bb+QMM2+i2/VX h?2 bii2b Q7 i?2 +HB2Mib `2 `2T`2b2Mi2/
+QHb2i aii2 4 rBi? _1.u % .Aa* % *PL % qAhc +QHb2i hQTB+tZQa 4 T`Q/m+i hQTB+ ZQac +QHb2i GBbihQTB+tZQa 4 HBbi hQTB+tZQac
+QHb2i *HB2Miaii2 4 `2+Q`/ iQTB+b , GBbihQTB+tZQa bii2 , aii2
TB/ , SA.c
+QHb2i *HB2Mitaii2 4 T`Q/m+i *HB2Mi *HB2Miaii2c
6B;X jX*QHQm` b2i /2}MBiBQMb mb2/ 7Q` KQ/2HHBM; +HB2Mi bii2X
#v i?2*HB2Mitaii2+QHQm` b2i r?B+? Bb T`Q/m+i Q7 *HB2MiM/*HB2Miaii2X h?2 +QHQm` b2i*HB2Miaii2mb2/ iQ `2T`2b2Mi i?2 bii2 Q7 +HB2Mi r?B+? +QMbBbib Q7 HBbi Q7 hQTB+tZQa- aii2- M/ SA.X lbBM; i?Bb- +HB2Mi biQ`2b i?2 iQTB+b Bi Bb bm#b+`B#2/ iQ- M/ i?2 [mHBiv Q7 b2`pB+2 H2p2H Q7 2+? bm#b+`BTiBQMX
h?2 *HB2MiS`Q+2bbBM; bm#KQ/mH2 BM 6B;X 9 KQ/2Hb HH i?2 QT2`iBQMb i?i +HB2Mi +M +``v QmiX *HB2Mib +M #2?p2 b b2M/2`b M/ `2+2Bp2`b- M/ i?2 }p2 bm#biBimiBQM i`MbBiBQMb *PLL1*h- Sl"GAa>- al"a*_A"1- lLal"a*_A"1 M/
.Aa*PLL1*h ?b #22M +QMbi`m+i2/ iQ +Tim`2 #Qi? #2?pBQm`bX q2 ?p2 bi`m+@
im`2/ i?2 #`QF2` bBKBH`Hv b r2 ?p2 /QM2 7Q` +HB2MibX h?Bb +M #2 b22M 7`QK 6B;X 8 r?B+? b?Qrb i?2"`QF2`S`Q+2bbBM;bm#KQ/mH2X h?2 *QMM2+i2/*HB2MibTH+2 F22Tb i?2 BM7Q`KiBQM Q7 HH +HB2Mib b T2`+2Bp2/ #v i?2 #`QF2`X h?Bb TH+2 Bb /2bB;M2/ b +2Mi`H biQ`;2- M/ Bi Bb mb2/ #v i?2 #`QF2` iQ /Bbi`B#mi2 i?2 K2bb;2b Qp2` i?2 M2irQ`FX h?2 #`QF2` #2?pBQm` Bb /Bz2`2Mi 7`QK i?i Q7 i?2 +HB2Mib- bBM+2 Bi rBHH ?p2 iQ KM;2 HH i?2 `2[m2bib M/ ;2M2`i2 `2bTQMb2b 7Q`
b2p2`H +HB2Mib i i?2 bK2 iBK2X
9 JQ/2H *?2+FBM; M/ 1tT2`BK2MiH _2bmHib
AM i?Bb b2+iBQM r2 b?Qr ?Qr r2 ?p2 T2`7Q`K2/ br22T@HBM2 #b2/ KQ/2H +?2+FBM;
Q7 i?2 *SL JZhh KQ/2H M/ T`2b2Mi i?2 `2bmHib 7`QK i?2 2tT2`BK2MibX
9XR S`Q;`2bb J2bm`2
h?2 }`bi i?BM; r2 M22/ iQ +QMbB/2` Bb ?Qr r2 /2}M2 i?2 T`Q;`2bb K2bm`2 Q7 i?2 KQ/2HX aBM+2 i?2 KQ/2H `mMb BM M +v+HB+ +QM};m`iBQM Ui?2`2 Bb }MH bii2 r?2`2 HH i?2 +HB2Mib `2 /Bb+QMM2+i2/V- r2 ?p2 /2}M2/ i?2 T`Q;`2bb K2bm`2 Qp2`
i?2 /Bz2`2Mi bii2b i?2 +HB2Mib +M ;Q i?`Qm;?X AM i?2 2tT2`BK2Mib- r2 +QMbB/2`
irQ +HB2Mib- bQ i?2 BMBiBH bii2 Bb K/2 mT rBi? i?2 irQ +HB2Mib BM i?2_1.ubii2 M/ i?2 }MH bii2 Bb `2+?2/ r?2M #Qi? +HB2Mib `2 BM .Aa* bii2X
Clients In/Out
ClientxState In/Out
CtoB Out
BrokerxMessages Out
BtoC In
ClientxMessages In
PUBLISH PUBLISH PUBLISH
SUBSCRIBE SUBSCRIBE SUBSCRIBE
UNSUBSCRIBE UNSUBSCRIBE UNSUBSCRIBE
DISCONNECT DISCONNECT DISCONNECT CONNECT CONNECT CONNECT 2
1`(client(1),{topics=[],state=READY,p id=0})++
1`(client(2),{topics=[],state=READY,p id=0})
1 1`[]
1 1`[(client(1),[]),(client(2),[])]
6B;X 9X*HB2MiS`Q+2bbBM; bm#KQ/mH2X
b r2 ?p2 irQ +HB2Mib ?M/HBM; 7Qm` /Bz2`2Mi bii2b- Qm` /2}MBiBQM Q7 i?Bb T`Q;`2bb K2bm`2 Qp2` i?2 TQbbB#H2 +QK#BMiBQMb rBHH bTHBi Qm` bii2 bT+2 BMiQ Re Hv2`bX aBM+2 i?2 T`Q;`2bb K2bm`2 Bb /2}M2/ bm+? i?i i?2 T`Q;`2bb pHm2b
`2 BMi2;2`b- r2 ?p2 bbB;M2/ R 7Q`_1.u- k 7Q`qAh- j 7Q` *PLM/ 9 7Q` .Aa*X Ai Bb BKTQ`iMi iQ MQi2 i?i i?2 +HB2Mib +MMQi ;Q #+F iQ T`2pBQmb bii2- 7Q`
BMbiM+2- B7 +HB2Mi R `2+?2b i?2*PLbii2- Bi +M M2p2` #2 ;BM BM i?2qAhbii2X b r2 M22/ iQ F22T ;HQ#H MQiBQM Q7 T`Q;`2bb K2bm`2- r2 +QKTmi2 Bi mbBM; i?2 7QHHQrBM; 2[miBQM rBi? c1 M/c2 #2BM; +HB2Mi R M/ +HB2Mi k- `2bT2+iBp2Hv,
ψc=B∗state(c1) +state(c2)
M/ r?2`2BBb #b2X 1bb2MiBHHv- r2 BMi2`T`2i i?2 bii2b Q7 i?2 irQ +HB2Mi b #b2 B MmK#2` r?2`2B Bb `2[mB`2/ iQ #2 H`;2` i?M i?2 MmK#2` Q7 bii2b Q7 2+? +HB2MiX AM Qm` 2tT2`BK2Mib- r2 ?p2 mb2/B= 10- BX2X- i?2 /2+BKH MmK#2`BM;
bvbi2KX
b r2 ?p2 BKTH2K2Mi2/ i?2 KQ/2H BM KQ/mH` M/ T`K2i2`Bx2/ 7b?BQM- r2 `2 #H2 iQ +QMi`QH b2p2`H 2H2K2Mib- 7Q` BMbiM+2- i?2 MmK#2` Q7 +HB2Mib- i?2 QT2`iBQMb i?Qb2 +HB2Mib +M T2`7Q`K U+QMM2+i- bm#b+`B#2- 2i+XV- M/ i?2 bBx2 Q7 i?2
CtoB In
BrokerxMessages Connected
Clients
Out ClientsxState
BtoC Out
ClientxMessages Process
DISCONNECT ProcessDISCONNECT ProcessDISCONNECT
Process UNSUBSCRIBE ProcessUNSUBSCRIBE ProcessUNSUBSCRIBE
Process CONNECT ProcessCONNECT ProcessCONNECT
Process PUBLISH ProcessPUBLISH ProcessPUBLISH Process SUBSCRIBE ProcessSUBSCRIBE ProcessSUBSCRIBE
In
Out
1 1`[] Out
1 1`[]
1
1`[(client(1),[]),(client(2),[])]
6B;X 8Xh?2"`QF2`S`Q+2bbBM; KQ/mH2X
[m2m2b 7Q` ?M/HBM; K2bb;2bX LQi2 i?i- BM Q`/2` iQ Q#iBM }MBi2 bii2 bT+2- r2 ?p2 iQ HBKBi i?2 MmK#2` Q7 +HB2Mib M/ iQTB+b- M/ HbQ #QmM/ i?2 T+F2i B/2MiB}2`bX h?2 T+F2i B/2MiB}2`b `2 BM+`2K2Mi2/ i?`Qm;?Qmi i?2 2t2+miBQM Q7 i?2 /Bz2`2Mi T?b2b Q7 i?2 T`QiQ+QH U+QMM2+i- bm#b+`B#2- /i 2t+?M;2- mMbm#@
b+`B#2- M/ /Bb+QMM2+iVX h?Bb K2Mb i?i r2 +MMQi mb2 bBM;H2 ;HQ#H #QmM/
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