.BZ %BOJFM+BDLTPO $PNQVUFS4ZTUFNTweb.mit.edu/6.033/2001/Ü>ÀÊÃÌ ÀÞ\Ê iÌÃv>«i½ÃÊ`i Ãi...
Transcript of .BZ %BOJFM+BDLTPO $PNQVUFS4ZTUFNTweb.mit.edu/6.033/2001/Ü>ÀÊÃÌ ÀÞ\Ê iÌÃv>«i½ÃÊ`i Ãi...
�
%BOJFM�+BDLTP
O������$
PNQVUFS�4ZTUFNT
.BZ��� �����
�
�`>
Þ½ÃÊÌ�«�VÃ
TPGUXBS
F�TZT
UFN
�EFT
JHO
rB�GFX
�JEFB
T�JO
TQJSFE
�CZ�#SP
PLT�T�.
ZUIJDBM�.
BO�.
POUI
rJMMVTUSB
UFE�CZ�TP
NF�XBS
�TUP
SJFT
�CFD
BVTF
��ZP
V�SF�TUVCCPSO
�BOE�QSP
CBC
MZ�X
PO�U�CFMJFWF
�NF�PUI
FSXJTF
��XF�EPO�U�SFB
MMZ�LOPX�X
IBU�X
F�SF
�UBMLJO
H�BC
PVU
UISF
F�BO
E�B�IBMG�JE
FBT
r����D
PODF
QUV
BM�JOUFHS
JUZ
#SP
PLT�XBT
�SJHIU �CVU�TUJMM�DP
OUSPWF
STJBM
r����Q
MBO�UP�UISP
X�POF�BX
BZ
#SP
PLT�XBT
�BMN
PTU�SJHIU
r����Q
VTI
�UIF�FO
WFMP
QF
#SP
PLT�EJE
O�U�N
FOUJPO�JU �CVU�IVHF
MZ�JN
QPSUBO
U
r����E
FDPN
QPTJUJPO
#SP
PLT�HP
U�JU�X
SPOH
�
�£\ÊV��
Vi«ÌÕ>
�Ê��Ìi}
À�ÌÞ
#SP
PLT�TB
ZT
riUI
F�N
PTU�JN
QPSUBO
U�DP
OTJEFS
BUJP
O�JO�TZT
UFN
�EFT
JHOw
XIBU rTZT
UFN
�JT�EFT
JHOFE
�BSP
VOE�B�TN
BMM�TF
U�PG�DP
IFS
FOU�JE
FBT
rGVODUJP
OBMJUZ�GMPXT�GSPN
�B�VOJGZJOH�DP
ODF
QUV
BM�N
PEFM
XIZ rFBT
F�PG�VTF
�JN
QMFN
FOUBUJPO �F
YUFOTJPO
FYBN
QMF
rBMN
PTU�BMM�EPDV
NFO
U�QSP
DFTTPST�CBT
FE�PO�QBS
BHSB
QIT
rJEFB
�JOWF
OUFE�BU�9FS
PY�1
"3$�JO���T��CBT
JT�PG�8
PSE
�FUD
�
��ÜÊÌ�Ê}i
ÌÊ�
4UV
EZ�TZ
TUFN
T�UI
BU�IBW
F�JU �B
OE�CVJME�PO�UIFN
������
r.FN
PSZ
�BCTUSB
DUJP
OT��WJSUV
BM�N
FNPSZ
�($ �T
USPOH�UZ
QFT
r$PODV
SSFO
DZ�BCTUSB
DUJP
OT��UISF
BET �MPDL
T �USB
OTB
DUJP
OT
r$PN
NVOJDBUJP
O�BCTUSB
DUJP
OT��BTZ
OD�'*'
0�N
FTTB
HFT
-FB
SO�UP�BSUJDVMBUF�DPODF
QUT�BOE�BOBMZ[
F�UI
FN������
r4FU�SFMBUJP
O�N
PEFMMJOH�I
FMQT�FY
QSF
TT�TZT
UFN
�DPODF
QUT
r%BUB�BC
TUSB
DUJP
O�IFMQT�GBDU
PS�PVU�SF
QSF
TFOUBUJPO�EFUBJMT
r%FQ
FOEFO
DJFT
�IFMQT�EFD
PVQMF�DPODF
QUT�JO�JN
QMFN
FOUBUJPO
�
iÝ>�
«�iÃ
OPU�FW
FSZP
OF�IFS
F�IBT
�UBL
FO������ �T
P�y
TFU�SF
MBUJPO�N
PEFMMJOH
rTUZ
MF��1
BSBH
SBQI�����4
UZMF
rOFY
U��4UZ
MF�����4
UZMF
rCBT
FEPO��4
UZMF��� �4UZ
MF
rGPSN
BU��4
UZMF����'PSN
BU
EBUB�BC
TUSB
DUJP
O
rTUZ
MF�HFU@GPSN
BU�iUZQ
FGBD
Fw�IJE
FT�SFQ
�PG�TUZMF�IJFSB
SDIZ
EFQ
FOEFO
DJFT
rXBO
U�UP
�HFU�GSP
N�TUZ
MF�UP�QBS
BT �C
VU�BW
PJE
�EFQ
FOEFO
DF
rTP�4UZ
MF�EFQ
FOET�PO�4UZ
MFE0CK �BO
E�1
BSBH
SBQI�JT�4UZMFE0CK
�
��ÃÌ�À�V>�Ê>Ã�`i
UIFT
F�JE
FBT�JO
WFOUFE�JO������T
r&OUJUZ
�SFMBUJP
OTI
JQ�$IFO
���
r"CTUSB
DUJP
O�GVODUJP
OT�)
PBS
F �����IJE
JOH�1
BSOBT
�����EBUB�
BCTUSB
DUJP
O�(VUUBH
��� �$
-6�-JTLPW ���
r6TF
T�EJBHS
BN�1BS
OBT
���
JOUFSF
TUJO
HMZ �#
SPPLT�N
JTTF
E�UIFN
rTBJE�1
BSOBT
�XBT
�XSP
OH�BC
PVU�IJE
JOH
rUIPVHI
U�TUFQ
XJTF�SF
GJOFN
FOU�UP
Q�E
PXO�EFT
JHO�X
BT�N
BKPS�BE
WBODF
�
��ÜÊÌ�Ê>Û��`Ê�
OFW
FS�IBW
F�JU
rGFB
UVSF
�ESJWF
O �P
VUTJE
F�JO
�EFT
JHO
UZQJGJFE�CZ�.
JDSP
TPGU�T�$
MJQQZ �SFD
FOUMZ�SF
UJSF
E
HFU�JU�X
SPOH
rPWF
S�HF
OFS
BMJ[F��N
JTT�JN
QPSUBO
U�EJTUJODUJP
O
6OJY�T�VOJGJDBUJP
O�PG�EBUB���QSP
HSBN
�GJMFT
MPTF
�JU
rOFX
�GVODUJP
OBMJUZ�OPU�BO
UJDJQBUFE
TFDUJP
OT�JO
�8PSE
�IBS
E�UP�JN
QPTF
�PO�QBS
B�TUSV
DUVSF
GPOUT�FWF
SZXIFS
F�O
PU�KV
TU�CPME
�JUBMJD��X
JEUI
�TXBT
I �MJHBUVSF
T
XFC
�QBH
FT�JO�8
JOEPXT�TBW
F�B�QBH
F�JO
�*&�BOE�TFF
�XIBU�JU�EPFT
y
�
�Ã�½ÌÊÌ�iÊV�
`iÊi��
Õ}�¶
XIZ�OPU�FY
QSF
TT�DPODF
QUT�JO�DPEF
rDPEF�JT�B�CBE
�NFE
JVN
IBS
E�UP�SFB
E��P
CTD
VSF
T�HMPCBM�QSP
QFS
UJFT
DBOhU�BOBMZ[
F�BV
UPN
BUJDBMMZ
IBS
E�UP�GJY�X
IFO
�XSP
OH
rDPEF�JT�UPP�MBUF
BT�4BMU[FS
�TBZ
T �iGJOE�CBE
�JEFB
T�GBTUw
rXJUIPVU�TF
QBS
BUF�EFT
JHO
DBO�U�EFMFH
BUF�PS�XPSL
�FBT
JMZ�JO
�B�UFB
N
CVU�$*�IBT
�CJH�FGGFD
U�PO�DPEF
rUFO
ET�UP
�TJN
QMJGZ�JOUFSGBD
FT
rNPSF
�GVO�UP�DPEF �GFX
FS�TFS
JPVT�CVHT
�
Ü>ÀÊÃÌ�
ÀÞ\Ê
/�-
XIBU�IBQ
QFO
T�JG�BMM�ZPV�IBW
F�JT�UIF�DP
EF
BJS�USBGGJD�DP
OUSPM�UP
PM�TV
JUF �CVJMU�CZ�/"4"�JO������T
rEFT
JHO�HSF
X�BSP
VOE�BMHPSJUI
NT
rDPEF�JT�X
FMM�XSJUUFO
�BOE�X
FMM�DP
NN
FOUFE
rTZT
UFN
�IBT
�CFB
VUJGV
M�6* �QFS
GPSN
T�XFMM �X
PO�/
"4"�BXBS
E
rEFQ
MPZF
E�JO�BCPVU����BJSQPSUT
OPX�'""�X
BOUT�UP�iSV
HHFE
J[Fw
�GPS�XJE
F�EFQ
MPZN
FOU
rUPP�SJTLZ�UP
�TUBSU�BHB
JO
rLOPXMFEHF
�USB
QQFE
�JO�DPEF
rQBZ
JOH����N
�UP�$
4$�UP�X
SBQ�JO�MBZ
FST�PG�BE
EJUJP
OBM�DPN
QMFYJUZ
��
Ã>�«�iÊ/�
-Ê«À�L
�i�Ã
GMJHIU�JE
FOUJGJFS
T
rPSJHJOBMMZ�KVTU�GMJHI
U�OVN
CFS
rCVU�TZ
TUFN
�DSB
TIFE
�CFD
BVTF
�PG�QMBO�GPS�EFQ
BSUJOH�GMJHIU
rTP�BEEFE
�EFQ
BSUV
SF�BJSQPSU
QMBUGPSN
�EFQ
FOEFO
DFT
rVTF
T�4PMBSJT�TQ
FDJGJD�EBUB�TUSV
DUVSF
�MJC
SBSZ
r.PUJG�6*�VTF
E�GPS�TD
IFE
VMJOH�UP
P
r-JO
VY�QPSU�B�GPSN
JEBC
MF�UBT
L
rTDI
FEVMJOH�QSP
CMFN
T
��
�Ó\ʺ«�>�
ÊÌ�ÊÌ�À�ÜÊ��i
Ê>Ü>Þ
»
1MBO�UP�UISP
X�POF�BX
BZ��Z
PV�X
JMM�BO
ZIPX
rJN
QMFN
FOU�XIPMF�TZT
UFN
��USZ
�JU��UIFO
�TUBSU�BHB
JO
#SP
PLT�OPX�BEN
JUT
rEJBHO
PTJT�XBT
�SJHIU �CVU�UI
F�SF
NFE
Z�XBT
�XSP
OH
rQSP
CMFN
�XBT
�3PZD
F�T�XBUFS
GBMM
rJOTUFB
E��B
U�FW
FSZ�TUBH
F �B�SVOOJO
H�TZ
TUFN
QMBO
EFT
JHO
DPEF
UFTU
��
�i�
�½ÃÊë�À>�Ê�
�`i�
OPUF rHFUUJOH�UP
�DPEF�TP
PO�EPFT
O�U�N
FBO�PN
JUUJOH�EFT
JHO�
rB�MPDB
M�OPU�B�HMPCBM�PSE
FS
rTPN
F�HMPCBM�EFT
JHO�GSB
NFX
PSL
�FTTFO
UJBM QMBO
EFT
JHO
DPEF
UFTU
��
�ÌiÀ>Ì�ÛiÊ`i
Ûi��«�
i�Ì
JEFB
�JT�OPX�DPN
NPOQMBDF
r.JDSP
TPGU��O
JHIUMZ�CVJME
r0QFO
�TPVSD
F�N
PWF
NFO
U��CVJME�FBS
MZ �C
VJME�PGUFO
r&YUSFN
F�QSP
HSBN
NJO
H��CVJME�CBT
JD �U
IFO
�SFGBD
UPS
XIBU�JT�91
rBO�BQQSP
BDI�UIBU�DPN
CJO
FT�O
FX�BOE�PME
�JEFB
T�,
FOU�#FD
L ��
���
riUFTU�GJSTU�QSP
HSBN
NJO
Hw��JN
QMFN
FOU�UI
F�UFTUT�CFGPSF
�UIF�DP
EF
riQBJS�QSP
HSBN
NJO
Hw��U
XP�BU�B�UFSN
JOBM�MJLF�#SP
PLT�T�UFBN
�PG�UX
P
riSF
GBDUPSJOHw
��BQQMZ�TUBOEBS
E�USB
OTGPSN
BUJP
OT�UP
�SFT
USVDU
VSF
GJSTU��iTJN
QMFTU�UIJO
H�UI
BU�DPVME
�QPTTJC
MZ�X
PSL
w
rCVU�OP�EFT
JHO�CMV
FQSJOU���
B�CBE
�JEFB
�
��
Ü>ÀÊÃÌ�ÀÞ\Ê�
iÌÃV>«
i½ÃÊ`i
��Ãi
/FUTD
BQF�HS
PXT�SB
QJE
MZ
r������/
FUTD
BQF�TI
JQT�/BW
JHBUPS���� �C
BTFE
�PO�.
PTB
JD
���EFW
FMPQFS
T ����LMPD
r������
�����/
��HSP
XT�GBTU �X
PSL
T�PO�GFB
UVSF
T �JHO
PSF
T�EFT
JHO
$PN
NVOJDBUPS�����IBT
�����EFW
FMPQFS
T ��N
MPD
NFB
OXIJMF�CBD
L�JO�3
FEN
POEy
r������.
JDSP
TPGU�TIJQ
T�*O
UFSO
FU�&
YQMPSF
S����
r/5�GSP
N�TDS
BUDI
�0GGJDF�SF
TUSV
DUVSF
E �*
&����SFE
FTJHOFE
/FUTD
BQF�USJFT�BH
BJO
r$PN
NVOJDBUPS�����GSP
N�TDS
BUDI
�.P[JMMB��
���BT
�PQFO
�TPVSD
F
rCVU�UP
P�MBUF��/
FUTD
BQF�T�TI
BSF�ESP
QT�GSPN
�_�����UP�����
GVMM�TUPSZ�FTQ��Q
MBUGPSN
�JOEFQFO
EFO
DF�JO��.
JDIBFM�"��$
VTVNBO
P�BOE�%BWJE�#��:
PGGJF��$
PNQFUJOH�PO�*OUFSOFU�5JN
F��-FTTPOT�GSPN�/
FUTDBQ
F�BO
E�JUT�
#BUUMF�XJUI�.
JDSPTPGU �'
SFF�1SFTT ������
��
�Î\Ê«ÕÃ�ÊÌ�iÊi�
Ûi��«i
POF�UI
BU�#
SPPLT�N
JTTF
E�QFS
IBQ
T�CFD
BVTF
�PG�04�GPDV
T
rSFMBUFE
�UP�FOE�UP�F
OE�BSH
VN
FOU
JNQPSUBO
DF�PG�SF
RVJSFN
FOUT
rNBO
Z�EFW
FMPQN
FOUT�GBJM�CFD
BVTF
�UIFZ
�TPMWFE
�UIF�XSP
OH�QSP
CMFN
$*�OP�HPPE�JG�ZP
V�IBW
F�UI
F�XSP
OH�DP
ODF
QUT�
rBMM�BWJPOJDT�TP
GUXBS
F�BD
DJEFO
UT�EVF�UP
�SFR
VJSFN
FOUT
SFRVJSFN
FOUT��Q
VTI
�UIF�CPVOEBS
Z
rCFZ
POE�TQFD
�XIBU�UP
�HPBMT�X
IZ
rCFZ
POE�N
BDIJO
F�UP
�QIZT
JDBM�FOWJSP
ON
FOU
rCFZ
POE�N
BDIJO
F�UP
�TPDJBM�FOWJSP
ON
FOU
��
vÀ��
Êëi
VÊÌ�Ê}�>
�Ã
JT�DBMM�GP
SXBS
EJO
H�USBO
TJUJWF
rJG�1��
2�BOE�2
��3 �U
IFO
�1��
3
rEFQ
FOET�PO�HPBM�;BW
F
iGPMMPX�N
Fw���OP��i
EFMFH
BUFw
���ZF
T
11
22
12
3
GPMMPX�N
F
EFMFH
BUF
��
vÀ��
�>V���i
ÊÌ�Ê«�
ÞÃ�V>�Êi�Û
�À��
�i�
Ì
"JSCVT�"����BDD
JEFO
U�BU�8
BSTB
X�BJSQPSU
rQMBOF�UP
VDI
FE�EPXO�JO�X
FU�BOE�X
JOEZ�XFB
UIFS
rQJMPU�SF
RVFT
UFE�SFW
FSTF
�UISV
TU �C
VU�JO
UFSMPDL
�QSF
WFOUF
E�JU
XIBU�X
FOU�XSP
OH
rTQFD
JGJDBUJP
O�TBJE
iEJTBC
MF�SFW
FSTF
�UISV
TU�X
IFO
�OP�X
IFF
M�QVMTFT
w
rTIPVME
�IBW
F�HP
OF�CFZ
POE�N
BDIJO
F�UP
�FOWJSP
ON
FOU
0O(SP
VOE�����8
IFF
M1VMTFT
XSP
OH�
%JTBC
MF35�����O
PU�8
IFF
M1VMTFT
TP�0
O(SP
VOE����O
PU�%JTBC
MF35
XSP
OH�
FOW
NBD
IJO
F
JOUFSGBD
F
��
vÀ��
�>V���i
ÊÌ�ÊÃ�V�>�Êi�Û
�À��
�i�
Ì
QBUJFOU�N
POJUPSJOH
rNVTU�N
BUDI
�DPN
QVUFS�*%
T�UP
�QBUJFOU�JE
FOUJUZ
rMJLF�LFZ
�QSJODJQBM�CJO
EJO
H�EJTDV
TTFE
�JO����
FBSMZ�.
BDJO
UPTI
rUP�EFMFUF�B�EJTL �S
FQMBDF
�TZT
UFN
�EJTL
��
�{\Ê`iV��
«�Ã�Ì���
TUFQ
XJTF�SF
GJOFN
FOU���UP
Q�E
PXO�EFT
JHO
r#SP
PLT�JE
FOUJGJFT
�BT�CFT
U�JE
FB�PG�EFD
BEF��
��T
rCVU�JU�T�CFF
O�B�GBJMV
SF
XIBU�JT�UP
Q�EPXO�EFT
JHO
rTUBSU�X
JUI�B�CPY�N
BSLFE
�i4ZT
UFN
w
rJO�FBD
I�TUFQ �T
QMJU�B�CPY�JOUP
�B�UXP�PS�N
PSF
�TVC�C
PYFT
rXIFO
�CPYFT
�BSF
�FMFN
FOUBSZ
�QSP
HSBN
�TUBUFN
FOUT �T
UPQ
XIZ�EPFT
O�U�JU�XPSL
rOP�FOWJSP
ON
FOU�N
BDIJO
F�EJTUJODUJP
O�TF
F�QVTI
JOH�FO
WFMP
QF
rEPFT
O�U�FYQMPJU�X
IBU�ZPV�BMSFB
EZ�IBW
F �PS�LOPX�IPX�UP�EP
rUIF�N
PTU�SJTLZ�BQ
QSP
BDI
��
À�Ã�Ê��
ÊÌ�«
�`�Ü
�Ê`i
�}�
UP�N
JUJHBUF�SJTL
T
rNBL
F�EFD
JTJP
OT�XIFO
�ZPV�I
BWF�JO
GP
rHFU�FBS
MZ�GFF
ECBD
L
CVU�JO
�UPQ�E
PXO�EFT
JHO
rWFS
Z�GJSTU�EFD
PN
QPTJUJPO�JT�N
PTU�N
BKPS
rTZT
UFN
�JT�N
BEF�PG�"�BOE�#
�CVU�EPO�U�LOPX�X
IBU�"
�BOE�#
�BSF
�
rFSSPST�JO�FBS
MJFT
U�EFD
PN
QPTJUJPO�O
PU�EJTDP
WFSF
E�VOUJM�UI
F�FO
E
��
>Ê��ÀiÊÃÕLÌ�iÊVÀ�Ì�µÕ
i
DPN
QMFYJUZ�BS
JTFT
�GSP
N�EJGGFSF
OU�BT
QFD
UT
rDPOTJEFS
�B�IPTQ
JUBM�JOGP
SNBUJP
O�TZT
UFN
EBUB�N
PEFM�UP�TUP
SF�QBUJFOU�JO
GP
BVEJUJO
H�PG�VTF
ST
BVUI
FOUJDB
UJPO�BOE�DPOGJEFO
UJBMJUZ
SFDP
WFSJOH�GSPN
�GBJMV
SFT
JO�UPQ�E
PXO�EFT
JHO
rDPOTJEFS
�UIFT
F�BMM�BU�PODF
rFBD
I�N
PEVMF�I
BT�BMM�BTQ
FDUT
PCKFDU�P
SJFO
UFE�QSP
HSBN
T�IBW
F�UI
JT�QSP
CMFN
rBMM�BTQ
FDUT�PG�GV
ODUJP
OBMJUZ�JO
�FWF
SZ�PCKFDU
rEFT
JHO�QBUUFSO
T�W
JTJUPS �PCTF
SWFS
�FUD�USZ�UP
�NJUJHBUF�UI
JT
��
Ã�ÊÜ�>
ÌÊÌ�
Ê`�¶
POF�BQ
QSP
BDI
rTPMWF�FB
DI�TVCQSP
CMFN
�TFQ
BSBU
FMZ
rUIFO
�USZ
�BOE�DPN
QPTF
�TPMV
UJPOT�UP
�TVCQSP
CMFN
T
XIZ�JT�UIJT�HPPE
rFBD
I�TVCQSP
CMFN
�VOQPMMVUFE�CZ�PUI
FST
rXIFO
�ZPV�GBD
F�UI
F�IBS
E�QSP
CMFN
�
ZPV�LOPX�X
IBU�ZPV�SF�DP
NQPTJOH
��
«>ÀÌ��}ÊÜ�À`Ã
i5IF�.
BDJO
UPTI
�JT�MJLF�TB
VTB
HFw�(
BTTF
F
rUBT
UFT�EFMJDJPVT�CVU�ZP
V�EPO�U�X
BOU�UP
�LOPX�X
IBU�UIFZ
�QVU�JO
�JU
rEPO�U�GPDV
T�PO�GVODUJP
OBMJUZ�BO
E�BQQFB
SBODF
�BMPOF
rEFT
JHO�N
BUUFST�
SFN
FNCFS
�������BOE������
rBOE�ZPV�N
BZ�FTD
BQF�UI
F�FS
SPST�PG�UI
F�QBT
U