NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 %...

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�2à�ã�ãÎÆ ñ%Ó«�´Ó~ñ ó éIÞëØ�Ù�ÝCà ö ÙIØ�CbeâáÞßØ�Ù�ÝbÜ�ÝmØçáê V à8Ý^Ü�ågÞßØ�Ù<Knà8Û^]�_^Ü�ê`BðÚ�à ö K�Ù ö"ö àsàå V* L�À��CÀ VJÜ�Ý?Ý+C ö"ö ÙbÞzÚbÜëä ÞëØ�Ùiå DGFaO�98�a X� * LQ�����(V=5�kLQ�(VÙ�Û�Ü�ÝbÞßÝúàå V ÞßØ�Ù ö Ü�å�Ü ö ÜcbbÜ�ådB·�ÃÝCàÞzÜ�ÝYXuÙ�Ý SfehgYijUkg

L/UÀ:=TPTCRI?ÎHKJPMÚç/:=ÌEv�c&FaR t <\:=D«çËM�D{D!: H UÎHKJPM5�=:=<>FQ:=HKFIUVO�:=R;TP<>UViPRaMfD L>XVA�öÖV>±2l;M5[�_KMHKJPM%b:VN8HrHKJ`:=H?PI¼iLZ�ÂVuF|_r:G��FaRai`M�<>H�_KT�:VN\MVA;¼ÎM$OPM�M�o�H U!�VM�<>Fµb~?!HKJ`:=H * ° L�À��KÀ¸V;F|_r_KH <>UVO t Ra?M�RIRaFaTPH F|NML�N8UEM�<\N8FI�VMV>±`F�A÷M�A

* ° LZ�´���kVlFx� ª�ª � ª«ª Y½ ¾ ®±°U² � 6(��Å�3�õ

¼ÎMzHKJPM�<>M8b~UV<>M%<>M�¶V[PFa<>MÈ � È ) �8� * � ) LQ�%V�� ) Fx� È � � Y� � 6��fÅI� �m6=�#Åw� � õ

^�HÙb~UVRIRaU)lr_;HKJ`:=H

* ° LZ�´���kV ³ µ ° È � È ) õ%�õW���+* � ) LZ�nV õ%�õ%� )F � µ ° LZ¿��(V Y³ � ª � ª Y½ ¾ ®¸°U²F � ª�ª � ª«ªÁY½�¾z®¸°U² õL;JCM%�`O�:=RÉ_KHKMfTeD!:=nVMh_Ù[`_KM$U=b"H JCM-·gUVFIO�Nf:=<�ýM�v�@C<>FIM�o�<KFQN}J`_8ÍEFaOPM�¶V[`:=RaFaH�?V±`:=O`o�HKJPMmb:VN\HmH J`:=H��F|_;Ð�M�<>U{UVOIô Ä õ�@�"!��z�  �¡�¢on`¢p%rqù¥@¦snmÒ@Ï�Î�¢pt '5Òî¨ç¢

¼ÎM�N�:=O�:=TPTPRa?pH JCM�_>:=D{M�TP<>U�N\M�o�[C<>M!H UÓH JPM&�VM�N8HKUV<{�=:=RI[PM�o¾Nf:V_KMVA Z UVO`_KF|o�M�<-HKJPMT`:=<>HKFQ:=R*osF�Ñ�M�<>MfO�HKFQ:=R�M�¶V[`:=HKFaUVO*±

È ) È u È v õõW� )�w � )�u�v LZ�%V õ%� uõW� v ³ �8�Q� FaOw� �ó ³ k�� UVOwô Ä �sõ%�?�È ) È u È v w � )�u�v LQ�%V õW� uõ%� v �, ) ³ ��z� UVO^ô ¼ ³ õ%�x- ô Ä õ

j

Page 18: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

² t :=FIO/±E[`_KFaO t :�´�<>M�M�O*Í�_db~UV<>D-[PR|:4b~UV<;M�:VN>J�N\UVDGT�UVOPM�O�H�U=b�óÀ_KM�T`:=<\:=HKMfRa?V±Vl;MrUViPH>:=FIO!HKJPM�):=<>F|:=H FaUVO`:=R�TP<>UViCRIM�D&±

* ° L ó��X��V ³ �kLz��V�� ó^Å<ym�m6k�mÅzym� L>XVõ�jÖVl�JCMf<>M * ° L ó��X��V ³ µ ° È � È ) È u È v õ%�H�õ%� )�w � )�u�v LQ�%V õ%� uõ%� v �

�kLz��V ³ µ ° È � �H�ë�8��N µ û ¾ È � ����H�z�:=O`o�H JCM�_KT`:VN8MHy �xLQPI¼KLQ��VXV Ç F|_ t Fa�VM�O5i�?

y ³({ �5Å^LQP ¼ LQ��VXV Ç ºU� ª ûKü ³ kJ|VõL/U{:=TPTCRI?GHKJPM�ç/:=ÌEv�c&FaR t <\:=D çËM�D{D!: FIO�H JCFQ_4Nf:V_KMV±�l;M%<>M�¶ [PFI<>MmH J`:=H

È �c} ) È u } v �8��~ ) w � )�u�v LQ�%V�� u ~ v Fx� È �c} ) L��8�"~ ) V Y � 6��fÅI�?�76=�"ÅI� � �76r~{ÅI� Ç õ² t :=FIO�l;M t MfHr_KH <>UVO t MfRaRaFITPHKF|N\FaH�?IL�N8UEM�<\N8FI�(FIHÊ?�V"i�?

* ° L ó��8óOV ³ µ ° È � È ) È u È v õ%���õ%� )�w � )�u�v LQ�%V õ%� uõ%� vF � µ ° È �c} ) L õ%���õ%� ) V Y³ � ª ó ª Y½�¾Z®±°U²F � ª�ª ó ª�ªÁY½ ¾ ®¸°U² õ

¼ÎM-N8UVO`N8RI[`osMzi�?�[`_KFIO t ·gUVFaO`N�:=<ùýM�v1@C<>FaMhos< F|N>J`_8Í(FIOPM�¶ [`:=RIFaH�?V±`:=O�o&HKJPM$b:VN8H�HKJ`:=H$ópF|_�Ð�M�<>UUVOIô Ä õ6"7j� �¤�C�#��îAH��A�� �

L;JCM!M�¶V[`:=HKFIUVO�_6U=b�RaFaOPM�:=<6MfR|:V_KHKFQN8FaH�?pDGU]o�M�R2H JCMÚo�F|_KTPR|:VN8MfDGM�O�H6óOLZ�nV�U=b%:&i�U]o�?��l�JCFQN}J{F|_w�`ÌEM�oG:=RIUVO t :$T�UV<>H FaUVOGU=b*FIH>_2i�UV[PO`oP:=<>?V±Uô Ä ±�:=O`o�FQ_2_K[PiCÕ�MhN8H�HKU-:6_K[P<Kb:VN8M;b~UV<\N8MU=bÈosMfO�_KFIH�?eâ�:=RIUVO t H JPM�UVH JPM�<�T`UV<>HKFIUVOÓU=b�HKJPM!i�UV[PO`oP:=<>?V±Oô ¼ ³ õ%��-?ô Ä õ�L;JPM!i�U]os?F|_z:=R|_KUÚ_K[CiPÕ�M�N8HzHKU�:!�VUVRa[PDGM6b~UV<\N8MGFaOÀFaH>_$FIO�HKMf<>FaUV<{L�_K[`N>Jp:V_ t <\:��(FIHÊ?�V t Fa�VM�OÀi�?m�V±É_KM�M@gF t [P<>M6XVAIXVA

X�k

Page 19: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

ô ¼

ô Ä��M�����h�+� �M���h���h�����

.Ü â ¶��â ¶h�

¶ �

� ¶ �

@gF t [P<>M6XVAIXVº ² B]:=DGTPRaM%�rUVD!:=FIOL;JCM{M�¶ [`:=H FaUVO`_$U=brRIFaOPM�:=<zM�R|:V_KH F|N8FIHÊ? E÷�VW8G±�E �V�UG�±�E �EW8G±�:=<>M!:eN\UV[CTPRIM�oeM�RIRaFaTPH F|N!_K?�_KH M�D&±

:=O`o�N�:=O5i�Mzl4<>FIHKHKMfO�FaO&H JPMÈb~UV<>D� � ) LKótV ³ �Èu } v É ¼ ´� )�u�vc��u�v LKótV���È) É ¼ õ � � )õ%� ) LKóOV ³ �8�y� FaOd�?�ó ª ûKü ³ k��¦:=O�o �È) É ¼ � � ) LKóOV �, ) ³ � � UVOdô ¼ ³ õ%��- ô Ä õ

L;JCMz_K?EDGDGM�H <>F|NrHKJP<>M�Mfv�i�?Ev�HKJP<>M�MMÝbÞyÚïÙ�Ý�Ý�D!:=H <>FaÌ`± � � ) LKóOV��CFQ_ t FI�VM�O�i�?� � ) L óOV ³ X� L õ%���õ%� ) N õ%� )õW�ù� V>õ

L;JCM�HKM�O`_KUV<u ´� )�u�v FQ_;:6_K?(DGD{M�HK<>FQN=±(T`UE_KFaHKFI�VM%o�M8�`OPFaHKM�UVT�Mf<\:=HKUV<;l�JCFQN}J{UVT�M�<\:=H M�_2UVO5_K?(DGvDGM�H <>F|N$H JC<>MfM�v�i�?Ev�HKJP<>M�MzD!:=HK<>FQN8M�_�A � � ) FQ_%N�:=RaRIM�o H JPMSÝbÞzÚ�àÜ�åPA[.ܽF|_4H JPM�UV[PH�l�:=<\o�OPUV<>D!:=RUVOIô ¼ õ

@C<>UVD :¬´�<>M�M�O*Í�_2b~UV<>D�[PRQ:�± l;MzUViPH>:=FaO5HKJPM%�):=<>F|:=HKFIUVO`:=R�b~UV<>D�[PR|:=H FaUVO

* ° LKó��X��V ³ �(Lz��V�� ó^Å<y`�<6k�^Å<ym�l�FaHKJ

* ° LKór�X�îV ³ µ °�È�c} ) É ¼ � � ) LKótV � � ) Lz��V�� �kLz��V ³ µ °

�È�¸É ¼ �8�h�8��N µHû ¾ �È �¸É ¼ ��h�8�Q�XVX

Page 20: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

:=O`o y ³({ �5ÅoLZP ¼ LZ�ÂV�V � º#� ª ûKü ³ kJ|Võ² _KT`M�N8F|:=R"N�:V_KM-U=b�FaO]HKM�<>M�_KH%FQ_ml�JCMfOÎHKJPMGD!:=H M�<>F|:=RÉTC<>UVT`M�<>HKFIM�_$:=<>M-FaO`o�M�T`M�O`osMfO�HrU=b

T�UE_KFIHKFIUVO/±EF�AùMVAdH JPMmD¬:=HKM�<>FQ:=R�F|_÷Øçá ö á�B�ÙbåkÙ�áæÖÝ\±�:=O`oGHKJPM$i`M�J`:0�EFaUV<2U=bÉHKJPMzD!:=HKM�<>FQ:=RPF|_;HKJPM_>:=DGMrFIO&:=RIR�o�Fa<>M�N\HKFaUVO`_�±EF�A÷M�AdH JCM%D!:=H M�<>F|:=R`F|_?Ü�ÝCáÞzÚ�áie�Üëä�g4^�O�H JCFQ_2HKJPMzN�:V_KM%HKJPM$Mh¶ [`:=HKFIUVO`_b~UV<�HKJPM6_KH <\:=FaO�<>Mhos[`N8M�HKU

� � ) LKóOV ³Z� L �Èu É ¼ ��u�u L óOVXV��i� ) N½�h� � � ) LKóOV³õ�4M�<>M � F�k4:=O`o���@�k�:=<>M�HKJPM;ç*:=DsýM"N8UEMiv5N8FIM�O�H>_�±�l�JPF|N>J$<>M�TP<>M�_KMfO�HPTCJ]?�_KFQN�:=R=TP<>UVT�Mf<>HKFaMh_U=b�H JCMzD!:=HKMf<>F|:=R�A���_KFaO t b:=D{FaRaFQ:=<;OPUVH>:=HKFIUVO`_�±(l;Mm�`O`oGHKJ`:=H

� � ) L óOV ³o� L �Èu É ¼ õ%� uõ%� u V��i� ) N��´L õ%���õ%� ) N õ%� )õ%� � V���È) É ¼ õ � � )õW� ) L óOV ³ �È) É ¼ L � L �Èu É ¼ õW� uõW� u V�� � ) N��´L õ%���õ%� ) N õ%� )õW� � VXV ³ � � �UV< � �Èu É ¼ õWY�� uõ%���ëõ%� u N�� �È) É ¼ õ%Y����õW� Y) N õWY�� )õ%���ëõ%� ) ³ � � õL;JCMh_KMmMh¶ [`:=HKFIUVO`_4N�:=O&i`M%l4<>FIHKHKMfO�:V_�È) É ¼ � õ%Y����õ%��Y) NFL � N��´V õ%Y�� )õW�ù�ëõW� ) ³ �8�Q� L>XVõIX�kÖVUV< �M�&ó�NsL � N/�´VQ¿�¿ À=ó ³ �Võ L>XVõIXVXV

L/U�TP[CH-HKJPM5M�¶ [`:=H FaUVOªFIOª�):=<>F|:=H FaUVO`:=R2b~UV<>D&±�l;M�D-[PRaHKFITPRa?�M�¶ [`:=H FaUVOgL>XVAIX�kÖV$i]?5� � �FaO]HKM t <\:=H MmU)�VM�<�� �P_K[PD¯U=�VM�<u�":=O`o�FaO]HKM t <\:=H Mmi]?GT`:=<>H>_�Ag¼ÎMzHKJPM�O&UViPH>:=FIO

µ ° � �È �¸É ¼ �È) É ¼ õ%�H�õW� ) õW���õ%� ) NsL��cN � VXL �È�¸É ¼ õ%�H�õ%��� VXL �È) É ¼ õ%� )õ%� ) V ³ µ °�È�¸É ¼ �H���8��N µKû ¾ �È �±É ¼ ����H��õ

² t :=FIO�l;M$MfÌ(TP<>M�_>_2H JCFQ_ÙFIO&HKM�<\_KM%OPUVH>:=H FaUVOÚ:V_�±

* ° LKór�X�îV ³ �(Ly�îV�� ó^Å�y`��6k�mÅzyÎõ L>XVõIX��ÖV² O&M�¶V[PFa�):=RaMfO�H2b~UV<>D�[PRQ:mb~UV< * ° LKó��X��V;[`_KFaO t H JCM�_KHK<>M�_>_2D¬:=HK<>FaÌ � � ) L óOV2FQ_ t FI�VM�O�i]?

* ° LKó����îV ³ µ ° �h� �È �¸É ¼ �È) É ¼ � � ) LKóOV � � ) Lz��VkN � L �È �±É ¼ õW�8�õW�ù� V�L �È) É ¼ õW� )õW� ) V>õ L>XVõIX�yÖVX��

Page 21: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

L;JCM{TC<>UEU=b�HKJ`:=H * ° LKó��X��V���:V_ t FI�VM�OpFaOpM�¶V[`:=HKFaUVOsL³XVAaX�yÖV>±gFQ_6_KHK<>UVO t Ra?�M�RIRaFaTPH F|NSL1N8UVvM�<\N8FI�VMV%FaO½HKJPMoLZPI¼iLQ��VXV � OPUV<>DøF|_6OPUVOCvHK<>Fa�EF|:=RA�LÙJPF|_6F|_6i�MhN�:=[`_KM�l;M!OPM�M�oÎH UÎi�UV[PO`o:=RaR"N8UVD-iPFaO`:=HKFIUVO`_ÈU=b 0 �+ 0¢¡�£ i�?�N8UVD-iPFaO`:=HKFIUVO`_4U=b�HKJPM�b~UV<>D ¼Y L 0 �+ 0f¡�£ N 0 � £0¢¡   V>õÉLÙJPM6b~UVRaRaU)l4FIO tFaOPM�¶V[`:=RaFIHÊ?�±Vo�[CM�HKUúpmUV<>O�L³X�jVkVjÖV>±(Mh_KH>:=iPRaFQ_KJCMh_g_KHK<>UVO t M�RaRIFaTPHKFQN8FaH�?"L�N8UEM�<\N8FI�(FIHÊ?�V�:=O`o6JPM�O`N8MM�ÌEF|_KH M�O`N8M6:=O`o�[POPF|¶V[PM�OPM�_>_db~UV<�HKJPM$�):=<>F|:=H FaUVO`:=R�TP<>UViPRaM�D L³XVAaX��ÖV³A�2à�ã�ãÎÆ ñ%Ó � Ó~ñ L�¤&Ý�ÅVÜ�ÕIêôýÜ*àâ�/ó*ÆPß|ôaÄ�� E÷�VöG±�EùyVx8G�±hE Y)kGëV�ó�é�õ%� Ü�Ý¥KOÜ e�ÝCäiØâÜ�Þ�b�è^äßé�g§¦�¨h©�ªQèÞßØ�Ùbå ª«ª ó ª«ªÁY½ ¾ ®¸°U² ì �HLQ��VXL µ ° È �c} ) � Y� ) LKóOVkN ª«ª ó ª«ªÁY¬ ­ V>õ² N\UVO�_KMh¶ [PM�O`N8M%U=b�p%UV<>O/Í�_2FaOPM�¶V[`:=RaFaH�?GFQ_�±PN}b A�E÷�VWG�±ÿ#�*àEÝ�Å)àsã ñ%Ó � Ó~ñ ó éJÞßØ�Ù ö Ù�à8Ýbæ�Ú�Ù"á¯é�ô Ä �xõ%�»Ü�Ý«BðÚ�Ù�àÞXÙbÚ{ÞßØçàå¥bHÙbÚ�á�àå Vy ³({ �5Å^LQP ¼ LQ��VXV Ç ºU� ª ûKü ³ kJ|U�ÞßØ�Ùbå � ª�ª ó ª�ª Y½ ¾ ®¸°U² ì µ ° È �c} ) � Y� ) LKótV ì � ª«ª ó ª«ª Y½ ¾ ®±°U² � 6gó^Å<yÀõ

L;JCMz_KH <>UVO t M�RIRaFaTPH F|N8FIHÊ?�L�N8UEM�<\N8FI�(FIHÊ?�V;U=b�H JPM$iPFaRIFaOPM�:=<2b~UV<>DÏb~UVRaRIU=l�_db~<>UVD&±

* ° L ó��8óOV ³ µ ° �h� �È �±É ¼ �È) É ¼ � Y� ) LKóOVkN � L �È�¸É ¼ õW���õW��� V YF µ ° �h� �È �±É ¼ �È) É ¼ � Y� ) LKóOVF �h�k� ª«ª ó ª«ª Y½ ¾ ®¸°U² õ^�O`_KHKM�:Vo�U=buHKJPM-ç/:=D\ýM-N8U(Mbv5N8FaMfO�H>_�±�l;M-Nf:=Oel;UV<>n5l4FIHKJ�¸dUV[PO t Í�_�DGU�o�[PRa[`_�±­¬���:=O`o

·gUVF|_>_KUVO*Í�_�<\:=HKFIUP±¯®â��o�M8�`OPM�oGFaDGTPRIF|N8FIHKRa?{i�?V±

�S³ ¬2®L>X÷Ns®�VXL³X°p�d®�V � � ³ ¬XøN�® õ

�r_KFIO t HKJPM�_KMzT`:=<\:=DGM�HKMf<\_�± H JPM6o�FµÑ�M�<>M�O�H F|:=R�Mh¶ [`:=HKFIUVOmL>XVAIXVXV2i`M�N8UVDGM�_¬XøNs® L��&ó�N X°�®

X&p�d® ¿�¿ À�óOV ³ �Võ L>XVõIX���Vq4UVH M$HKJ`:=H�HKJPM6_KMhN8UVO`o�N8UEMiv5N8FIM�O�H;iPRaU)lr_;[PT&:V_E®!:=TPTP<>UE:VN}JPM�_rXR)��õ

X�y

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6"7¢± ² AH:oA��O= � �C=´³ =M:m�î�¶µU~#>·� �C�#�p��A8��A9� ��@�¹¸u��� ºu¥�¦n§ Î?Ï�Òpq¯»�¥½¼

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� ¼ � Y

@wF t [P<>M%��AaXVº2BE[Pi�o�UVD!:=FIO�_gb~UV<$B]N}J]l�:=<>ÐVÍ�_"c M�H JPU�o� ³ � ¼�� � Y UVO�l�JCFQN}J!l;Mzl4FQ_KJ�HKU{_KUVRa�VM4��� ³ � FaOI�?�

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q4M�l£HKJPM�UV<>M�H F|N�:=RÉHKUEUVR|_4b~UV<%HKJPM-:=O`:=Ra?]_KF|_4U=buD�[PRaH FaTPRaFQN�:=HKFI�VM6B�N>J�l�:=<>Ðz_>N>JCMfDGM�_4J`:0�VMÕ�[`_KHg<>M�N8MfO�HKRI?mi`M�M�O{o�M��VM�RaUVT`M�o�AgS4MhN8M�O�Hgl;UV<>n%UVO6H JCM;H�l;U%_K[Pi`_KT`:VN8M"N�:V_KM2b~UV<gH JCM�N\UVO�HKFIOCv[PUV[`_dTP<>UViPRaM�D¦J`:V_2i�M�M�OÚo�UVOCM�i�?!ç�FaUVO`_�E÷WVxGz_P_KMfM%:=R|_KU-q4MfT�UVDGO�?E:V_>N>JPFanEJIEùöVxG�A�@PUV<;HKJPM�`OPFaHKM-M�RIM�DGM�O�Hrb~UV<>D-[PR|:=HKFIUVO&HKJPM-HÊl;UÚ_K[Pi�_KT`:VN8M-Nf:V_KM�J`:V_ri�M�MfOpo�F|_>N8[`_>_KM�o&FaOÀ9/Õ å=<\_KH>:VoE÷WG±Pce:=O`o�M�R*:=O`o!ceN Z UV<>DGFQN}nBE÷ö=�GÉ:=O`o�9/Õ å=<\_KH³:Vo�:=O`o�c�:=O`osMfR�E YHGA2c&UV<>M t M�OPM�<\:=R�H JPM�vUV<>FaMh_�b~UV<%H JCM{N�:V_KM-U=b;DGUV<>M6H JPM�OeH�l;UÚ_K[Ci`_KT`:VN8M�_�J�:��VM6i�M�MfOÎFaO�H <>U�o�[`N8M�o�i]?�¼�F|o�Ra[PO`oE÷xVWG*:=O`o!c�:=HKJPM�l»EùöVWG�A"LÙJPM%DGUE_KH�_K[`N�N8M�_>_Êb~[PR`<>M�_K[PRaH>_;_KU6b:=<�J�:��VMri�MfM�O&UViPH>:=FaOPM�oG�VM�<>?<>M�N8MfO�HKRI?$i�?z92<\:=D-iCRIMV±)·d:V_>N\F|:=n`±=¼p:=O t ±V:=O`o ]�[IE�X�ö8G�Ag¼ÀM;<>M��(FIM�lªH JPM�Fa<":=i`_KHK<\:VN8H*HKJPM�UV<>?l�JCFQN}J{N�:=OGi`Mr[`_KM�o6FaO!:=O`:=Ra?EÐ�FIO t D�[PRIHKFaTPRIF|N�:=H Fa�VM;�):=<>F|:=O�H³_gU=b�HKJPM%:=R t UV<>FaH JCD¬_/TP<>M�_KM�O�H M�oFaO5HKJPF|_;HKJPM�_KFQ_�A

² _>_K[PDGM&l;MÎJ`:��VM ; _K?EDGDGMfHK<>F|NoLFaO¹HKJPM * L�À«�KÀ V{FaOPOPM�<�TP<>U]o�[�N\HiV>±rT`UE_KFaH Fa�VMÀ_KM�DGFavo�M8�`OPFaHKM%RIFaOPM�:=<�UVT�M�<\:=H UV<\_����*U=b�OPUV<>DÏi�UV[PO`o�M�oGi�?�� ¹ ��õP�rM8�`OPM¾¬u�/i�?

¬u� ³ L��¾����ßVXL��ç���� í ¼ VùÀKÀKÀKL��¾�� ¼ V>õL;JCM�� � :=<>M5M�FaH JPM�<GTP<>UVÕ�M�N8HKFIUVO`_ UVO�H UÎHKJPM�_K[Pi`_KT`:VN8M�_23 � UV<!:=TPTC<>U)Ì(FID!:=HKFIUVO`_mHKJPM�<>MfU=b AL;JCM-M8Ñ�M�N8HKFI�VM�OPM�_>_mU=buHKJPM-T�:=<>H F|N8[PRQ:=<rD�[PRIHKFaTPRIF|N�:=H Fa�VM-:=R t UV<>FIHKJPD¢FQ_$o�M�H M�<>DGFaOPM�o�i]?&HKJPM<>M�o�[`N8HKFIUVO�FIO�HKJPM%M�<><>UV<;b~UV<4UVOPMzN8UVDGTPRIM�HKMzFaHKMf<\:=HKFaUVO5U=bgH JPM6_>N>JCMfDGMV±(FA÷MVAI±

ª ¬���� ª ì � ª � ª õédÌETPRaFQN8FaH"i�UV[PO`oC_gUVO � :=<>MrOPU=l�:��=:=FIR|:=iPRaM�A/¼ÎM%o�M�D{UVO�_KH <\:=HKM�i�M�RIU=l�JPU=l�HKJPUE_KM�i�UV[PO`oP_N�:=O5i�M$UViPH³:=FaOPM�o�A

¼ÎM%��<\_KH"OPUVHKM$H�l;U-[`_KM8b~[PR�F|o�M�O�H FaHKFIM�_

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Page 96: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

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õ � . æ è è èç�hK�/f_\!j . ` � `�` `�� `��ce\!p¤çs\!m�ridgf . è `�� `�� `����hK�HfKX . ` � `�è �3æ ��]í . ` . � v . � ]��Þ �i���[d?pe�Hk)d��HÄ `�� v ` � v ] è_`�� ` u�u ]æ¡cedgf_\�ked��WÄ | 0õ � ] v ` � ` � èç�hK�/f_\!j ] `�` ` . `Kæ `Kæce\!p¤çs\!m�ridgf ] `�� `�] ` u `�]��hK�HfKX ] ` � ��� �_` . �í v ��� . ` ]�è æ�æÞ �i���[d?pe�Hk)d��HÄ ��è `Kæ�æ v ��� `�è u è ��] v ]

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Page 101: NYU Computer Science · 2015. 11. 18. · 6 = ! g ) g = ! ) ! ) d p ! p ¡¢ - 2 g E 6 £ ¤ % 2 % w E 6 ¦¥¨§5© - g ) ª « ¬ ® ) p 6 ¥¯ ( G w w V ) /° 9;:=?5@;ACBEDGFIHKJ

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õ � . æ æ æ æç�hK�/f_\!j . `�` `�] ` u `Kæce\!p¤çs\!m�ridgf . è `�` `�` `�`Þ �i���[d?pe�Hk)d��HÄ `�� v ` � v ] è_`�� ` u�u ]æ¡cedgf_\�ked��WÄ | 0õ � u æ æ æ æç�hK�/f_\!j u `�� ` u ` v ` vce\!p¤çs\!m�ridgf u `�` `�� `�� `��Þ �i���[d?pe�Hk)d��HÄ ��è `Kæ�æ v ��� `�è u è ��] v ]

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