]b8}z˝s˝$bt bp gs——st˝k i‡r‡—%‡r b$˝y p‡t‡—sj...
TRANSCRIPT
![Page 1: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/1.jpg)
]B8}Z�s�$Bt BP Gs��st�k i�R��%�R b$�Y p�t��sj7�B{YsR�${ 7sj�R _�B{�RR�R
z$IksIYs� p� �Zj,s�t$*�}s��8�t� BP !}��s�$BtR i�R�s�{Y
=t$%��R$�k BP WB��Y ]s�Bj$ts]Ys}�j <$jj� W�]� 1�x��TndM(%,Zj,s�to�8s$j�Zt{��IZ
7YsZT7Y$st� Fs7sA��
d esR� �$�,bBBI BZj�%s�I7BZ�Yjs,�� q��E(�1
RYsZTRY$st� `soRsA���{B8
FZt� E� 1((d
VAR��s{�
Gs��st�k ��R��%� stsjkR$R $R ZR�I Ak }�BIZ{��R �B I�{$I� Bt �Y� s8BZt� BP
8Bt�k �Y�k t��I �B R�� sR$I� �B {B%�� bs��st�k {js$8R s�$R$t� IZ�$t� �Y� j$P� {k{j�
BP s }�BIZ{�� 3B� {B8}Z�$t� �Y� s}}�B}�$s�� bs��st�k ��R��%�� b� h�R� Z�$j$9�
h�R� stI R�{BtI 8B8�t�R BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I bs��st�k {BR� s�$R$t�
P�B8 s R$t�j� Rsj�� k ZR$t� �Y�R� ��RZj�R $t {Bt`Zt{�$Bt b$�Y R�B{YsR�${ 8BI�jR
BP �Y� Rsj�R }�B{�RR�R� b� {B8}Z�� �Y� 8�st stI %s�$st{� BP �Y� }�BIZ{��:R �B�sj
I$R{BZt��I bs��st�k {BR� BP s�����s�� Rsj�R B%�� �Y� }�BIZ{� j$P� {k{j�� 3$tsjjk�
b� ZR� �Y�R� JZst�$�$�R �B I��$%� �Y� j�%�j BP bs��st�k ��R��%� Ak ZR$t� s WB�8sj
s}}�B-$8s�$Bt� =tI�� �Y$R R��Z{�Z��� b� {BtR$I�� PBZ� I$&���t� ,$tIR BP bs�T
�st�k }Bj${$�RU ����� ��t�bsAj� P���T��}js{�8�t�� tBtT��t�bsAj� P���T��}js{�8�t��
}�B �s�s� stI tBtT��t�bsAj� 8$t$8sjT��}s$� bs��st�k }Bj${$�R� *$&���t� ,$tIR BP
R�B{YsR�${ Rsj�R }�B{�RR�R s�� I$R{ZRR�I $t �Y$R bB�,� ����� tBtYB8B��t�BZR {B8T
}BZtI _B$RRBt }�B{�RR� R�B{YsR�${ }�B{�RR b$�Y $tI�}�tI�t� $t{��8�t�R� As�{Y ��T
t�bsj }�B{�RR� stI �s�,B% 8BIZjs��I }�B{�RR� G� $jjZR��s�� b$�Y R�%��sj R$8}j�
�-s8}j�R�
$
![Page 2: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/2.jpg)
d yt��BIZ{�$Bt
yt BZ� �%��kIsk j$P�� b� P��JZ�t�jk }Z�{YsR� �BBIR bY${Y $t{jZI� s bs��st�k� V bs�T
�st�k }�B%$I�R st sRRZ�st{� �B �Y� {BtRZ8�� ���s�I$t� �Y� JZsj$�k BP �Y� }�BIZ{� RBjI�
y� {BZjI A� B&���I PB� �BBIR sR �-}�tR$%� sR sZ�B8BA$j�R B� sR {Y�s} sR j$�Y� AZjAR�
�%�t �YBZ�Y b� ZRZsjjk IB tB� }sk 8Z{Y s���t�$Bt �B �Y� bs��st�k Bt {Y�s} $��8R�
V{�Zsjjk� �Y� �s�tZRBtT�BRR Gs��st�k V{� BP d��x >dEH 8stIs��R �Ys� }�BIZ{��R 8ZR�
B&�� s bs��st�k PB� sjj {BtRZ8�� }�BIZ{�R RBjI PB� 8B�� �Yst hP���t IBjjs�R� 7B8� BP
�Y� }�BIZ{��R ZR� bs��st�$�R sR s �BBj �B }�B8B�� �Y�$� }�BIZ{�R� stI\B� I$R�$t�Z$RY
�Y�$� }�BIZ{�R P�B8 �Y� {B8}��$�B�R�
V bs��st�k $R s {Bt��s{� A��b��t �Y� }�BIZ{�� stI �Y� {BtRZ8�� �B �Zs�st��� s Rs�T
$RPs{�B�k }��PB�8st{� BP �Y� $��8 IZ�$t� s h-�I }��$BI BP �$8�� y� IB�Rt:� `ZR� I�ht�
�Y� �$�Y�R BP �Y� {BtRZ8��� AZ� sjRB I�ht�R �Y� ��R}BtR$A$j$�k stI j$sA$j$�k BP �Y� }�BT
IZ{��� Vj�YBZ�Y bs��st�$�R s�� ZR�I Ak }�BIZ{��R sR s {B8}��$�$%� R��s���k �B ABBR�
�Y�$� 8s�,�� RYs��� }�Bh�sA$j$�k� stI $8s��� �Y�k s�� tB� P���� 7$t{� �Y� }�BIZ{�� YsR �B
��}js{� B� ��}s$� �Y� Ps$j�I $��8R IZ�$t� �Y� bs��st�k }��$BI� s bs��st�k {BR�R 8Bt�k�
e%�t �YBZ�Y RB8��$8�R �Y� bs��st�k {BR� $R tB� %��k js���� $� IB�R s&�{� �Y� }�BIZ{��:R
��%�tZ�� 3�B8 �Y� {BtRZ8��:R }B$t� BP %$�b� �Y� JZ�R�$Bt $R bY��Y�� $� $R bB��Y }sk$t�
PB� �Y� bs��st�k� $P �Y��� $R s {YB${�� qYZR� b� {st R�� �Ys� �Y� bs��st�k {BR� stsjkR$R
$R $8}B��st� PB� AB�Y �Y� }�BIZ{��R stI �Y� {BtRZ8��R�
qY� bs��st�k {BR� �B �Y� }�BIZ{��R stI {BtRZ8��R b$jj I�}�tI Z}Bt �Y� �k}� BP bs�T
�st�k }Bj${k� qY� }�BIZ{��R {st ZR� �Y�R� bs��st�k {BR�R sR s ��P���t{� bY�t �Y�k bst�
�B 8s,� s I�{$R$Bt sABZ� bY${Y bs��st�k }Bj${$�R �B B&�� stI B�Y�� }�${$t� }Z�}BR�R�
qY� {BtRZ8��R: {BR� ZtI�� RB8� I$&���t� bs��st�k }Bj${$�R {BZjI sjRB A� {B8}Z��I stI
}�B%$I�I �B �Y� {BtRZ8��R bY�t �Y�k t��I �B {YBBR� A��b��t R�%��sj B}�$BtR� �BR� BP
�Y� �$8�R� �Y� PBjjBb$t� �Y��� �k}�R BP {BR�R s�� $8}B��st�U �-}�{��I bs��st�k {BR� }��
Zt$� Rsj�� �-}�{��I {BR� BP B}��s�$t� s Zt$� B%�� $�R j$P��$8�� stI �-}�{��I bs��st�k {BR�
B%�� �Y� }�BIZ{� j$P� {k{j�� $���� �Y� }��$BI B%�� bY${Y �Y� }�BIZ{�� {Bt�$tZ�R �B RZ}}jk
�Y� }�BIZ{�� es{Y BP �Y�8 $R ZR�PZj $t s}}�B}�$s�� {Bt��-�R�
_�BIZ{��R }jst PB� bs��st�k {BR�R �Y�BZ�Y �Y� {��s�$Bt BP s PZtI {sjj�I bs��st�k ��R��%��
d
![Page 3: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/3.jpg)
qY�R� PZtIR s�� R�� sR$I� s� �Y� A��$tt$t� BP �Y� Rsj�R }��$BI PB� �Y� bs��st�k {BR�R BP
sjj PZ�Z�� Rsj�R� qY� {sj{Zjs�$Bt BP �Y� bs��st�k ��R��%� I�}�tIR Bt �bB 8s$t sR}�{�R BP
�Y� 8BI�jU �Y� �k}� BP bs��st�k PB� �Y� }�BIZ{� wbY${Y I����8$t�R �Y� bs��st�k {BR�R
BP s R$t�j� Rsj�D� stI �Y� R�B{YsR�${ ts�Z�� BP �Y� Rsj�R }�B{�RR B%�� �Y� }�BIZ{� j$P� {k{j�
wbY${Y� �B���Y�� b$�Y �Y� h�R�� I����8$t�R �Y� �B�sj bs��st�k {BR� B%�� sjj �Y� Rsj�RD�
7�%��sj sZ�YB�R Ys%� {BtR$I���I �Y� }�BAj�8 BP bs��st�k ��R��%�� ��t,�>�H �R�$8s��R
�Y� �-}�{��I �B�sj bs��st�k ��R��%� ��JZ$��I PB� s h-�I jB� R$9� BP Zt$�R� �s{Y b$�Y st
�-}Bt�t�$sj Ps$jZ�� �$8� I$R��$AZ�$Bt� V8s�B stI VtI��RBt>dH �-��tI ��t,�:R 8BI�j
�B sjjBb PB� I$R{BZt�$t� stI }�${� sI`ZR�8�t�R� _s�st,s� stI GB�8>d1H I��$%� }��T
I${�$Bt $t���%sjR PB� bs��st�k ��R��%�R stI {sRY 4Bb� qs}$��B stI _BRt��>d;H }��R�t�
st sj���ts�$%� s}}�Bs{Y �B 8BI�j$t� bs��st�k ��R��%�R� qYB8sR>dxH htIR �Y� �-}�{��I
bs��st�k ��R��%� {BR� }�� Zt$� b$�Y I$R{BZt�$t� PB� Ps$jZ�� I$R��$AZ�$BtR �Ys� $t{jZI� �Y�
Zt$PB�8� �s88s� stI G�$AZjj� j$R{Y,� stI �Z��Yk>1H $R st �-{�jj�t� ��P���t{� ABB,
Bt �Y� RZA`�{� BP bs��st�k {BR� 8BI�jR� yt ]Ys}��� � BP �Y$R ABB,� �Y�k {BtR$I�� �bB
�k}�R BP Rsj�R� R$t�j� jB� Rsj�R stI {Bt�$tZBZR Rsj�R wb$�Y I����8$t$R�${ Rsj�R �s�� PZt{T
�$BtD� stI {B8}Z�� �Y� s}}�B}�$s�� bs��st�k ��R��%�R PB� �Y� $��8R {B%���I Ak �Y� }�B
�s�s bs��st�k }Bj${k� ej$sRYA���� 7$t�}Z�bsjjs� stI G$jRBt>nH {BtR$I�� �Y� }�BAj�8 BP
sRR�RR$t� �Y� R$9� BP s ��R��%� t��I�I Ak �Y� 8stZPs{�Z��� �B 8��� PZ�Z�� {js$8R PB� s
�bBTI$8�tR$Btsj bs��st�k�
yt Fs stI �Zj,s�t$>xH� b� {BtR$I���I PBZ� I$&���t� bs��st�k }Bj${$�RU ��t�bsAj� P���T
��}js{�8�t�� tBtT��t�bsAj� P���T��}js{�8�t�� }�B �s�s� stI tBtT��t�bsAj� 8$t$8sjT
��}s$� bs��st�k }Bj${$�R� stI 8BI�j�I �Y� Rsj�R }�B{�RR Ak s tBtYB8B��t�BZR _B$RRBt
}�B{�RR� yt s R�}s�s�� }s}��� Fs �� sj� >;H {BtR$I���I s 8$t$8sjT��}s$� }Bj${k b$�Y �$8�
I�}�tI�t� ��}s$� {BR�R� 8BI�j�I �Y� Rsj�R s }�B{�RR sR s ��t��sj tBtTI�{��sR$t� R�B{YsRT
�${ }�B{�RR b$�Y $tI�}�tI�t� $t{��8�t�R� VjRB� b� �-}j${$�jk �BB, $t�B s{{BZt� �Y� Ps{�
�Ys� �Y� PZtIR $t �Y� ��R��%� s{{BZt� {st �s�t $t����R�� qYZR �Y� s8BZt� BP PZtIR $t �Y�
bs��st�k ��R��%� 4Z{�Zs��R b$�Y �$8�� $t{��sR$t� IZ� �B s{{�Z�I $t����R�� stI I�{��sR$t�
bY�t�%�� s bs��st�k {js$8 $R R���j�I� G� RYBb�I YBb �B R�s�� �Y� }�BIZ{�$Bt {k{j� b$�Y
RZ^{$�t� bs��st�k ��R��%� RB �Ys� �Y� }�BAsA$j$�k �Ys� �Y� s{�Zsj bs��st�k {BR� P�B8 sjj
PZ�Z�� Rsj�R �-{��IR �Y$R j�%�j $R ABZtI�I sAB%� Ak s R8sjj }��R�� �Bj��st{�� qY$R bsR
IBt� Ak s}}�B-$8s�$t� �Y� I$R��$AZ�$Bt BP �Y� �B�sj �-}�{��I bs��st�k {BR� Ak s WB�8sj
1
![Page 4: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/4.jpg)
I$R��$AZ�$Bt� V �$�B�BZR `ZR�$h{s�$Bt BP �Y� WB�8sj s}}�B-$8s�$Bt bsR �$%�t �Y����
qY� 8s$t {Bt��$AZ�$Bt BP �Y$R }s}�� $R �Ys� b� �-��tI �Y� ��RZj�R BP Fs stI �Zj,s�t$>xH �B
}�B%$I� s Zt$h�I ���s�8�t� ZtI�� s ��t��sj R�B{YsR�${ Rsj�R }�B{�RR stI �Y�t R}�{$sj$9�
�B %s�$BZR RZAT{jsRR�RU R�B{YsR�${ }�B{�RR�R b$�Y $tI�}�tI�t� $t{��8�t�R� As�{Y ��t�bsj
}�B{�RR�R� stI �s�,B% 8BIZjs��I }�B{�RR�R�
qY� B��st$9s�$Bt BP �Y$R }s}�� $R sR PBjjBbR� G� h�R� ��R�s�� �Y� ��RZj�R Bt �Y� h�R�
stI R�{BtI 8B8�t�R BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I bs��st�k {BR� BP s R$t�j� Rsj� $t
R�{�$Bt 1� qY�t� b� {B8}Z�� �Y� 8�st stI %s�$st{� BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I
bs��st�k {BR� BP sjj Rsj�R IZ�$t� �Y� j$P� {k{j� BP �Y� }�BIZ{� $t R�{�$Bt n� 3$tsjjk� b�
}��R�t� s 8��YBI �B {B8}Z�� �Y� bs��st�k ��R��%� $t 7�{�$Bt ;� qY� }s}�� �tIR b$�Y
tZ8��${sj stI R$8Zjs�$Bt ��RZj�R $t 7�{�$Bt ;�1 �B RZ}}B�� �Y� s}}�B-$8s�$Bt b� ZR� �B
{B8}Z�� �Y� bs��st�k ��R��%��
1 VtsjkR$RU 7$t�j� 7sj�
3B� �Y� Rs,� BP ��sIk ��P���t{�� b� ��R�s�� �Y� ��RZj�R wb$�YBZ� }�BBPD P�B8 Fs stI
�Zj,s�t$>xH ���s�I$t� �Y� h�R� stI R�{BtI 8B8�t�R BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I
bs��st�k {BR� BP s R$t�j� Rsj� PB� PBZ� I$&���t� bs��st�k }Bj${$�RU ��t�bsAj� P���T��}js{�8�t��
tBtT��t�bsAj� P���T��}js{�8�t�� }�B �s�s� stI tBtT��t�bsAj� 8$t$8sjT��}s$� bs��st�k
}Bj${$�R� 7}�{$sj {sR�R BP RB8� BP �Y�R� ��RZj�R Ys%� A��t ��}B���I $t �s8�� >�H stI >MH�
W�Zk�t stI �Z��Yk >d(H stI >ddH� s8Bt� 8stk B�Y��R� qY�R� JZst�$�$�R s�� t��I�I $t
�Y� stsjkR$R BP �Y� bs��st�k {BR�R PB� s�����s�� Rsj�R�
3$�R� RB8� ���8$tBjB�kU Gs��st�k }��$BI P $R �Y� h-�I }��$BI BP �$8� IZ�$t� bY${Y
�Y� }�BIZ{�� YsR �Y� ��R}BtR$A$j$�k �B ��}js{� B� ��}s$� �Y� Ps$j�I $��8R� N$P� {k{j� U
$R �Y� h-�I }��$BI B%�� bY${Y �Y� }�BIZ{�� {Bt�$tZ�R �B RZ}}jk �Y� $��8� qY� j$P�T
�$8�R BP �Y� $��8 s�� sRRZ8�I �B A� $�$�I� w$tI�}�tI�t� stI $I�t�${sjjk I$R��$AZ��ID b$�Y
8�st � {B88Bt {�I�P� w{Z8Zjs�$%� I$R��$AZ�$Bt PZt{�$BtD B wND stI �Y� {B���R}BtI$t���t�bsj PZt{�$Bt -wND� GY�t �Y� j$P��$8�R s�� {Bt�$tZBZR �stIB8 %s�$sAj�R� b� ZR�
WwND sR }�I�P� w}�BAsA$j$�k I�tR$�k PZt{�$BtD� �w0D ) Ww0Db>d � B w0DH sR Ps$jZ�� �s�� � stI
Ew0D ) Q-w0DbQ0 sR �Y� ��t�bsj I�tR$�k� qY� ��}s$� B� ��}js{�8�t� {BR� BP �Y� 7�Y
n
![Page 5: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/5.jpg)
Ps$jZ��� ;7� $R s �stIB8 %s�$sAj�� Vjj ;7:R s�� $�$�I� b$�Y {B88Bt 8�st o>;H stI R�{BtI
8B8�t� o>;1H� stI s�� $tI�}�tI�t� BP �Y� Ps$jZ�� �$8�R� qY� {Bt�$tZBZR I$R{BZt� Ps{�B�
$R k (� $���� �Y� }��R�t� %sjZ� BP {BR� cg $t{Z���I s� �$8� 0 $R cg�� 0� 7Z}}BR� st
$��8 $R RBjI s� �$8� (� qY�t $� $R {B%���I ZtI�� bs��st�k PB� �Y� }��$BI >(,P H� .wP D $R
�Y� �B�sj I$R{BZt��I wAs{, �B �$8� 9��BD bs��st�k {BR� BP s R$t�j� Rsj� b$�Y s bs��st�k
}��$BI P � ]j�s�jk� .wP D I�}�tIR Bt �Y� bs��st�k }Bj${$�R�
G� 8s,� �Y� PBjjBb$t� sRRZ8}�$BtR �Y�BZ�YBZ� �Y$R }s}��U
VRRZ8}�$Bt dU VP��� s Ps$jZ��� �Y� $��8 {st A� ��}js{�I Ak s t�b Bt� B� ��}s$��I As{,
�B �Y� {BtI$�$Bt BP �Y� $��8 $88�I$s��jk }�$B� �B $�R Ps$jZ���
VRRZ8}�$Bt 1U qY� ��}s$� �$8� $R 9��B� wyt {B8}s�$RBt �B �Y� bs��st�k }��$BI stI
j$P� {k{j� BP �Y� $��8� $� $R ��js�$%�jk %��k R8sjj�D
VRRZ8}�$Bt nU qY� {BtRZ8��R ,��} {js$8$t� �Y� bs��st�k Zt�$j �Y� $��8 $R tB� {B%���I
Ak �Y� bs��st�k stk8B���
1�d i�t�bsAj� 3���Ti�}js{�8�t� Gs��st�k _Bj${k
=tI�� s P���T��}js{�8�t� bs��st�k }Bj${k� �Y� }�BIZ{�� YsR �B RZ}}jk sR 8stk ��}js{�T
8�t�R sR t��I�I IZ�$t� �Y� bs��st�k }��$BI stI }sk sjj �Y� {BR�� yt �Y$R RZAR�{�$Bt b�
I�sj b$�Y �Y� {sR� �Ys� �Y� bs��st�k }��$BI $R ��t�b�I sP��� �s{Y ��}js{�8�t�� qYZR
$P �Y� {BtRZ8�� }Z�{YsR�R �Y� $��8 s� �$8� ( stI �Y� $��8 Ps$jR s� �$8� ? c P � �Y�
}�BIZ{�� YsR �B }�B%$I� s ��}js{�8�t� bY${Y {B8�R b$�Y s t�b PZjj bs��st�k }��$BI P �
<Bb�%��� $P �Y� $��8 Ps$jR s� �$8� ? �P �Y�t �Y� {BtRZ8�� {sttB� {js$8 �Y� bs��st�k�
G� R�s�� o>.wP DH stI o>.1wP DH $t �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt d wFs stI �Zj,s�t$>xH� qY�B��8 dD U =tI�� s ��t�bsAj� P���T��}js{�8�t�
bs��st�k }Bj${k�
o>.wP DH )o>;H KB w ,P D
d� KB w ,P D, wdD
stI
o>.1wP DH )o>;1Hwd� KB w ,P DD KB w1 ,P D L 1o1>;H KB w ,P D KB w1 ,P D
wd� KB w ,P DDwd� KB w1 ,P DDw1D
bY���
KB w ,P D )8 P
(�� ?QB w?D3 wnD
;
![Page 6: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/6.jpg)
1�1 WBtTi�t�bsAj� 3���Ti�}js{�8�t� Gs��st�k _Bj${k
=tI�� s tBtT��t�bsAj� P���T��}js{�8�t� bs��st�k }Bj${k� $P s {BtRZ8�� }Z�{YsR�R st
$��8 s� �$8� ( stI �Ys� $��8 Ps$jR s� �$8� ? c P �Y�t �Y� }�B%$I�� YsR �B }�B%$I� s
P��� ��}js{�8�t� bY${Y {B8�R b$�Y �Y� bs��st�k }��$BI P � ?� G� R�s�� o>.wP DH stI
o>.1wP DH $t �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt 1 wFs stI �Zj,s�t$>xH� qY�B��8 1D U =tI�� s tBtT��t�bsAj� P���T��}js{�8�t�
bs��st�k }Bj${k�
o>.wP DH ) o>;H8 P
(�� 0Q-w0D, w;D
stI
o>.1wP DH ) 1o1>;H8 P
8)(
8 P
`)8�� w`L8DQ-w`� 8DQ-w8D
Lo>;1H8 P
(��1 `Q-w`D3 wxD
1�n _�B is�s Gs��st�k _Bj${k
=tI�� s }�B �s�s bs��st�k }Bj${k� �Y� {BtRZ8�� YsR �B }sk �Y� PZjj }�${�� Q� �B ��� s
t�b Bt� $P �Y� $��8 Ps$jR sP��� �Y� bs��st�k }��$BI� P � yP st $��8 Ps$jR s� �$8� ? stI
? c P � �Y�t �Y� {BtRZ8�� ���R s t�b $��8 PB� }�${� Q ?P� 7$t{� �Y� {BtRZ8��R }sk
PB� �Y� }s�� �Y�k ZR�I� �Y� bs��st�k }��$BI P $R ��t�b�I sP��� �s{Y Ps$jZ��� qY� t�-�
}�B}BR$�$Bt �$%�R �Y� h�R� stI R�{BtI 8B8�t� BP .wP D� G� ZR� �Y� tB�s�$Bt KB w ,P D
P�B8 �JZs�$Bt wnD�
_�B}BR$�$Bt n wFs stI �Zj,s�t$>xH� qY�B��8 nD U =tI�� s }�B �s�s bs��st�k }Bj${k�
o>.wP DH )Q$P( wd� ?
PD�� ?Ww?DQ?
d� KB w ,P D, wED
stI
o>.1wP DH )
Q1wd� KB w ,P DD$P( wd� ?
P D1��1 ?Ww?DQ?L 1Q1
$P( wd� ?
P D�� ?W w?DQ?
$P( wd� ?
P D��1 ?Ww?DQ?
wd� KB w ,P DDwd� KB w1 ,P DD3
w�D
x
![Page 7: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/7.jpg)
1�; WBtTi�t�bsAj� �$t$8sjTi�}s$� Gs��st�k _Bj${k
=tI�� �Y$R }Bj${k� �Y� }�BIZ{�� YsR �B 8$t$8sjjk ��}s$� �Y� Ps$jZ�� Ys}}�t$t� IZ�$t�
�Y� bs��st�k }��$BI w(,P H stI }sk PB� �Y� ��}s$� {BR�� $���� �Y� Ps$jZ�� �s�� BP �Y� Ps$j�I
}�BIZ{� ��8s$tR �Y� Rs8� BP �Y� Bt� $88�I$s��jk }�$B� �B $�R Ps$jZ�� sP��� �s{Y ��}s$��
qY� t�-� }�B}BR$�$Bt �$%�R �Y� h�R� stI R�{BtI 8B8�t� BP .wP D�
_�B}BR$�$Bt ; wFs stI �Zj,s�t$>xH� qY�B��8 ;D U =tI�� s tBtT��t�bsAj� 8$t$8sjT
��}s$� bs��st�k }Bj${k�
o>.wP DH ) o>;H8 P
(�w0D�� 0Q0, wMD
stI
o>.1wP DH ) o>;1H8 P
(�w0D��1 0Q0 L o1>;Hw
8 P
(�w0D�� 0Q0D1 w�D
bY��� �w0D $R �Y� Ps$jZ�� �s���
n V�����s�� 7sj�RU 7�B{YsR�${ 7sj�R _�B{�RR�R
yt �Y$R R�{�$Bt� b� ZR� �Y� ��RZj�R P�B8 �Y� }��%$BZR R�{�$Bt �B AZ$jI s 8BI�j BP 8Zj�$}j�
Rsj�R B%�� �Y� j$P� {k{j� BP �Y� }�BIZ{�� G� 8BI�j �Y� tZ8A�� BP $��8R RBjI IZ�$t� �Y�
j$P� {k{j� sR s ��t��sj tBtTI�{��sR$t� R�B{YsR�${ }�B{�RR� qY$R YsR tB� A��t {BtR$I���I
$t �Y� �s�j$�� j$���s�Z�� �-{�}� PB� RB8� R}�{$sj {sR�R sR $t BZ� �s�j$�� }s}��R >xH stI >;H�
i�{sjj �Ys� U $R �Y� j$P� {k{j� BP �Y� }�BIZ{�� $���� �Y� 8stZPs{�Z�� stI Rsj�R BP �Y� $��8
s�� I$R{Bt�$tZ�I sP��� �$8� U� <Bb�%��� �Y� bs��st�k j$sA$j$�$�R BP sjj $��8R RBjI Z} �B
U s�� YBtB��I� qYZR PB� �Y� tBtT��t�bsAj� bs��st�k }Bj${$�R� �Y� 8stZPs{�Z��� $R P���
BP bs��st�k j$sA$j$�$�R s� �$8� U LP s� �Y� js��R�� bY��� P $R �Y� bs��st�k }��$BI BP
�Y� }�BIZ{�� 3B� �Y� ��t�bsAj� bs��st�k }Bj${$�R� �Y� 8stZPs{�Z��� 8sk t��I �B R��%�
�Y� bs��st�k B%�� st Ztj$8$��I �$8� }��$BI� N�� �w0D A� �Y� tZ8A�� BP $��8R RBjI
IZ�$t� >(, 0H� G� sRRZ8� �Ys� �w(D ) (� stI \�w0D, 0 � (i $R s tBtTI�{��sR$t� R�B{YsR�${}�B{�RR� stI �Ys� �Y��� �-$R� PZt{�$BtR � " stI ' RZ{Y �Ys�
ow�w0L _D��w0DD ) w0L _D� w0D L Lw_D, 0, _ � (, wd(D
oww�w0L _D��w0DD1D ) "w0 L _D� "w0D L Lw_D, 0, _ � (, wddD
E
![Page 8: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/8.jpg)
oww�wXL _dD��wXDDw�w0 L _1D��w0DDD
) 'wXL _d, 0L _1D� 'wX, 0L _1D� 'wXL _d, 0D L 'wX, 0D L Lw_d_1D,
0, X, _d, _1 � (, >0, 0L _1H � >X, XL _dH ) !3 wd1D
yP �Y� PZt{�$BtR � " stI ' s�� I$&���t�$sAj�� �Y� sAB%� �JZs�$BtR {st A� b�$���t 8B��
��stR}s��t�jk sR
ow�w0L _D��w0DD ) Iw0D_L Lw_D, 0, _ � (, wdnD
oww�w0 L _D��w0DD1D ) " Iw0D_L Lw_D, 0, _ � (, wd;D
oww�wXL _dD��wXDDw�w0L _1D��w0DDD
)(1
(X(0'wX, 0D_d_1 L Lw_d_1D, 0, X, _d, _1 � (, >0, 0L _1H � >X, X L _dH ) !3 wdxD
]j�s�jk�
w0D ) ow�w0DD
b$jj bB�, PB� sjj $t{��sR$t� R�B{YsR�${ }�B{�RR�R b$�Y �Y� Lw_D ���8 �JZsj �B 9��B� <BbT
�%��� �Y� �-}��RR$BtR PB� "w0D stI 'wX, 0D s�� tB� �sRk �B I��$%� PB� ��t��sj R�B{YsR�${
}�B{�RR�R� G� I��$%� �Y�8 PB� R}�{$sj {jsRR�R bY�t t��I�I�
N�� x wUD A� �Y� �B�sj I$R{BZt��I wAs{, �B �$8� 9��BD bs��st�k {BR� BP sjj �Y� Rsj�R IZ�$t�
�Y� j$P� {k{j� U� wG� RYBZjI ��sjjk ZR� �Y� tB�s�$Bt x wU,P D $tR��sI BP x wUD �B Y$�Yj$�Y�
�Y� I�}�tI�t{� Bt P � YBb�%��� b� R�${, b$�Y x wUD PB� �Y� Rs,� BP A��%$�k�D ]j�s�jk�
x wUD I�}�tIR Bt �Y� R�B{YsR�${ Rsj�R }�B{�RR stI �Y� bs��st�k }Bj${k� qY� ��RZj�R s��
�$%�t $t ���8R BP o>.wP DH stI o>.1wP DH bY��� .wP D $R �Y� �B�sj I$R{BZt��I wAs{, �B
�$8� 9��BD bs��st�k {BR� BP s R$t�j� Rsj� b$�Y s bs��st�k }��$BI P � qY�R� JZst�$�$�R
b��� R�s��I $t �Y� }��%$BZR R�{�$Bt PB� I$&���t� bs��st�k }Bj${$�R� G� I��$%� o>x wUDH
stI ~ y�wx wUDD $t �Y� t�-� }�B}BR$�$Bt� qY�k s�� ZR�PZj $t �Y� stsjkR$R BP �Y� bs��st�k
��R��%� $t R�{�$Bt ;�
�
![Page 9: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/9.jpg)
_�B}BR$�$Bt x U N�� \�w0D, 0 � (i A� s tBtTI�{��sR$t� R�B{YsR�${ Rsj�R }�B{�RR� qY�t
o>x wUDH ) o>.wP DH8 U
(�� 0Q w0D wdED
stI
~ y�wx wUDD ) ~ y�w.wP DD8 U
(��1 0o>Q�w0DH L o1>.wP DH
8 U
(��1 0Q"w0D
L1o1>.wP DH8 U
`)(
8 U
8)`�� w`L8DQ`Q8'w`, 8D
�wo>x wUDHD13 wd�D
_�BBP U G� }s��$�$Bt �Y� �$8� YB�$9Bt >(, UH $t � �JZsj $t���%sjR BP j�t��Y _ ) U��
N�� ��7 k ( A� �Y� tZ8A�� BP $��8R RBjI $t �Y� $t���%sj ww7 � dD_, 7_H stI .7,iwP D A�
�Y� �B�sj I$R{BZt��I bs��st�k {BR� BP �Y� i�Y Rsj� bY${Y $R RBjI $t ww7 � dD_, 7_H b$�Y sbs��st�k }��$BI P � N��
x�wUD )�37)d
��73i)d
�� 7_.7,iwP D3 wdMD
]j�s�jk�
x�wUD � x wUD � � _x�wUD ) � U� x�wUD3
7$t{� \.7,iwP D, i ) d, 1, N N N ,��7i s�� $�$�I� PB� sjj 7� o>.7,iwP DH ) o>.wP DH PB� sjj 7 stI
i� qY���PB��� b� ���
o>x�wUDH )�37)d
o>.wP DH�� 7_o>��7H3 wd�D
WBb� R$t{�
j$8��
� U� ) d,
b� Ys%�
o>x wUDH ) j$8��
o>x�wUDH )8 U
(o>.wP DH�� 0Q w0D3 w1(D
<�t{� b� ��� �JZs�$Bt wdED�
qY� R�{BtI 8B8�t� $R I��$%�I $t s R$8$js� bsk� k ZR$t� �JZs�$BtwdMD� b� Ys%�
x 1�wUD ) w
�37)d
��73i)d
�� 7_.7,iwP DD1 w1dD
)�37)d
��73i)d
��1 7_.17,iwP D L 1
�37)d
��73i)d
��73>)iLd
��1 7_.7,iwP D.7,>wP D
L1�37)d
�3i)7Ld
��73>)d
��i3q)d
�� w7LiD_.7,>wP D.i,qwP D w11D
M
![Page 10: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/10.jpg)
bY${Y k$�jIR
o>x 1�wUDH ) o>.1wP DH
�37)d
��1 7_o>��7H L o1>.wP DH�37)d
��1 7_o>w��7D1 ���7H
L1o1>.wP DH�37)d
�3i)7Ld
�� w7LiD_o>��7��iH w1nD
N���$t� � � sR A�PB��� b� Ys%�
o>x 1wUDH ) o>.1wP DH8 U
(��1 0Q w0D L o1>.wP DH
8 U
(��1 0wQ"w0D� Q w0DD
L1o1>.wP DH8 U
`)(
8 U
8)`�� w`L8DQ`Q8'w`, 8D3 w1;D
7ZAR�$�Z�$t� $t ~ y�wx wUDD ) o>x 1wUDH � o1>x wUDH� ZR$t� �Y� j$t�s�$�k }�B}���k BP �Y�
�-}�{�s�$Bt stI ~ y�w.wP DD ) o>.1wP DH�o1>.wP DH� b� ��� �JZs�$Bt wd�D�
W�-� b� I$R{ZRR �Y��� R}�{$sj {sR�R BP R�B{YsR�${ Rsj�R }�B{�RR�R $t �Y� PBjjBb$t� B�I��U
d� 7�B{YsR�${ Rsj�R }�B{�RR�R b$�Y $tI�}�tI�t� $t{��8�t�R�
1� s�{Y ��t�bsj Rsj�R }�B{�RR�R�
n� �s�,B% 8BIZjs��I Rsj�R }�B{�RR�R�
n�d 7�B{YsR�${ 7sj�R _�B{�RR�R b$�Y ytI�}�tI�t� yt{��8�t�R
yt �Y$R R�{�$Bt� b� sRRZ8� �Ys� \�w0D, 0 � (i $R s R�B{YsR�${ Rsj�R }�B{�RR b$�Y $tI�T}�tI�t� $t{��8�t�R� wqY$R }�B{�RR bsR stsjk9�I Ak s I$&���t� 8��YBI $t Fs �� sj� >;H�D
3B� �-s8}j�� �Y� _B$RRBt }�B{�RR� {B8}BZtI _B$RRBt }�B{�RR� tBtYB8B��t�BZR _B$RRBt
}�B{�RR� stI tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR s�� }�B{�RR�R b$�Y $tI�}�tI�t�
$t{��8�t�R� G� I��$%� �Y� PB�8ZjsR BP o>x wUDH stI ~ y�wx wUDD $t �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt E U N�� \�w0D, 0 � (i A� s R�B{YsR�${ Rsj�R }�B{�RR b$�Y $tI�}�tI�t� $t{��T
8�t�R� b$�Y $t����sAj� PZt{�$BtR
�w0D ) ow�w0DD,
stI
8w0D ) zs�w�w0DD3
�
![Page 11: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/11.jpg)
qY�t
o>x wUDH ) o>.wP DH8 U
(�� 0Q�w0D w1xD
stI
~ y�wx wUDD ) ~ y�w.wP DD8 U
(��1 0Q�w0D L o1>.wP DH
8 U
(��1 0Q8w0D3 w1ED
_�BBP U VR 8�t�$Bt�I �s�j$��� �Y� PZt{�$Bt $R �$%�t Ak
w0D ) ow�w0DD ) �w0D3 w1�D
eJZs�$Bt 1x PBjjBbR P�B8 eJZs�$BtR dE stI 1�� 7$t{� \�w0D, 0 � (i YsR $tI�}�tI�t�$t{��8�t�R� w�w0L _D��w0DD $R $tI�}�tI�t� BP �w0D� <�t{�
~ y�w�w0L_DD ) ~ y�w�w0L_D��w0DL�w0DD ) ~ y�w�w0L_D��w0DDL~ y�w�w0DD3 w1MD
qY���PB���
~ y�w�w0L _D��w0DD ) ~ y�w�w0L _DD� ~ y�w�w0DD3
<�t{�
oww�w0 L _D��w0DD1D ) ~ y�w�w0L _D��w0DD L wow�w0L _D��w0DDD1
) ~ y�w�w0L _DD� ~ y�w�w0DD L Lw_D3
qY$R $8}j$�R
"w0D ) ~ y�w�w0DD ) 8w0D3 w1�D
3$tsjjk� $tI�}�tI�t{� BP $t{��8�t�R k$�jIR �Y� PBjjBb$t�
oww�wXL _dD��wXDDw�w0 L _1D��w0DDD ) ow�wXL _dD��wXDDow�w0L _1D��w0DD
) w wXL _dD� wXDDw w0L _1D� w0DD,
bY${Y $8}j$�R
'wX, 0D ) wXD w0D, X W) 03 wn(D
=R$t� eJZs�$Bt n( b� ���
1o1>.wP DH8 U
`)(
8 U
8)`�� w`L8DQ`Q8'w`, 8D
) o1>.wP DH8 U
`)(
8 U
8)(�� w`L8DQ w`DQ w8D
) wo>.wP DH8 U
`)(�� `Q w`DD1
) wowx wUDD13 wndD
d(
![Page 12: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/12.jpg)
eJZs�$Bt 1E PBjjBbR P�B8 RZAR�$�Z�$t� eJZs�$BtR nd stI n( $t eJZs�$Bt d��
qY� ��RZj� P�B8 �Y$R }�B}BR$�$Bt 8s�{Y�R �Y� Bt� $t Fs �� sj� >;H� G� $jjZR��s�� �Y� sAB%�
}�B}BR$�$Bt b$�Y st �-s8}j��
e-s8}j� d U N�� \�w0D, 0 � (i A� s tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR b$�Y�s�� PZt{�$Bt w0D stI $�$�I� As�{Y R$9�R V b$�Y {B88Bt 8�st o>V H stI R�{BtI 8B8�t�
o>V 1H� <��� b� sRRZ8� w0D $R �Y� $tR�st�st�BZR R�jj$t� �s�� w$t As�{Y�R\�$8�D s� �$8�
0� y� $R �sRk �B R�� �Ys�
w0D ) �w0Do>V H wn1D
stI
"w0D ) �w0Do>V 1H wnnD
bY���
�w0D )8 0
(wXDQX3 wn;D
qY���PB��� b� ���
Q w0D ) w0Do>V HQ0 wnxD
stI
Q"w0D ) w0Do>V 1HQ03 wnED
k RZAR�$�Z�$t� $t �JZs�$Btw1xD stI w1ED� b� ���
o>x wUDH ) o>.wP DHo>V H8 U
(�� 0w0DQ0 wn�D
stI
~ y�wx wUDD ) w~ y�w.wP DDo>V H L o1>.wP DHo>V 1HD8 U
(��1 0w0DQ03 wnMD
]j�s�jk� �Y� _B$RRBt }�B{�RR� {B8}BZtI _B$RRBt }�B{�RR� stI �Y� tBtYB8B��t�BZR _B$RT
RBt }�B{�RR s�� R}�{$sj {sR�R BP �Y$R �-s8}j�� 3B� �-s8}j�� $P b� j�� o>V H ) o>V 1H ) d�
b� Ys%�
o>x wUDH ) o>.wP DH8 U
(�� 0w0DQ0 wn�D
stI
~ y�wx wUDD ) o>.1wP DH8 U
(��1 0w0DQ0 w;(D
bY${Y s�� �Y� ��RZj�R PB� tBtYB8B��t�BZR _B$RRBt }�B{�RR� qY� tZ8��${sj ��RZj� BP �Y$R
�-s8}j� $R �$%�t $t 7�{�$Bt ;�1�
dd
![Page 13: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/13.jpg)
n�1 s�{Y i�t�bsj 7sj�R _�B{�RR�R
yt �Y$R R�{�$Bt� b� sRRZ8� �Ys� �Y� R�B{YsR�${ Rsj�R }�B{�RR \�w0D, 0 � (i $R s As�{Y��t�bsj }�B{�RR sR I�ht�I A�jBb�
*�ht$�$Bt U N�� \p7, 7 � di A� s R�JZ�t{� BP $�$�I� tBtTt��s�$%� $t�����T%sjZ�I �stIB8%s�$sAj�R stI \]w0D, 0 � (i A� s ��t�bsj }�B{�RR �Ys� $R $tI�}�tI�t� BP \p7, 7 � di� VR�B{YsR�${ }�B{�RR \�w0D, 0 � (i I�ht�I sR
�w0D )]w0D37)d
p7
$R {sjj�I s As�{Y ��t�bsj }�B{�RR�
WB�� �Ys� s As�{Y ��t�bsj }�B{�RR $R s R}�{$sj {sR� BP ��t�bsj ��bs�I }�B{�RR�R� !t�
{st �Y$t, BP �Y� Rsj�R sR B{{Z��$t� $t As�{Y�R� b$�Y p7 sR �Y� tZ8A�� BP $��8R RBjI $t
�Y� 7�Y As�{YTRsj�� stI ]w0D sR �Y� �B�sj tZ8A�� BP As�{YTRsj�R Z} �B �$8� 0�
N�� twND A� �Y� {�I�P� BP �Y� �$8� A��b��t �bB {BtR�{Z�$%� As�{Y Rsj�R� stI sRRZ8��Ys� tw(D ) (� RB �Ys� 8B�� �Yst Bt� As�{Y Rsj�R IBt:� B{{Z� R$8Zj�st�BZRjk� qYZR
\]w0D, 0 � (i $R s ��t�bsj }�B{�RR ��t��s��I Ak twND� N�� -tw0D ) o>]w0DH A� �Y�
��t�bsj PZt{�$Bt sRRB{$s��I b$�Y twND� N�� o>pH stI o>p1H A� �Y� {B88Bt 8�st stI
R�{BtI 8B8�t� BP \p7, 7 � di� G� I��$%� o>x wUDH stI ~ y�wx wUDD PB� �Y� As�{Y ��t�bsjRsj�R }�B{�RR�R $t �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt � U N�� \�w0D, 0 � (i A� s As�{Y ��t�bsj Rsj�R }�B{�RR sR I�R{�$A�I sAB%��
qY�t
o>x wUDH ) o>.wP DHo>pH8 U
(�� 0Q-tw0D w;dD
stI
~ y�wx wUDD ) w~ y�w.wP DDo>pH L o1>.wP DHo>p1HD8 U
(��1 0Q-tw0D
L1o1>.wP DHo1>pH8 U
`)(
8 U
8)`�� w`L8DQ-tw`DQ-tw8 � `D
�wo>x wUDHD13 w;1D
d1
![Page 14: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/14.jpg)
_�BBP U G� h�R� {B8}Z�� w0D� "w0D� stI 'wX, 0D� G� Ys%�
w0D ) ow�w0DD ) owpD-tw0D3 w;nD
3B� R8sjj _� �Y��� {st A� s� 8BR� Bt� As�{Y Rsj� $t �Y� $t���%sj w0, 0 L _D� <�t{��
oww�w0L _D��w0DD1D ) owp1Dw-tw0L _D�-tw0DD L Lw_D3
qY$R $8}j$�R
"w0D ) owp1D-tw0D3 w;;D
3$tsjjk� PB� R8sjj _d stI _1� stI 0 k XL _d� b� ���
oww�w0L _1D��w0DDw�wXL _dD��wXDDD
) owppIDw-twXL _dD�-twXDDw-tw0� XL _1D�-tw0� XDD L Lw_D3
bY��� p stI pI s�� $tI�}�tI�t� ��t��${ �stIB8 %s�$sAj�R b$�Y �Y� Rs8� I$R��$AZ�$Bt
sR \p7, 7 � di� qY� sAB%� �JZs�$Bt k$�jIR
QXQ0'wX, 0D ) o1>pHQ-twXDQ-tw0� XD, 0 k X3 w;xD
VP��� RZAR�$�Z�$t� �JZs�$BtR w;nD� w;;D� stI w;xD $t�B �JZs�$BtR wdED stI wd�D $t }�B}BT
R$�$Bt x� b� ��� �JZs�$BtR w;dD stI w;1D�
G� $jjZR��s�� �Y� sAB%� }�B}BR$�$Bt b$�Y s R$8}j� �-s8}j��
e-s8}j� 1 U 7Z}}BR� �Y� $t�����t�bsj I$R��$AZ�$Bt twND $R o�qyz/w1, D� $����
tw0D ) 10��03
k ZR$t� �Y� Ns}js{�T7�$�j�`�R q�stRPB�8R BP twND� b� ���
-tw0D )
1w0 L
��10
1� d
1D3
G� Ys%�
8 U
(�� 0Q-tw0D )
8 U
(�� 0
1wd� ��10DQ0
)
1w��w L1DU � d
L 1Ld� �� U
D,
dn
![Page 15: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/15.jpg)
8 U
(��1 0Q-tw0D )
8 U
(��1 0
1wd� ��10DQ0
)
;w��1w LDU � d
L Ld� ��1 U
D,
stI
8 U
`)(
8 U
8)`�� w`L8DQ-tw`DQ-tw8 � `D
)8 U
`)(
8 U
8)`�� w`L8D
1
;wd� ��1`Dwd� ��1w8�`DDQ8Q`
)1
;>d
wd� ��1 U
1 L��1 U � �� U
D
� d
L 1wd� ��1 U
1 L��1 U � ��w L1DU
� 1 D
� d
wd� ��w1 L1DU
1 L 1L��w1 L1DU � �� U
L 1D
Ld
L 1wd� ��w1 L1DU
1 L 1L��w1 L1DU � ��w L1DU
DH3
k RZAR�$�Z�$t� $t �JZs�$BtR w;dD stI w;1D� b� {st ��� �Y� ��RZj�R BP �Y$R �-s8}j��
n�n �s�,B% �BIZjs��I 7sj�R _�B{�RR�R
yt �Y$R R�{�$Bt� b� 8BI�j �Y� Rsj�R }�B{�RR sR s �s�,B% 8BIZjs��I tBtYB8B��t�BZR
{B8}BZtI _B$RRBt }�B{�RR sR I�ht�I A�jBb�
*�ht$�$Bt U N�� \.w0D, 0 � (i A� s ]q�] w{Bt�$tZBZR �$8� �s�,B% {Ys$tD Bt R�s��
R}s{� \d, 1, 3 3 3 , zi� N�� \�7w0D, 0 � (i w7 ) d, 1, 3 3 3 , zD A� z $tI�}�tI�t� tBtYB8B��T
t�BZR {B8}BZtI _B$RRBt }�B{�RR�R b$�Y $t����sAj� �s�� PZt{�$BtR 7w0D stI $�$�I� As�{Y
R$9�R \V7,i, i � di� N�� \�w0D, 0 � (i A� s R�B{YsR�${ }�B{�RR RZ{Y �Ys� �w(D ) ( stI
Q�w0D )z37)d
Q�7w0D N d\.w0D)7i
bY��� d\ $R st $tI${s�B� �stIB8 %s�$sAj� BP �Y� �%�t� \� qY� R�B{YsR�${ }�B{�RR
\�w0D, 0 � (i $R {sjj�I s �s�,B% 8BIZjs��I tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RRw8BIZjs��I Ak �Y� ]q�] \.w0D, 0 � (iD�
�s�,B% 8BIZjs��I tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR�R s�� s ZR�PZj 8BI�j BP
s Rsj�R }�B{�RR bY�t �Y� Rsj�R �s�� I�}�tIR Z}Bt �Y� R�s�� BP �Y� 8s�,�� wABB8$t��
d;
![Page 16: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/16.jpg)
I�{j$t$t�� ��{�D� yt RZ{Y s {sR�� .w0D $R �Y� R�s�� BP �Y� 8s�,�� s� �$8� 0� WB�� �Ys� 7w0D
I�}�tIR Z}Bt 0� �Y� �jBAsj �$8�� stI tB� Z}Bt �Y� �$8� R$t{� �t���$t� �Y� {Z���t� R�s���
G� I��$%� o>x wUDH stI ~ y�wx wUDD PB� RZ{Y s Rsj�R }�B{�RR $t �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt M U N�� \�w0D, 0 � (i A� s tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR
8BIZjs��I Ak s ]q�] \.w0D, 0 � (i sR I�ht�I sAB%�� N�� o>V7H stI o>V17 H A� �Y� h�R�
stI R�{BtI 8B8�t�R BP �Y� $�$�I� As�{Y�R \V7,i, i � di� qY�t
o>x wUDH ) o>.wP DHz37)d
o>V7H8 U
(7w0D�
� 0h�\.w0D ) 7iQ0 w;ED
stI
~ y�wx wUDD
)z37)d
w~ y�w.wP DDo>V7H Lo1>.wP DHo>V 17 HD
8 U
(7w0D�
�1 0h�\.w0D ) 7iQ0
L1o1>.wP DHz37)d
z3i)d
o>V7Ho>Vi H
8 U
`)(
8 U
8)`�� w`L8D7w`Diw8Dh�\.w`D ) 7, .w8D ) iiQ8Q`
�wo>x wUDHD13 w;�D
_�BBP U VR A�PB��� b� h�R� I��$%� �-}��RR$BtR PB� �Y� PZt{�$BtR � " stI '� 7$t{�
\�7w0D, 0 � (i w7 ) d, 1, 3 3 3 , zD s�� z $tI�}�tI�t� tBtYB8B��t�BZR {B8}BZtI _B$RRBt
}�B{�RR�R� P�B8 �JZs�$BtR wnxD stI wnED� b� Ys%�
o>�7w0L _D��7w0DH ) o>V7H7w0D_L Lw_D w;MD
stI
o>w�7w0 L _D��7w0DD1H ) o>V 1
7 H7w0D_L Lw_D3 w;�D
3�B8 �Y� I�ht$�$Bt BP �s�,B% 8BIZjs��I Rsj�R }�B{�RR�R� b� Ys%�
o>�w0L _D��w0DH ) o>z37)d
w�7w0L _D��7w0DD N d\.w0D)7iH L Lw_D
)z37)d
o>�7w0 L _D��7w0DHh�\.w0D ) 7iL Lw_D
)z37)d
o>V7H7w0Dh�\.w0D ) 7i_L Lw_D3 wx(D
<�t{�� b� ���Q
Q0 w0D )
z37)d
o>V7H7w0Dh�\.w0D ) 7i3 wxdD
dx
![Page 17: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/17.jpg)
=R$t� s R$8$js� s��Z8�t�� b� Ys%�
o>w�w0L _D � �w0DD1H
) o>wz37)d
w�7w0L _D��7w0DD N d\.w0D)7iD1H L Lw_D
) o>z37)d
w�7w0L _D��7w0DD1 N d\.w0D)7i
L1z37)d
z3i)7Ld
w�7w0L _D��7w0DDw�iw0L _D��iw0DD N d\.w0D)7,.w0D)iiH L Lw_D
) o>z37)d
w�7w0L _D��7w0DD1 N d\.w0D)7iH L Lw_D
)z37)d
o>w�7w0 L _D��7w0DD1Hh�\.w0D ) 7iL Lw_D
)z37)d
o>V 17 H7w0Dh�\.w0D ) 7i_L Lw_D3 wx1D
<�t{�� b� ���Q
Q0"w0D )
z37)d
o>V7H7w0Dh�\.w0D ) 7i3 wxnD
3$tsjjk� PB� 8 k `L _d� b� Ys%�
o>w�w`L _dD��w`DDw�w8 L _1D��w8DDH
) o>wz37)d
w�7w`L _dD��7w`D N d\.w`D)7iDwz3i)d
w�iw8 L _1D��iw8DD N d\.w8D)iiDH L Lw_d_1D
)z37)d
z3i)d
o>w�7w`L _dD��7w`DDw�iw8 L _1D��iw8DDHh�\.w`D ) 7, .w8D ) iiL Lw_d_1D
)z37)d
z3i)d
o>�7w`L _dD��7w`DHo>�iw8 L _1D��iw8DHh�\.w`D ) 7, .w8D ) iiL Lw_d_1D
)z37)d
z3i)d
wo>V7H7w`D_dDwo>ViHiw8D_1Dh�\.w`D ) 7, .w8D ) iiL Lw_d_1D
)z37)d
z3i)d
o>V7Ho>ViH7w`Diw8Dh�\.w`D ) 7, .w8D ) ii_d_1 L Lw_d_1D3 wx;D
qY$R $8}j$�R
(1
(`(8'w`, 8D )
z37)d
z3i)d
o>V7Ho>ViH7w`Diw8Dh�\.w`D ) 7, .w8D ) ii3 wxxD
VP��� RZAR�$�Z�$t� �JZs�$Bt wxdD� wxnD� stI wxxD $t�B �JZs�$Bt wdED stI wd�D $t }�B}BR$T
�$Bt x� b� ��� �JZs�$BtR w;ED stI w;�D�
dE
![Page 18: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/18.jpg)
]B8}Z�s�$Bt BP h�\.w0D ) 7i stI h�\.w`D ) 7, .w8D ) ii U <��� b� I�R{�$A� YBb�B {B8}Z�� �B h�\.w`D ) 7, .w8D ) ii stI h�\.w0D ) 7i sR t��I�I $t �Y� }��%$BZR}�B}BR$�$Bt� N�� < A� �Y� �s�� 8s��$- BP \.w0D, 0 � (i� y A� $�R $t$�$sj I$R��$AZ�$Bt� N��
h7iw0D ) h�\.w0D ) i / .w(D ) 7i3
3�B8 ]Ys}��� E BP �Zj,s�t$>EH� b� ,tBb
h7iw0D ) >�<0H7i,
h�\.w0D ) 7i ) >y�<0H7, wxED
stI PB� 8 k `�
h�\.w`D ) 7, .w8D ) ii ) h�\.w8D ) i / .w`D ) 7ih�\.w`D ) 7i) h7iw8 � `D>y�<`H7
) >�<w8�`DH7i>y�<`H7 wx�D
bY���
�<0 ) { L 3z)d
w<0Dz
z�3 wxMD
7$t{� $� $R tB� �sRk �B {B8}Z�� �Y� $t����s�$Bt $t%Bj%$t� h�\.w0D ) 7i stI h�\.w`D )7, .w8D ) ii� b� BP��t ZR� tZ8��${sj $t����s�$Bt� �-{�}� bY�t \�w0D, 0 � (i $R s �s�,B%8BIZjs��I _B$RRBt }�B{�RR stI �Y� �$��t%sjZ�R BP �s�� 8s��$- < s�� I$R�$t{�� yt �Y�
t�-� }�B}BR$�$Bt� b� I��$%� �Y� stsjk�${sj ��RZj� PB� �Y$R {sR��
G� h�R� $t��BIZ{� RB8� 8B�� tB�s�$Bt bY${Y $R t��I�I $t �Y� t�-� }�B}BR$�$Bt� N��
\ d, 1, 3 3 3 , zi A� �Y� I$R�$t{� �$��t%sjZ�R BP <� \ A� s z z 8s��$- bYBR� 7�Y {BjZ8t$R �Y� �$��t%�{�B� {B���R}BtI$t� �B �Y� 7�Y �$��t%sjZ� 7 PB� 7 ) d, 3 3 3 , z � ; A� s z z
I$s�Btsj 8s��$- bYBR� w7, 7D0_ �j�8�t� $R 7 PB� 7 ) d, 3 3 3 , z� K A� s {BjZ8t %�{�B� BP
R�jj$t� �s��R \d, 1, 3 3 3 , zi� K� A� s z z I$s�Btsj 8s��$- bYBR� w7, 7D0_ �j�8�t� $R 7
PB� 7 ) d, 3 3 3 , z� J A� s z z I$s�Btsj 8s��$- bYBR� w7, 7D0_ �j�8�t� $R
d� �w 7� DU
� 7PB� 7 ) d, 3 3 3 , z,
d�
![Page 19: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/19.jpg)
stI � $R s 8s��$- bYBR� w7, iD0_ �j�8�t� $R
E7,i
i � w�w i� DUw�w 7� i� DU � dD
7 � i � Ld� �w 7�1 DU
7 � 1 D PB� 7, i ) d, 3 3 3 , z
bY��� E7,i $R �Y� w7, iD �j�8�t� BP 8s��$- \�dK�\�
_�B}BR$�$Bt � U N�� \�w0D, 0 � (i A� s _B$RRBt }�B{�RR 8BIZjs��I Ak s ]q�] \.w0D, 0 �(i b$�Y �s�� 8s��$- Ys%$t� I$R�$t{� �$��t%sjZ�R� qY�t
o>x wUDH ) o>.wP DHy\J \�dK wx�D
stI
~ y�wx wUDD ) o>.1wP DHy\J1 \�dKL 1o1>.wP DHy\�\�dK� wo>x wUDHD13 wE(D
_�BBP U
o>x wUDH ) o>.wP DHz37)d
7
8 U
(�� 0h�\.w0D ) 7iQ0
) o>.wP DHz37)d
7
8 U
(�� 0>y�<0H7Q0
) o>.wP DHz37)d
7
8 U
(�� 0>y\�;0\�dH7Q0
) o>.wP DH8 U
(�� 0wy\�;0\�dDQ0K
) o>.wP DHy\w8 U
(�� 0�;0Q0D\�dK
wEdD
bY��� �Y� h�R� �JZsj$�k {B8�R P�B8 �JZs�$Bt w;ED� 7$t{� �� 0�;0 $R s z z I$s�Btsj
8s��$- bYBR� w7, 7D0_ �j�8�t� $R �w 7� D0 PB� 7 ) d, 3 3 3 , z� b� t��I �B {B8}Z��8 U
(�w 7� D0Q0
bY${Y �JZsjRd� �w 7� DU
� 73
7ZAR�$�Z�$t�� b� ��� �JZs�$Bt wx�D�
=R$t�
o>x 1wUDH ) o>.1wP DH37
8 U
(7��1 0h�\.w0D ) 7iQ0
L1o1>.wP DH37
3i
8 U
`)(
8 U
8)`7i�
� w`L8Dh�\.w`D ) 7, .w8D ) iiQ8Q`,
wE1D
dM
![Page 20: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/20.jpg)
bY${Y $R P�B8 �JZs�$Bt w;�D� stI �JZs�$BtR wx�D� wx�D wb$�Y 1 $tR��sI BP D stI �Y�h�R� �JZsj$�k BP wEdD� b� Ys%�
o>x 1wUDH
) o>.1wP DHy\J1 \�dK
L1o1>.wP DH37
3i
8 U
`)(
8 U
8)`7i�
� w`L8D>�<w8�`DH7,i>y�<`H7Q8Q`
) o>.1wP DHy\J1 \�dK
L1o1>.wP DH37
3i
8 U
`)(
8 U
8)`7i�
� w`L8D>\�;w8�`D\�dH7,i >y\�;`\�dH7Q8Q`
) o>.1wP DHy\J1 \�dKL 1o1>.wP DH
8 U
`)(
8 U
8)`�� w`L8Dwy\�;`\�dDK�w\�;w8�`D\�dDKQ8Q`
) o>.1wP DHy\J1 \�dKL 1o1>.wP DHy\w
8 U
`)(
8 U
8)`�� w`L8D�;`w\�dK�\D�;w8�`DQ8Q`D\�dK3
wEnD
7$t{� �� w`L8D�;`w\�dK�\D�;w8�`D $R s z z 8s��$- bYBR� w7, iD0_ �j�8�t� $R
E7,i�w 7� i� D`Lw i� D8 PB� 7, i ) d, 3 3 3 , z bY��� E7,i $R �Y� w7, iD0_ �j�8�t� BP 8s��$-
\�dK�\ � b� t��I �B {B8}Z��
8 U
`)(
8 U
8)`E7,i�
w 7� i� D`Lw i� D8Q8Q`
bY${Y �JZsjRE7,i
i � w�w i� DUw�w 7� i� DU � dD
7 � i � Ld� �w 7�1 DU
7 � 1 D3
qY���PB��� b� ��� �JZs�$Bt wE(D�
; Gs��st�k i�R��%�
y� $R s {B88Bt }�s{�${� $t $tIZR��k �B R�� sR$I� s h-�I RZ8 BP 8Bt�k� {sjj�I s bs�T
�st�k ��R��%�� �B {B%�� �Y� PZ�Z�� bs��st�k j$sA$j$�$�R� 3B� �-s8}j�� {BtR$I�� s {B8}stk
}�BIZ{$t� stI R�jj$t� s}}j$st{�R bY${Y s�� {B%���I Ak tBtT��t�bsAj� P���T��}js{�8�t�
bs��st�k }Bj${$�R P�B8 �Y� Is�� BP Rsj�� qY$R {B8}stk t��IR �B R�� sR$I� �tBZ�Y PZtIR
$t s bs��st�k ��R��%� s{{BZt� �B {B%�� �Y� {BR� BP {B%��$t� �Y� bs��st�k {js$8R s�$R$t�
P�B8 sjj �Y� Rsj�R IZ�$t� �Y� j$P� {k{j� BP �Y� }�BIZ{��
yt �Y$R R�{�$Bt� b� ZR� �Y� ��RZj�R P�B8 �Y� }��%$BZR R�{�$Bt� ts8�jk� o>x wUDH stI
~ y�wx wUDD� �B �R�$8s�� �Y� s}}�B}�$s�� bs��st�k ��R��%�� qY$R $t%Bj%�R ZR$t� s WB�8sj
d�
![Page 21: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/21.jpg)
s}}�B-$8s�$Bt PB� �Y� I$R��$AZ�$Bt BP �Y� �B�sj I$R{BZt��I bs��st�k {BR�� yt R�{�$Bt ;�d�
b� RYBb bY�t �Y$R WB�8sj s}}�B-$8s�$Bt {st A� �Y�B���${sjjk `ZR�$h�I� yt R�{�$Bt ;�1�
b� ZR� R$8Zjs�$Bt �B %sj$Is�� �Y$R s}}�B-$8s�$Bt bY�t �Y�B���${sj `ZR�$h{s�$Bt $R tB�
s%s$jsAj��
;�d Gs��st�k i�R��%� V}}�B-$8s�$Bt
G� ��{sjj �Y� 8��YBI BP �R�$8s�$t� �Y� bs��st�k ��R��%� sR I��$%�I $t Fs stI �Zj,s�t$>xH�
7Z}}BR� b� R�s�� b$�Y s bs��st�k ��R��%� BP R$9� ?� 7Z}}BR� �Y� bs��st�k ��R��%� s{{�Z�R
$t����R� {Bt�$tZBZRjk RB �Ys� Bt� IBjjs� $t �Y� ��R��%� s� �$8� ( ��BbR �B � 0 IBjjs�R s�
�$8� 0� $t �Y� sAR�t{� BP stk b$�YI�sbsjR� N�� �w?D A� �Y� }�BAsA$j$�k �Ys� �Y� bs��st�k
��R��%� $R t�%�� I�}j���I �$%�t �Ys� �Y� $t$�$sj ��R��%� $R ? IBjjs�R� qY�t �w?D $R �$%�t
Ak �Y� t�-� }�B}BR$�$Bt�
_�B}BR$�$Bt d( wFs stI �Zj,s�t$>xH� qY�B��8 MD U
�w?D ) h�\x wUD � ?i3 wE;D
yt }�s{�${�� b� s�� $t����R��I $t R���$t� �Y� $t$�$sj bs��st�k ��R��%� ? RZ{Y �Ys� �w?D )
d� # PB� RB8� R8sjj # wRsk (3(xD� qB {B8}Z�� RZ{Y st ? ��JZ$��R ,tBbj�I�� BP �Y� I$RT��$AZ�$Bt BP x wUD� qY$R $R� $t 8BR� {sR�R� �BB {B8}j${s��I� qB {$�{Z8%�t� �Y$R I$^{Zj�k�
b� s}}�B-$8s�� �Y� I$R��$AZ�$Bt BP x wUD Ak s WB�8sj I$R��$AZ�$Bt b$�Y 8�st o>x wUDH
stI %s�$st{� ~ y�wx wUDD wbY${Y b��� {B8}Z��I $t �Y� }��%$BZR R�{�$BtD� qY$R {st A�
`ZR�$h�I PB� {���s$t Rsj�R }�B{�RR�R Ak RYBb$t� �Ys� x wUD $R sRk8}�B�${sjjk WB�8sj� sR
�B�sj Rsj�R �B �B $tht$�k� GY�t RZ{Y st sRk8}�B�${ ��RZj� $R tB� s%s$jsAj�� b� ZR� $� sR
st s}}�B-$8s�$Bt�
yt �Y� t�-� }�B}BR$�$Bt� b� �R�sAj$RY �Y� sRk8}�B�${ WB�8sj$�k BP x wUD bY�t �Y� R�BT
{YsR�${ Rsj�R }�B{�RR $R s tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR�
_�B}BR$�$Bt dd U 7Z}}BR� �Y� Rsj�R }�B{�RR $R s tBtYB8B��t�BZR {B8}BZtI _B$RRBt
Rsj�R }�B{�RR b$�Y $t����sAj� $tR�st�st�BZR Rsj�R �s�� >w0D ) > N w0D stI $�$�I� As�{Y
R$9�R� qY�t�x wUD� o>x wUDH�
~ y�wx wUDD
Q7X0�� ]w(, dD wExD
sR >� � bY��� ]w(, dD $R �Y� R�stIs�I WB�8sj %s�$sAj��
1(
![Page 22: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/22.jpg)
_�BBP U N�� ] A� �Y� �B�sj tZ8A�� BP As�{YTRsj�R B%�� >(, UH� 7$t{� �Y� Rsj�R }�B{�RR
$R s tBtYB8B��t�BZR {B8}BZtI _B$RRBt }�B{�RR� ] $R s _B$RRBt �stIB8 %s�$sAj� b$�Y
}s�s8���� �>wUD bY���
�>wUD )8 U
(>wXDQX ) >
8 U
(wXDQX3
N�� �wUD )$ U( wXDQX stI \�7, 7 � (i A� s R�JZ�t{� BP $�$�I� �stIB8 %s�$sAj�R b$�Y }IP
w0D�wUD
, ( � 0 � U� 3�B8 �Y� }�B}���$�R BP �Y� �%�t� �$8�R $t s tBtYB8B��t�BZR {B8}BZtI
_B$RRBt }�B{�RR w$t �Y� qY�B��8 x�d1 BP �Zj,s�t$>EHD stI
>w0D
�>w0D)
w0D
�w0D,
b� R�� �Ys�� �$%�t ] ) z� �d, �1, N N N , �z {st A� �YBZ�Y� BP sR �Y� �$8�R bY�t �Y� z
As�{YTRsj�R B{{Z���I� wqY� 7�Y As�{YTRsj� B{{Z�R s� �Y� 7�Y $t{��sR$t� B�I�� R�s�$R�${R
BP �d,�1, N N N , �z�D qY� �B�sj I$R{BZt��I bs��st�k {BR� BP s R$t�j� As�{YTRsj� B{{Z��$t�
s� �$8� ( $R �$%�t Ak�p7
i)d.iwP D bY��� p7 $R �Y� tZ8A�� BP $��8R $t �Y$R As�{YTRsj�
stI .iwP D $R �Y� �B�sj I$R{BZt��I bs��st�k {BR� BP �Y� i�Y $��8 RBjI $t �Y$R As�{YTRsj��
<�t{� �Y� �B�sj I$R{BZt��I bs��st�k {BR� BP s R$t�j� As�{YTRsj� BP R$9� p7 B{{Z��$t� s�
�$8� �7 $R �$%�t Ak �� �7
�p7
i)d.iwP D� N��
V7 ) �� �7
p73i)d
.iwP D PB� 7 ) d, 1, 3 3 3 , ]3 wEED
WBb� �Y� �B�sj I$R{BZt��I bs��st�k {BR� {st A� b�$���t sR
x wUD ) Vd L V1 L N N NL V] wE�D
bY${Y $R �YZR s �stIB8 RZ8 BP $�$�I� �stIB8 %s�$sAj�R� 7$t{� s _B$RRBt �stIB8 %s�$sAj�
b$�Y }s�s8���� �>wUD $R sRk8}�B�${sjjk WB�8sj sR > �� � �Y� ��RZj� PBjjBbR ]B�Bjjs�k; $t iBAA$tR>dnH�
3�B8 �Y� }��%$BZR }�B}BR$�$Bt� b� ,tBb �Ys� $P �Y� Rsj�R }�B{�RR $R s tBtYB8B��t�BZR
{B8}BZtI _B$RRBt }�B{�RR� �Y� I$R��$AZ�$Bt BP x wUD $R �-}�{��I �B A� %��k {jBR� �B WB�T
8sj sR jBt� sR �Y� �-}�{��I tZ8A�� BP As�{YTRsj�R Z} �B U� �$%�t Ak �>wUD� $R RZ^{$�t�jk
js����
1d
![Page 23: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/23.jpg)
WBb j�� wND A� �Y� R�stIs�I WB�8sj {Z8Zjs�$%� I$R��$AZ�$Bt PZt{�$Bt w9��B 8�st stIZt$� %s�$st{�D stI .# A� �Y� tZ8A�� RZ{Y �Ys�
d� w.#D ) #3
qY� WB�8sj s}}�B-$8s�$Bt $8}j$�R �Ys� $P �Y� �-}�{��I tZ8A�� BP Rsj�R $R js���� �Y�
s}}�B-$8s�� bs��st�k ��R��%� $R �$%�t Ak
PpwUD ) o>x wUDH L .#�~ y�wx wUDD,
$���� PB� �Y$R PpwUD� �wPpwUDD � d� #� G� R�ZIk �Y� }��PB�8st{� BP �Y$R s}}�B-$8sT�$Bt $t �Y� t�-� RZAR�{�$Bt�
;�1 WZ8��${sj stI 7$8Zjs�$Bt i�RZj�R
<��� b� ZR� �Y� ��RZj�R BP �Y� }��%$BZR R�{�$Bt �B {B8}Z�� �Y� bs��st�k ��R��%� PB� �Y�
PBjjBb$t� R$�Zs�$Bt�
7Z}}BR� �Y� }�BIZ{� $R {B%���I Ak �Y� tBtT��t�bsAj� P���T��}js{�8�t� bs��st�k }Bj${k
b$�Y Bt�Tk�s� bs��st�k }��$BI wP ) dD� �Y� j$P��$8� I$R��$AZ�$Bt BP �Y� $��8 $R �-}BT
t�t�$sj b$�Y 8�st Bt� k�s� w� ) dD� �Y� ��}js{�8�t� {BR�R s�� h-�I stI �Y�k s�� Bt�
YZtI��I IBjjs�R wo>;H ) d((� o>;1H ) d((((D� �Y� j$P� {k{j� BP �Y$R $��8 $R h%� k�s�R
wU ) xD� stI �Y� I$R{BZt� Ps{�B� }�� k�s� $R (�(EM w ) (3(EMD bY${Y j�sIR �B �0 sttZsj
$t����R� �s��� 3�B8 �JZs�$BtR w;D stI wxD� b� Ys%�
o>.wP DH )�o>;Hwd� �� P D
)d d(( wd� ��(3(EM dD
(3(EM) �E3E�xM
stI
o>.1wP DH )o1>;H�1wd� �� P D1
1Lo>;1H�wd� ��1 P D
1
)d((1 d1 wd� ��(3(EM dD1
(3(EM1Ld(((( d wd� ��1 (3(EM dD
1 (3(EM) dME�E3(dd�3
qYZR �Y� �-}�{��I bs��st�k {BR� BP Bt� $��8 $R c�E�EM� stI �Y� R�stIs�I I�%$s�$Bt $R
c�E�E�� qY� {B%��s�� }�BAsA$j$�k $R d� # ) (3�x� k$�jI$t� .(3(x � d3E; P�B8 �Y� tZ8��T
${sj �sAj� BP WB�8sj I$R��$AZ�$Bt� G� $jjZR��s�� �Y� ��RZj�R PB� h%� I$&���t� R�B{YsR�${
11
![Page 24: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/24.jpg)
Rsj�R }�B{�RR�R A�jBb� qY� }s�s8����R BP �Y�R� }�B{�RR�R s�� {YBR�t RB sR �B �$%� �Y�
�-}�{��I Rsj�R BP d((( Zt$�R B%�� �Y� }�BIZ{� j$P� {k{j� BP x k�s�R�
wsD _B$RRBt 7sj�R _�B{�RRU G� sRRZ8� �Y� R�jj$t� �s�� ) 1(( $��8R\k�s�� 3�B8
�JZs�$BtR wn�D stI w;(D� b� ���
o>x wUDH ) o>.wP DH8 U
(�� 0w0DQ0
) �E3E�xM8 x
(w��(3(EM0 1((DQ0
) Md�xx3n�;d
stI
~ y�wx wUDD ) o>.1wP DH8 U
(��1 0w0DQ0
) dME�E3(dd�8 x
(w��1 (3(EM0 1((DQ0
) dnxExdnM3��EM3
qY���PB���
o>x wUDH L .(3(x
�~ y�wx wUDD ) M���x3EnMM3
qYZR� $P b� R�s�� b$�Y s bs��st�k ��R��%� BP cM���E $t s Ast, s{{BZt� �s�t$t� �0 sttZsj
k$�jI� b� b$jj A� sRRZ��I BP {B%��$t� sjj �Y� bs��st�k {js$8R s�$R$t� BZ� �Y� Rsj� BP �Y�
d((( $��8R b$�Y }�BAsA$j$�k ��x� qY$R $R sRRZ8$t� �Y� _B$RRBt Rsj�R 8BI�j�
wAD ]B8}BZtI _B$RRBt 7sj�R _�B{�RRU 7Z}}BR� �Ys� {ZR�B8��R s��$%� s{{B�I$t� s
_B$RRBt }�B{�RR b$�Y �s�� d }�� Isk w$���� ) nEx {ZR�B8��R\k�s�D� stI �Y� tZ8A�� BP
$��8R }Z�{YsR�I AZk s {ZR�B8�� $R s _B$RRBt �stIB8 %s�$sAj� b$�Y 8�st 1((\nEx� qYZR
RB8� {ZR�B8��R AZk tB�Y$t�� bY$j� �Y� 8�st B�I�� R$9� $R 1((\nEx� �YZR k$�jI$t� Rsj�R
�s�� BP 1(( }�� k�s�� 3�B8 �JZs�$BtR wn�D stI wnMD� b� ���
o>x wUDH ) o>.wP DHo>V H8 U
(�� 0w0DQ0
) �E3E�xM 1((nEx
8 x
(w��(3(EM0 nExDQ0
) Md�xx3n�;d
stI
~ y�wx wUDD ) w~ y�w.wP DDo>V H L o1>.wP DHo>V 1HD8 U
(��1 0w0DQ0
1n
![Page 25: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/25.jpg)
) wwdME�E3(dd�� w�E3E�xMD1D 1((nEx
L w�E3E�xMD1 w1((nEx
L w1((
nExD1DD
8 x
(w��1 (3(EM0 nExDQ0
) d�1M(M��3xE(M3
qY���PB���
o>x wUDH L .(3(x
�~ y�wx wUDD ) MM��13�(nx3
qYZR� $t �Y$R {sR� b� t��I s Rj$�Y�jk js���� bs��st�k ��R��%� BP cMM��n� �%�t �YBZ�Y
�Y� 8�st bs��st�k {BR� BP sjj �Y� Rsj�R $R �Y� Rs8� sR $t �Y� _B$RRBt {sR�� qY$R $R �Y�
{BtR�JZ�t{� BP Rsj�R B{{Z�$t� $t �stIB8 As�{Y�R� stI As�{Y�R Ys%$t� js���� R}s{$t��
bY${Y $t{��sR�R �Y� B%��sjj %s�$sAj$�k�
w{D WBtYB8B��t�BZR _B$RRBt 7sj�R _�B{�RR U G� sRRZ8� �Y� R�jj$t� �s��
w0D )
T�����������������������z�����������������������Z
d(bnd PB� �Y� h�R� 8Bt�Y $t �s{Y k�s�d(b1M PB� �Y� R�{BtI 8Bt�Y $t �s{Y k�s�d;bnd PB� �Y� �Y$�I 8Bt�Y $t �s{Y k�s�d;bn( PB� �Y� PBZ��Y 8Bt�Y $t �s{Y k�s�d;bnd PB� �Y� hP�Y 8Bt�Y $t �s{Y k�s�1xbn( PB� �Y� R$-�Y 8Bt�Y $t �s{Y k�s�1xbnd PB� �Y� R�%�t�Y 8Bt�Y $t �s{Y k�s�1xbnd PB� �Y� �$�Y�Y 8Bt�Y $t �s{Y k�s�1xbn( PB� �Y� t$t�Y 8Bt�Y $t �s{Y k�s�d;bnd PB� �Y� ��t�Y 8Bt�Y $t �s{Y k�s�d;bn( PB� �Y� �j�%�t�Y 8Bt�Y $t �s{Y k�s�d(bnd PB� �Y� �b�jP�Y 8Bt�Y $t �s{Y k�s��
wEMD
V�s$t� �Y� }s�s8����R s�� {YBR�t �B k$�jI 1(( Rsj�R }�� k�s�� qY� sAB%� Rsj�R �s��
sRRZ8�R �Ys� �Y� Rsj�R BP �Y$R }�BIZ{� s�� R�sRBtsj� b$�Y �Y� b$t��� 8Bt�YR BP *�{�8A���
FstZs�k stI 3�A�Zs�k PB�8$t� �Y� RjBb R�sRBt� �Y� RZ88�� 8Bt�YR FZt� T 7�}��8A��
PB�8$t� �Y� Y$�Y R�sRBt� bY$j� �Y� ��R� PB�8$t� �Y� 8$jI R�sRBt� 3�B8 �JZs�$BtR wn�D
stI w;(D� b� ���
o>x wUDH ) o>.wP DH8 U
(�� 0w0DQ0
) �E3E�xM8 x
(��(3(EM0w0DQ0
) MdM1(3x(�;
stI
~ y�wx wUDD ) o>.1wP DH8 U
(��1 0w0DQ0
1;
![Page 26: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/26.jpg)
) dME�E3(dd�8 x
(��1 (3(EM0w0DQ0
) dnxd�1(131E��3 wE�D
qY���PB���
o>x wUDH L .(3(x
�~ y�wx wUDD ) M�Mx(3xnE13
qYZR �Y$R Rsj�R }�B{�RR ��JZ$��R R8sjj�� bs��st�k ��R��%� �Yst �Y� �s�j$�� �bB 8BI�jR�
qY$R $R s {BtR�JZ�t{� BP R�s��$t� �Y� Rsj�R $t 8Bt�Y d� �Y� RjBb R�sRBt� bY${Y }BR�}Bt�R
�Y� bs��st�k {BR�R �B �Y� PZ�Z��� �YZR ��IZ{$t� �Y�$� }��R�t� %sjZ��
wID s�{Y i�t�bsj 7sj�R _�B{�RRU WBb sRRZ8� �Ys� �Y� {ZR�B8��R s��$%� I����8$tT
$R�${sjjk� �-s{�jk Bt� }�� Isk� stI �Y� I$R��$AZ�$Bt BP �Y� tZ8A�� BP $��8R }Z�{YsR�I Ak
s {ZR�B8�� w�Y� As�{Y R$9�D p $R _B$RRBt b$�Y }s�s8���� 1((bnEx $��8R wRs8� sR $t {sR�
w{DD� 3�B8 �JZs�$BtR w;dD stI w;1D� b� ���
o>x wUDH ) o>.wP DHo>pHU nEx37)d
�� 7
nEx
) �E3E�xM 1((nEx
x nEx37)d
��(3(EM 7nEx
) Md�;�3�1�M
stI
~ y�wx wUDD
) w~ y�w.wP DDo>pH L o1>.wP DHo>p1HDU nEx37)d
��1 7nEx
L1o1>.wP DHo1>pHU nEx37)d
U nEx3i)7Ld
�� w7LiDnEx � wo>x wUDHD1
) wwdME�E3(dd�� w�E3E�xMD1D 1((nEx
L w�E3E�xMD1 w1((nEx
L w1((
nExD1DD
x nEx37)d
��1 (3(EM 7
nEx
L1 w�E3E�xMD1 w1((nEx
D1x nEx37)d
x nEx3i)7Ld
��(3(EM w7LiD
nEx � wMd�;�3�1�MD1
) dnxE1Edd3�1�M3
qY���PB���
o>x wUDH L .(3(x
�~ y�wx wUDD ) M��M�3;;1d3
qY� 8�st� stI %s�$st{� BP �Y� �B�sj I$R{BZt��I bs��st�k {BR�� sR b�jj sR �Y� bs��st�k
��R��%�� $t �Y$R {sR� j�RR �Yst �Y� {B8}BZtI {BR� {sR�� qY$R $R sR �-}�{��I� R$t{� I����T
8$t$R�${ s��$%sjR ��IZ{� %s�$sA$j$�k� stI I$R{BZt�$t� Y�j}R �Y� I����8$t$R�${ s��$%sjR 8B��
1x
![Page 27: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/27.jpg)
�Yst �Y� _B$RRBt s��$%sjR�
w�D �s�,B% �BIZjs��I _B$RRBt 7sj�R _�B{�RRU FZR� sR $t {sR� wAD� b� sRRZ8� �Ys�
�Y� 8s�,�� {k{j�R �Y�BZ�Y �Y��� R�s��R <$�Y w<D� ��I$Z8 w�D� stI NBb wND stI As{, �B
<$�Y� $t �Ys� B�I��� yt �Y� <$�Y R�s�� �Y� Rsj�R }�B{�RR $R _B$RRBt b$�Y �s�� n(( }�� k�s��
$t ��I$Z8 R�s�� �Y� �s�� $R 1d( k�s�� stI $t NBb R�s�� $� $R �( }�� k�s�� 3Z��Y��8B���
�Y� 8s�,�� $R $t <$�Y R�s�� �B A��$t b$�Y� =tj$,� $t �Y� tBtTYB8B��t�BZR _B$RRBt {sR��
b� sRRZ8� �Ys� $� R�skR $t �s{Y R�s�� PB� st �-}Bt�t�$sj s8BZt� BP �$8� b$�Y 8�st d\n
k�s�� qYZR �Y� Rsj�R }�B{�RR $R s �s�,B% 8BIZjs��I _B$RRBt }�B{�RR b$�Y �Y� �-���tsj
]q�] Ys%$t� R�s�� R}s{� \<� �� Ni� �Y� �s�� 8s��$-
< )
mNt�n n (( �n n( n �n
uU{ , w�(D
stI �Y� R�jj$t� �s��R n((, 1d(, �( ��R}�{�$%�jk� k ZR$t� �JZs�$BtR wx�D stI wE(D� b� ���
o>x wUDH ) M;dM;3x��� stI ~ y�wx wUDD ) �1;��E(�31�x�
qY���PB���
o>x wUDH L .(3(x
�~ y�wx wUDD ) ���x�3n�(M3
qY$R $R Y$�Y�R� bs��st�k ��R��%� t��I�I s8Bt� �Y� h%� {sR�R� qY$R $R A�{sZR� �Y� 8s�,��
$R sRRZ8�I �B R�s�� $t <$�Y 8BI�� �YZR $t{Z��$t� s jB� BP �Y� bs��st�k {BR�R �s�jk Bt�
qY�R� h%� {sR�R s�� RZ88s�$9�I $t qsAj� d�
WZ8��${sj i�RZj�R
]sR�R o>x wUDH ~ y�wx wUDD PpwUD ) o>x wUDH L .(3(x
�~ y�wx wUDD
wsD Md�xx�n�;d dnxExdnM���EM M���x�EnMMwAD Md�xx�n�;d d�1M(M���xE(M MM��1��(nxw{D MdM1(�x(�; dnxd�1(1�1E�� M�Mx(�xnE1wID Md�;���1�M dnxE1Edd��1�M M��M��;;1dw�D M;dM;�x��� �1;��E(��1�x� ���x��n�(M
qsAj� dU WZ8��${sj ��RZj�R BP �Y� h%� {sR�R�
qYZR� B%��sjj� �Y� sAB%� {sj{Zjs�$BtR RZ���R� �Ys� b� t��I �B }�B%$I� A��b��t ��t �B hPT
���t }��{�t� 8B�� bs��st�k ��R��%� �Yst �Y� �-}�{��I {BR� �B s{{BZt� PB� �Y� %s�$sAj$�k�
I�}�tI$t� Bt �Y� Rsj�R }�B{�RR 8BI�j ZR�I�
1E
![Page 28: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/28.jpg)
WBb� �Y� Rsj�R }�B{�RR�R $t {sR�R wsD� wAD� stI w{D s�� R}�{$sj {sR�R BP tBtYB8B��t�BZR
{B8}BZtI _B$RRBt }�B{�RR�R� <�t{� b� s�� sRRZ��I BP sRk8}�B�${ WB�8sj$�k BP x wUD Ak
_�B}BR$�$Bt dd� <�t{� �Y� bs��st�k ��R��%� {sj{Zjs�$Bt {st A� �s,�t �B A� %sj$I� �R}�T
{$sjjk R$t{� �Y� �-}�{��I Rsj�R s�� sABZ� Bt� �YBZRstI PB� �s{Y {sR�� bY${Y $R RZ^{$�t�jk
js����
<Bb�%��� PB� {sR�R wID stI w�D� b� IB tB� Ys%� stsjk�${sj }�BBP BP sRk8}�B�${ WB�8sj$�k
BP x wUD� <�t{� b� ��RB�� �B R$8Zjs�$Bt �B %sj$Is�� �Y$R {js$8� qB IB �Y$R� b� ZR�I
R$8Zjs�$Bt �B ��R� �Y� WB�8sj$�k BP x wUD stI {B8}Z�� s �(0 {BthI�t{� $t���%sj BP �Y�
t$t��kThP�Y }��{�t�$j� BP x wUD� G� BA�s$t�I ��t �YBZRstI $tI�}�tI�t� ��}j${s�$BtR PB�
�s{Y {sR�� qY�R� ��t �YBZRstI $tI�}�tI�t� ��}j${s�$BtR b��� ��BZ}�I $t�B Bt� YZtI��I
�JZsjTR$9�I RZA��BZ}R stI �Y� t$t��kThP�Y }��{�t�$j� BP x wUD bsR {B8}Z��I PB� �s{Y
RZA��BZ}� qY�t �Y� �(0 {BthI�t{� $t���%sj BP �Y� t$t��kThP�Y }��{�t�$j� BP x wUD bsR
{B8}Z��I P�B8 �Y�R� Bt� YZtI��I BAR��%s�$BtR� G� sjRB {B8}Z��I �Y� {B%���I }��{�t�T
s�� � $���� �Y� }��{�t�s�� BP �Y�R� ��t �YBZRstI Rs8}j�R PB� bY${Y BZ� bs��st�k ��R��%�
s}}�B-$8s�$Bt $R RZ^{$�t� �B s%B$I B%��I�sb$t� �Y� s{{BZt�� PB� �s{Y {sR�� qY�k s��
j$R��I $t qsAj� 1�
7$8Zjs�$Bt i�RZj�R��st zs�$st{� �(0 ]BthI�t{� yt���%sj WB�8sj$�k ��R� {B%���I
]sR�R BP x wUD BP x wUD BP W$t��kThP�Y _��{�t�$j� I(U I$R��$AZ��I tB�8sjjk }��{�t�s��wsD Md�M;�En dnMMM�;E >MEM(��E; M�dxn�1(H tB� ��`�{��I �;�;�0wAD M1(1(�(M d�n;dn�M >M�1�E�n� �(d;(���H tB� ��`�{��I �;�E10w{D MdME1��x dn�Mdx�; >MEn�d�1n M�(M���dH tB� ��`�{��I �;�nE0wID M1(n��M( dnxdMMd( >MEEEn�;d M�d11�E�H tB� ��`�{��I �;�EM0w�D M;n(��MM �nx�n;nM >EM;;x�Ed d((d�;�dxH tB� ��`�{��I �;�x(0
qsAj� 1U 7$8Zjs�$Bt ��RZj�R BP �Y� h%� {sR�R�
3�B8 �Y� }��%$BZR �bB �sAj�R� b� htI �Ys� BZ� bs��st�k ��R��%� s}}�B-$8s�$Bt PB�
# ) (3(x PsjjR $t�B �Y� �(0 {BthI�t{� $t���%sj BP �Y� t$t��kThP�Y }��{�t�$j� BP �Y� R$8T
Zjs�$Bt ��RZj�R PB� �s{Y BP �Y�R� h%� {sR�R� G� sjRB htI �Ys� �Y� {B%���I }��{�t�s�� $R
%��k {jBR� �B �x0 wd � # ) (3�xD PB� �s{Y {sR�� 3B� {sR�R wsD� wAD� stI w{D� R$t{� b�
sj��sIk ,tBb �Y� sRk8}�B�${ WB�8sj$�k BP x wUD� �Y$R ��RZj� %sj$Is��R �Y� {B���{�t�RR BP
BZ� R$8Zjs�$BtR�
1�
![Page 29: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/29.jpg)
3B� {sR�R wID stI w�D� sj�YBZ�Y b� {sttB� RYBb �Y� WB�8sj$�k BP x wUD PB� s As�{Y ��T
t�bsj }�B{�RR B� �s�,B% 8BIZjs��I }�B{�RR stsjk�${sjjk� �Y� ��RZj�R BP �Y� WB�8sj$�k
��R� $t qsAj� 1 RYBbR �Ys� �YBR� ��t �YBZRstI BAR��%s�$BtR PB� {sR�R wID stI w�D s��
}BRR$Ajk I$R��$AZ��I WB�8sjjk� G� {st sjRB R�� �Y$R Ak �Y� P��JZ�t{k }jB�R $t 3$�Z��
d stI 1� y� RZ}}B��R BZ� sRRZ8}�$Bt �Ys� x wUD $R s}}�B-$8s��jk WB�8sj b$�Y 8�st
o>x wUDH stI %s�$st{� ~ y�wx wUDD� �%�t ZtI�� s As�{Y ��t�bsj Rsj�R }�B{�RR B� �s�,B%
8BIZjs��I Rsj�R }�B{�RR� qY���PB��� �Y$R ��RZj� %sj$Is��R �Y� s{{Z�s{k BP BZ� bs��st�k
��R��%� s}}�B-$8s�$BtR�
6.5 7 7.5 8 8.5 9 9.5 10
x 104
0
100
200
300
400
500
600
3$�Z�� dU 3��JZ�t{k }jB� BP {sR� wID�
x 7Z88s�k
yt �Y$R }s}��� b� Z�$j$9�I �Y� h�R� stI R�{BtI 8B8�t�R BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I
bs��st�k {BR� BP s R$t�j� Rsj� PB� R$t�j�T{B8}Bt�t� $��8R ZtI�� PBZ� I$&���t� ,$tIR
BP bs��st�k }Bj${$�RU ��t�bsAj� P���T��}js{�8�t�� tBtT��t�bsAj� P���T��}js{�8�t�� }�B
�s�s� stI tBtT��t�bsAj� 8$t$8sjT��}s$� bs��st�k }Bj${k� G� sjRB {B8}Z��I �Y� 8�st
1M
![Page 30: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/30.jpg)
4 5 6 7 8 9 10 11 12
x 104
0
100
200
300
400
500
600
700
3$�Z�� 1U 3��JZ�t{k }jB� BP {sR� w�D�
stI %s�$st{� BP �Y� }�BIZ{��:R �B�sj I$R{BZt��I bs��st�k {BR� BP �Y� s�����s�� Rsj�R PB�
R�%��sj I$&���t� R�B{YsR�${ Rsj�R }�B{�RR�RU ��t��sj R�B{YsR�${ Rsj�R }�B{�RR�R� R�B{YsR�${
Rsj�R }�B{�RR�R b$�Y $tI�}�tI�t� $t{��8�t�R� As�{Y ��t�bsj Rsj�R }�B{�RR�R� stI �s�,B%
8BIZjs��I Rsj�R }�B{�RR� G� ZR�I �YBR� JZst�$�$�R �B I��$%� �Y� bs��st�k ��R��%� Ak
s}}jk$t� s WB�8sj s}}�B-$8s�$Bt� 7�%��sj tZ8��${sj stI R$8Zjs�$Bt ��RZj�R s�� ZR�I �B
RZ}}B�� �Y� 8��YBI b� ZR� �B R�� �Y� bs��st�k ��R��%�� V P�b R$8}j� �-s8}j�R s�� sjRB
�$%�t $t �Y$R }s}���
1�
![Page 31: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/31.jpg)
i�P���t{�R
>dH <� W� V8s�B stI e� e� VtI��RBt� *����8$ts�$Bt BP bs��st�k ��R��%�RU Vt e-��tT
R$Bt� �sts��8�t� 7{$�t{�� 11� WB�d1� dn�dudn�;� d��E�
>1H G� i� j$R{Y,� stI *� W� _� �Z��Yk� Gs��st�k {BR� stsjkR$R� �s�{�j *�,,��� yt{��
d��;�
>nH F�YBRYZs ej$sRYA���� WB9�� *� 7$t�}Z�bsjjs� stI 7$8Bt _� G$jRBt� ]sj{Zjs�$t� �Y�
bs��st�k ��R��%� PB� �$8� stI ZRs�� $tI�-�I bs��st�k� �sts��8�t� 7{$�t{�� ;n�
WB��� �EEu��x� d����
>;H 7YsZT7Y$st� Fs� z� p� �Zj,s�t$� V� �$��s� stI F� p� _s�st,s�� V tBtT��t�bsAj�
8$t$8sjT��}s$� bs��st�k }Bj${k b$�Y �$8�TI�}�tI�t� {BR�R� 3B��Y{B8$t� $t yeee
q�stRs{�$BtR Bt i�j$sA$j$�k�
>xH 7YsZT7Y$st� Fs stI z� p� �Zj,s�t$� ]B8}Z�s�$Bt BP bs��st�k ��R��%�R PB� tBtT
R�s�$Bts�k Rsj�R }�B{�RR�R� q�{Yt${sj i�}B�� =W]\!i\qi��T(n� =t$%��R$�k BP
WB��Y ]s�Bj$ts s� ]Ys}�j <$jj� d����
>EH z� p� �Zj,s�t$� �BI�j$t� stI stsjkR$R BP R�B{YsR�${ RkR��8R� ]Ys}8st stI <sjj�
d��x�
>�H FBYt G� �s8��� ]BR� stsjkR$R BP }�B �s�s stI P���T��}js{�8�t� bs��st�$�R� Ws%sj
i�R�s�{Y NB�$R�${ +Zs����jk� 1�� WB�1� n;xunxE� d�M1�
>MH FBYt G� �s8��� *$R{BZt��I stI }�� Zt$� {BR�R BP }�BIZ{� bs��st�k� �sts��8�t�
7{$�t{�� nn� WB��� �dEu�n(� d�M��
>�H G� G� ��t,�� *����8$ts�$Bt BP bs��st�k ��R��%�R� �sts��8�t� 7{$�t{�� dx�
WB�d(� x;1ux;�� d�E��
>d(H *� p� W�Zk�t stI *� W� _� �Z��Yk� ]BR� stsjkR$R BP bs��st�k }Bj${$�R� Ws%sj
i�R�s�{Y NB�$R�${ +Zs����jk� nd� x1xux;d� d�M;�
>ddH *� p� W�Zk�t stI *� W� _� �Z��Yk� V ��t��sj 8BI�j PB� �R�$8s�$t� bs��st�k {BR�R
PB� ��}s$�sAj� }�BIZ{�R� yye q�stRs{�$BtR� dE� WB�;� n��unME� d�M;�
n(
![Page 32: ]B8}Z˝s˝$Bt BP Gs——st˝k i‡R‡—%‡R b$˝Y p‡t‡—sj …vkulkarn/papers/wargensp.pdfqY‡R‡PZtIRs—‡R‡˝sR$I‡s˝˝Y‡A‡˙$tt$t˙BP˝Y‡Rsj‡R}‡—$BIPB—˝Y‡bs——st˝k{BR˝RBP](https://reader031.vdocuments.pub/reader031/viewer/2022030423/5aaa7b827f8b9a9a188e495c/html5/thumbnails/32.jpg)
>d1H F� p� _s�st,s� stI p� <� GB�8� _��I${�$Bt $t���%sjR PB� bs��st�k ��R��%�R stI
{sRY 4Bb� �sts��8�t� 7{$�t{�� 1�� WB�1� 1n�u1;d� d�Md�
>dnH <��A��� iBAA$tR� qY� sRk8}�B�${ I$R��$AZ�$Bt BP �Y� RZ8 BP s �stIB8 tZ8A�� BP
�stIB8 %s�$sAj�R� Zjj��$t BP V8��${st �s�Y�8s�${R 7B{$��k� ;n� ddxduddEd� d�;M�
>d;H ]� 7� qs}$��B stI �� F� _BRt��� Gs��st�k ��R��%$t�� Ws%sj i�R�s�{Y NB�$R�${R� nx�
;�nu;��� d�MM�
>dxH �� =� qYB8sR� V }��I${�$%� 8BI�j PB� 8stZPs{�Z��� bs��st�k ��R��%�R� �sts��T
8�t� 7{$�t{�� nx� dxdxudxd�� d�M��
>dEH =�7� 3�I��sj q�sI� ]B88$RR$Bt y8}�B%�8�t� V{�� MM 7�s� 1dMn� d(dudd1� d��x�
nd