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ghcebgb_cihkueZxsbcihdheeZl_jZeyf\ha[m`^_gbyk³\uoh^Z´fha]ZgZ_]h³\oh^´ZlZd
`_ \g_rgbc dhglmj h[jZlguo k\ya_c hl j_amevlZlh\ hkms_kl\e_gguo ^_ckl\bc \h \g_rg_c
kj_^_h[hagZq_gguc[hevrhcimgdlbjghcebgb_c>h[Z\bebkvbg_cjhgu\^hev\gmlj_gg_]h
dhglmjZ ih \ha[m`^_gbyf dhlhjuo hkms_kl\ey_lky ³ij_^\hkobs_gb_´ j_amevlZlh\ ^_ckl\bc
Zdp_ilhjhfj_amevlZlh\^_ckl\bc
JZkkfhljbf \ujZ[hldm deZkkbq_kdh]h mkeh\gh]h j_ne_dkZ Imklv a - \u[jZgguc gZfb
mkeh\guckb]gZegZijbf_ja\hghdbb, cbd -klmddhjfmrdb\b^oe_[Zb^_ckl\b_oe_[ZgZ
\dmkh\u_j_p_ilhjuyaudZ[_amkeh\gucjZa^jZ`bl_ev
NZdlbq_kdb\k_imkdh\u_klbfmeuy\eyxlkyj_amevlZlZfb^_ckl\bc-^_ckl\b_fy\
ey_lky h`b^Zgb_ imkdh\h]h klbfmeZ b gZkljhcdZ k_gkhjgh]h ZiiZjZlZ ij_^\hkobs_gb_ \
l_jfbgheh]bbMGZck_jZgZ\hkijbylb_^Zggh]hklbfmeZZj_amevlZlhf^_ckl\bybh[jZl
ghc Znn_j_glZpb_c y\ey_lky kZf imkdh\hc klbfme < khhl\_lkl\bb k dhgp_ipb_c Ko_f
\hkijbylby MGZck_jZ kf jZa^_e b >GZck_j M @ ><bly_\ @ [_a lZdhc gZkljhcdb b
ij_^\hkobs_gby fu ijhklh g_ kfh`_f \hkijbgylv b g_ m\b^bf b g_ mkeurbf khhl\_lkl
\mxsbc imkdh\hc klbfme GZijbf_j qlh[u \hkijbgylv a\hghd a fu ^he`gu hkms_kl\blv
i_jp_ilb\gh_^_ckl\b_da ihgZkljhcd_gZ_]h\hkijbylb_Ihwlhfmfu^Ze__[m^_fjZkkfZl
jb\Zlvimkdh\u_klbfmeudZdwlZigu_j_amevlZlu
<_jgh b h[jZlgh_ - h[jZlgZy Znn_j_glZpby h[ mki_rghf aZ\_jr_gbb g_dhlhjh]h
wlZigh]h ^_ckl\by b ihemq_gb_ wlZigh]h j_amevlZlZ y\ey_lky imkdh\hc ^ey gZqZeZ ke_^mx
15
s_]h ^_ckl\by b ijh^he`_gby ^hklb`_gby p_eb ld fu g_ fh`_f ijh^he`blv ke_^mxs__
^_ckl\b_ihdZg_kh\_jr_ghij_^u^ms__GZijbf_jihke_lh]hdZdijha\mqZea\hghda`b
\hlgh_gZqbgZ_lke_^mxs__^_ckl\b_db -h`b^Zgb_klmdZdhjfmrdb>hklb`_gb_j_amevlZlZ
b - klmdZdhjfmrdb[m^_limkdh\uf^eygZqZeZke_^mxs_]hwlZiZ^_ckl\bc-ih^oh^Zddhj
fmrd_b\hkijbylb_oe_[ZdcIhemq_gb_j_amevlZlZc - \b^Zoe_[Z ³aZimklbl´ihke_^g__^_c
kl\b_ dd - ih_^Zgb_ oe_[Z k p_evx ihemq_gby dhg_qgh]h j_amevlZlZ d - hsms_gb_ oe_[Z j_
p_ilhjZfbyaudZ
³AZimkd´^_ckl\bydbfh`_l[ulvhkms_kl\e_gg_cjhghfdbijb^_ckl\bbgZg_]himk
dh\h]h klbfmeZ a ih aZdhghf_jghklb a ⇒ db. WlZ aZdhghf_jghklv [m^_l aZdj_ie_gZ \ lhf b
lhevdh \ lhf kemqZ_ _keb ^_ckl\b_ db ijb\_^_l d lZdhc h[jZlghc Znn_j_glZpbb Res(db) hl
j_amevlZlh\wlh]h^_ckl\bydhlhjZy\uah\_lj_amevlZlb, ^eydhlhjh]haZdhghf_jghklvb ⇒ d,
h[gZjm`_ggZyg_cjhghfd[m^_lbf_lv[hevrmxhp_gdm mkeh\ghc\_jhylghklbq_faZdhgh
f_jghklva ⇒ dhlij_^u^ms_]hwlZigh]hj_amevlZlZ<wlhfkemqZ_\khhl\_lkl\bbkbgnhj
fZpbhgghcl_hjb_cwfhpbc\hagbdrZyiheh`bl_evgZywfhpbyaZdj_ibl³aZimkd´^_ckl\bya
⇒ db Zdlb\Zpbx h[jZlghc Znn_j_glZpb_cRes(db) j_amevlZlZbihaZdhghf_jghklbRes(db)
⇒ b, ZlZd`_aZdhghf_jghklvb ⇒ d. Ihke_ihemq_gbymkeh\gh]hklbfmeZabaZimkdZ^_ckl
\by db ke_^mxsbf imkdh\uf klbfmehf klZg_l m`_ klbfme b, aZimkdZxsbc ^_ckl\b_ dc Z
wlZigufj_amevlZlhf[m^_lj_amevlZlc. Wlhlke_^mxsbcwlZi^_ckl\bcijb\_^_ld\ujZ[hld_
ZgZeh]bqguoaZdhghf_jghkl_cb ⇒ dc, Res(dc) ⇒ c bc ⇒ dbl^kf³AZimkd´^_ckl\by
da hkms_kl\ey_lky kZfhc fhlb\Zpb_c F ihkdhevdm fhlb\Zpby y\ey_lky g_ lhevdh Zdlb\b
jmxsbf\ha[m`^_gb_fghbklbfmehf³AZimkd´F⇒ da aZdj_iblkyihlhc`_ijbqbg_qlh
b^jm]b_aZimkdbldijb\_^_ldwlZighfmj_amevlZlma, ij_^kdZau\Zxs_fmihaZdhghf_jgh
klba ⇒ d ^hklb`bfhklvdhg_qgh]hj_amevlZlZk[hevr_c\_jhylghklvxq_fihaZdhghf_jgh
klbF⇒ d.
Ihemq_ggu_ihke_jZkkfhlj_gby\k_owlZih\^_ckl\byaZdhghf_jghklba ⇒ d, b ⇒ d bc
⇒ d[m^mlbf_lvihke_^h\Zl_evgh\hajZklZxsb_hp_gdbmkeh\guo\_jhylghkl_cLZdbfh[jZ
ahf gZ g_cjhgghf mjh\g_ fu \f_klh ihke_^h\Zl_evghklb a ⇒ b ⇒ c ⇒ d [m^_fbf_lvke_
^mxsmx ihke_^h\Zl_evghklv ]jZnbq_kdh_ ij_^klZ\e_gb_ wlhc ihke_^h\Zl_evghklb ijb\_^_
gh\
F⇒ da → Res(da) ⇒ a ⇒ db → Res(db) ⇒ b ⇒ dc → Res(dc) ⇒ c ⇒ dd → Res(dd) ⇒ d
(1)
]^_a ⇒, b ⇒, c ⇒ -mkeh\gu_k\yab³aZimkdZ´hq_j_^gh]hwlZiZ^_ckl\bc\ujZ[hlZggu_g_c
jhgZfb da,db,dc Klj_edZ → ihke_ ^_ckl\bc da,db,dc,dd hagZqZ_l kh\_jr_gb_ ^_ckl\bc \h
\g_rg_ckj_^_Res(da), Res(db), Res(dc), Res(dd) - h[jZlgu_Znn_j_glZpbb ihklmiZxsb_gZ
\oh^u g_cjhgh\ a,b,c,d ba \g_rg_c \gmlj_gg_c kj_^u b kb]gZebabjmxrb_ h ^hklb]gmlhf
j_amevlZl_^_ckl\bc
DZ`^h_ ^_ckl\b_ da, db,dc,dd \ khhl\_lkl\bb k jbk ih dheeZl_jZeyf i_j_^Z_l k\h_
\ha[m`^_gb_gZ³\oh^´fha]Zbke_^h\Zl_evghfh`ghkqblZlvqlh\ha[m`^_gb_hlfhlhjgh]h
g_cjhgZ da h^gh\j_f_ggh k Zdlb\Zpb_c kZfh]h ^_ckl\by i_j_^Z_l k\h_ \ha[m`^_gb_ gZ \oh^
g_cjhgZ a ^_ckl\b_ db gZ \oh^ g_cjhgZ b ^_ckl\b_ dc gZ \oh^ g_cjhgZ c b ^_ckl\b_ dd gZ
\oh^g_cjhgZ d. AgZqblgZ\oh^ug_cjhgh\j_amevlZlh\a,b,c,d ihklmiblg_lhevdhh[jZlgZy
Znn_j_glZpby Res(da), Res(db), Res(dc), Res(dd) hl j_amevlZlh\ hkms_kl\e_gguo ^_ckl\bc
ihklmiZxsZy ih \g_rg_fm dhglmjm gh b \ha[m`^_gby hl kZfbo ^_ckl\bc da,db,dc,dd ih
klmiZxsZyih\gmlj_gg_fmdhglmjmfha]Z Ihwlhfmko_fZmkeh\gh]hj_ne_dkZij_h[jZ
am_lky\ko_fm
16
FH[kGDFH[kGEFH[kGFFH[kGG
⇓↓
↓⇓
↓⇓
↓⇓
↓⇓
da ⇒ a ⇒ db ⇒ b ⇒ dc ⇒ c ⇒ dd ⇒ d,
⇓⇑ ⇑
⇓⇑ ⇑
⇓⇑ ⇑
⇓⇑ ⇑
Res(da)
Res(db)
Res(dc)
Res(dd)
<== Fha]
(2)
<== <g_rgbcFbj
A^_kv F - fhlb\Zpby ³ba\e_dZxsZy ba iZfylb´ Zdlb\Zpb_c ↓ (kf ih^jh[g__ ^Ze__ \kx p_
ihqdm^_ckl\bcieZg^_ckl\bcih^hklb`_gbxp_ebH[klZgh\hqgZyZnn_j_glZpbyH[kGD,
H[kGE, H[kGF, H[kGG ij_^klZ\ey_l kh[hc fgh`_kl\h \k_o g_h[oh^bfuo mkeh\bc mk
i_rgh]hkh\_jr_gbydZ`^h]hhl^_evgh]h^_ckl\byb^hklb`_gby\blh]_dhg_qgh]hj_amevlZ
lZ\^Zgghch[klZgh\d_ GbdZdh]h^jm]h]h^hihegbl_evgh]hkfukeZh[klZgh\hqgZyZnn_j_g
lZpby g_ bf__l H[klZgh\hqgZy Znn_j_glZpby Z\lhfZlbq_kdb \dexqblky \ aZdhghf_jghklb
FH[kGD⇒ da, DH[kGE⇒ db, EH[kGF ⇒ dc,FH[kGG ⇒ dddZd³kms_kl\_ggZy´
bgnhjfZpbyih\urZxsZymkeh\gmx\_jhylghklvijh]ghaZkfjbkhg_h[oh^bfuomkeh
\byo \hafh`ghklb ³aZimkdZ´ hq_j_^gh]h ^_ckl\by b ihemq_gby khhl\_lkl\mxs_]h wlZigh]h
j_amevlZlZ
DZd\b^ghbako_fu^hklb`_gb_p_ebij_^klZ\ey_lkh[hcihke_^h\Zl_evghklv³[eh
dh\´kfhl^_evguc[ehd\ko_f_dZ`^ucbadhlhjuogZqbgZ_lkybaZdZgqb\Z_lky^\mfy
ihke_^h\Zl_evgufb wlZigufb j_amevlZlZfb JZkkfhljbf kgZqZeZ ijhp_kk h[mq_gby b kh\_j
r_gkl\h\Zgby ^_ckl\bc \gmljb h^gh]h ³[ehdZ´ < ke_^mxsbo jZa^_eZo fu jZkkfhljbf dZd
fh`_l[ulvkms_kl\_gghbaf_g_g\_kvieZg^_ckl\bc
Ij_^klZ\bfko_fmq_j_aaZdhghf_jghklb\ha[m`^Zxsb_khhl\_lkl\mxsb_g_cjhgu
Wlhke_^mxsb_aZdhghf_jghklb\ujZ[Zlu\Z_fu_ko_fhc\ijhp_kk_h[mq_gby
FH[kGD⇒GDD0H[kGE⇒GEE0H[kGF⇒ GFF0H[kGG⇒ dd
H[kGDGF⇒ c
(3)
H[kGDGG⇒ d
H[kGDti)&datiH[kGEti)&dbtiH[kGFti)&dcti&
Res(dati) ⇒ dati+1
Res(dbti)⇒ dbti+1
Res(dcti) ⇒ dcti+1
H[kGGti)&ddti&
Res(ddti) ⇒ ddti+1
H[kGDGD⇒ a
da&Res(da) ⇒ a
H[kGEGE⇒ b
db&Res(db) ⇒ b
dc&Res(dc) ⇒ c
dd&Res(dd) ⇒ d
>Ze__\wlhfbke_^mxs_fjZa^_e_\k_wlbaZdhghf_jghklb[m^mlh[tykg_guHij_^_ebf
kgZqZeZqlhlZdh_gZijbf_j^_ckl\b_dc. >eywlh]haZf_lbfqlh\kykh\hdmighklvh[jZlguo
Znn_j_glZpbc hl j_amevlZlh\ ^_ckl\by dc dhlhjmx h[hagZqbf q_j_a GenRes(dc), ihklmiZ_l
gZ³\oh^´fha]Zg_ij_ju\gh\h\j_f_gbgZqbgZykfhf_glZgZqZeZ^_ckl\bybdhgqZy^hk
lb`_gb_f wlZigh]h j_amevlZlZ c KZfh ^_ckl\b_ dc \ \b^_ \ha[m`^_gby hl^_evgh]h g_cjhgZ
beb ]jmiiu g_cjhgh\ lZd `_ g_ij_ju\gh \h \j_f_gb i_j_^Z_l k\hb \ha[m`^_gby wnn_dlhj
guff_oZgbafZffurpZfhj]ZgZfbl^bh^gh\j_f_gghihdheeZl_jZeyfgZ³\oh^´fha]Z
JZkkfhljbf ih^jh[g__ \aZbfh^_ckl\b_ h[jZlghc Znn_j_glZpbb GenRes(dc) b ^_ckl\by dc \
ijhp_kk_h[mq_gbyQlh[m^_li_j\uf\h\j_f_gbklbfmehfbaGenRes(dc)dhgljhebjmxsbf
ijZ\bevghklv hkms_kl\e_gby ^_ckl\by dc" I_j\uf klbfmehf [m^_l kb]gZebaZpby h lZdhf
i_j\hf j_amevlZl_ kh\_jr_ggh]h ^_ckl\by dhlhjuc g_ \k_]^Z ^hklb]Z_lky ijb kh\_jr_gbb
wlh]h^_ckl\byl_wlhi_j\ucfhf_gl, \dhlhjhf^_ckl\b_fh`_lhldehgblvkyhlaZ^Zg
17
ghc p_eb b \ blh]_ g_ ^hklbqv j_amevlZlZ c ?keb h[jZlgZy Znn_j_glZpby ih^l\_j^bl ijZ
\bevghklv kh\_jr_gby ^_ckl\bylh^_ckl\b_fh`_l[ulvijh^he`_ghKe_^mxs_c h[jZlghc
Znn_j_glZpb_c ba GenRes(dc) dhgljhebjmxs_c ijZ\bevghklv kh\_jr_gby ^_ckl\by [m^_l
h[jZlgZyZnn_j_glZpbyhllZdh]hke_^mxs_]hfhf_glZ^_ckl\bydh]^Zhghkgh\Z\ijbgpbi_
fh`_lhldehgblvkyhlaZ^Zgghcp_ebAZnbdkbjm_ffgh`_kl\hfhf_glh\\j_f_gbWWWN\
dhlhjuo^_ckl\b_ dcti, L N\ijbgpbi_fh`_lhldehgblvkyhlp_ebb\dhlhjuoihemqZ_
fmxh[jZlgmxZnn_j_glZpbxRes(dcti) ke_^m_ldhgljhebjh\ZlvJZah[v_f^_ckl\b_dc gZmqZ
kldb dcti, L N I_j\uc mqZklhd ^_ckl\by aZimkdZ_lky dZd fu agZ_f aZdhghf_jghklvx
EH[kGF ⇒ dct1. Ihke_ihemq_gbyh[jZlghcZnn_j_glZpbbRes(dct1) h[mki_rghfaZ\_jr_
gbbwlh]hi_j\h]hmqZkldZ^_ckl\bydct1, ^_ckl\b_dc fh`_l[ulvijh^he`_ghIjh^he`_gb_
^_ckl\by ³aZimkdZ_lky´ aZdhghf_jghklvx Obc(dc t1)&dct1&Res(dct1) ⇒ dct2. WlZ aZdhghf_j
ghklv [m^_l h[gZjm`_gZ Z\lhfZlbq_kdb ld \k_ mkeh\by ³kms_kl\_ggu´ m^Ze_gb_ dZdh]heb[hmkeh\bykljh]hmf_gvrZ_lmkeh\gmx\_jhylghklvijZ\beZ\g_c^eyijh^he`_gby^_c
kl\by
>Ze__
^_ckl\b_
ijh^he`Z_lky
ih
j_dmj_glguf
aZdhghf_jghklyf
Obc(dcti)&dcti&Res(dcti) ⇒ dcti+1, i = 1,...,k-\dhlhjuo^_ckl\bydcti bdcti+1 fh]mlkh\iZ^Zlv
?keb ^ey g_dhlhjuo ihke_^h\Zl_evguo mqZkldh\ ^_ckl\by dcti,..., dcti+l, i+l ≤ N kh\_jrZ_lky
h^ghblh`_^_ckl\b_dctlhaZdhghf_jghklvijbf_l\b^Obc(dct)&dct& Res(dct) ⇒ dct, l_
^_ckl\b_ dct aZimkdZ_l kZfh k_[y _keb lhevdh h[klZgh\hqgZy b h[jZlgZy Znn_j_glZpbb kih
kh[kl\mxlijh^he`_gbx^_ckl\by. ?keb`_^_ckl\b_gZdZdhf-lhmqZkld_hldehgblvkyhlp_eb
beb[m^_l^hklb]gmldhg_p^_ckl\bydc, lhwlhkjZam`_hljZablkygZh[jZlghcZnn_j_glZpbb
Res, dhlhjZyaZimklbl^jm]mxaZdhghf_jghklvLZdbfh[jZahfh[jZlgZyZnn_j_glZpby[m^_l
kb]gZehf ^ey i_j_oh^Z eb[h d dhfi_gkZlhjguf ^_ckl\byf eb[h d aZimkdm gh\h]h mqZkldZ
^_ckl\by. AZdhghf_jghklb ihke_^h\Zl_evgh]h kh\_jr_gby mqZkldh\ ^_ckl\by h[hagZq_gu gZ
^\mfyjy^hfklhysbfbklj_edZfb⇓⇑<wlbaZdhghf_jghklbij_^klZ\e_gu\y\ghf\b
^_
Dh]^Z^_ckl\b_dc fh`ghkqblZlvaZ\_jr_ggufbqlhlZdh_hl^_evgh_^_ckl\b_"AZdh
ghf_jghkl_c Obc(dcti)&dcti&Res(dcti) ⇒ dcti+1 ^hklZlhqgh ^ey i_j_oh^Z hl h^gh]h mqZkldZ
^_ckl\by d ^jm]hfm Gh dh]^Z lj_[m_lky i_j_clb hl h^gh]h wlZigh]h ^_ckl\by d ^jm]hfm lh
gZ^hmq_klv\kxkh\hdmighklvihemq_gghch[jZlghcZnn_j_glZpbbbhij_^_eblvaZdhgq_gheb
wlZigh_^_ckl\b_bebg_ll_^hklb]gmlg_dhlhjucwlZigucj_amevlZlbebg_l<\_jhylghkl
guol_jfbgZojZa^_e_gb_^_ckl\bcda,db,dc,ddgZwlZiuhagZqZ_lqlhihke_dZ`^h]hbagbo
\ijbgpbi_fh`_lkh\_jrZlvkyfgh`_kl\h^jm]bo^_ckl\bcbihwlhfmij_^kdZaZgb_gZijb
f_j ^_ckl\by db dh]^Z _s_ hkms_kl\e_gh ^_ckl\b_ da \ ijbgpbi_ g_\hafh`gh >_ckl\by
GDGEGFGG ihlhfmb jZa^_e_guqlhhgb g_ij_^kdZau\Zxl^jm]^jm]ZDZdlh]^Zfh`_l
[ulv hkms_kl\e_g i_j_oh^ hl h^gh]h wlZigh]h ^_ckl\by d ^jm]hfm" Ihgylgh qlh h[jZlghc
Znn_j_glZpbb hl ihke_^g_]h mqZkldZ ^_ckl\by Res(dctk) g_ ^hklZlhqgh ^ey hij_^_e_gby aZ
\_jr_gghklb^_ckl\by dc>eygZ^_`gh]hij_^kdZaZgbyaZ\_jr_gghklb^_ckl\by\p_ehfg_
h[oh^bfh agZlv qlh \k_ mqZkldb ^_ckl\by mki_rgh ijhc^_gu l_ ^_ckl\b_ dc =
dct1&dct2&...&dctk \uiheg_gh b h[jZlgZy Znn_j_glZpby Res(dc) = Res(dct1)&Res(dct2)
&...&Res(dctk) hl\k_ofhf_glh\^_ckl\bcihemq_gZDZdfh`_lbkihevah\ZlvkywlZbgnhjfZ
pby^eyi_j_oh^Zdke_^mxs_fm^_ckl\bxdd?
Hlf_lbf ke_^mxsbc h[sbc ijbgpbi hj]ZgbaZpbb ij_^kdZaZgbc hkms_kl\ey_fuc
fha]hf _keb g_\hafh`gh hkms_kl\blv ij_^kdZaZgb_ gZ gbadhf mjh\g_ g_ ^Ze_dh hl
³\oh^Z´ fha]Z ]^_ bgnhjfZpby ^hklZlhqgh ^_lZevgZ b ehdZevgZ), lh ij_^kdZaZgb_ hkms_
kl\ey_lky q_j_a [he__ \ukhdb_ kehb fha]Z jZkiheh`_ggu_ gb`_ gZ jbk 3) hljZ`Zxsb_
bgl_]jZevgu_ b [he__ bg\ZjbZglgu_ kf jZa^ oZjZdl_jbklbdb \g_rg_c kj_^u Ijb
wlhfaZf_lbfqlhlZdZykljmdlmjZij_^kdZaZgbchij_^_ey_lkyg_kljh_gb_ffha]ZZkljmdlm
jhcij_^kdZaZgbc\g_rg_ckj_^udhlhjmxmeZ\eb\Z_lfha]JZkkfhljbfgZijbf_j_^_c
kl\bydcdZdwlhijhbkoh^bl<khhl\_lkl\bbkjbk³ex[hcj_p_ilhjbebdhf[bgZpbyj_p_i
lhjh\fh]ml[ulvk\yaZgukex[ufwnn_dlhjhfbebdhf[bgZpb_cwnn_dlhjh\´IhwlhfmgZ
18
f_kl_ex[h]h³i_j_dexq_gby´gZijbf_jkh³\oh^Z´Obc(dc)&dc&Res(dc)gZ\uoh^udd bd
(d -g_cjhgdhg_qgh]hj_amevlZlZ\k_]^Zkms_kl\mxlg_cjhg c,\ha[m`^Zxsbcky[_amkeh\gh
hl\ha[m`^_gbcObc(dc)&dc&Res(dc) bi_j_^Zxsbcwlh\ha[m`^_gb_gZ\oh^ug_cjhgh\dd
b d. LZd dZd g_cjhg c \ha[m`^Z_lky [_amkeh\gh hl \ha[m`^_gbc Obc(dc)&dc&Res(dc)lhhg
^he`_g gZoh^blvky \ j_r_ld_ dZd jZa ih^ \k_fb g_cjhgZfb Obc(dc)&dc&Res(dc) gZ jbk
gb`_bdZd[ugZf_kl_koh`^_gby\k_o\ha[m`^_gbchlwlbo\ur_klhysbog_cjhgh\Ij_`
^_\k_]haZf_lbf qlhihkdhevdm\ha[m`^_gb_Obc(dc)&dc&Res(dc) g_cjhgZci_j_^Z_lkygZ
\oh^g_cjhgZdbkb]gZebabjm_lh[mki_rghfaZ\_jr_gbbhq_j_^gh]hwlZiZ^_ckl\bclhg_c
jhghf d \ ijhp_kk_ h[mq_gby [m^_l \ujZ[hlZgZ aZdhghf_jghklv c ⇒ d WlZ aZdhghf_jghklv
[m^_lbf_lv[hevrmxhp_gdmmkeh\ghc\_jhylghklbq_faZdhghf_jghklvb ⇒ dhlij_^u^m
s_]hwlZiZ^_ckl\bcbke_^h\Zl_evgh\ha[m`^_gb_g_cjhgZc [m^_l\uau\Zlviheh`bl_evgu_
wfhpbb Wlb iheh`bl_evgu_ wfhpbb [m^ml aZdj_ieylv \_kv ³[ehd´ aZdhghf_jghkl_c ijb\_^
rbodwlhfmwlZighfmj_amevlZlmb\qZklghklbaZdhghf_jghklvObc(dc)&dc& Res(dc) ⇒ c.
G_cjhgc kgZqZeZ[m^_l\ha[m`^Zlvkyk\hbf\oh^hfObc(dc)&dc&Res(dc)[_amkeh\ghghaZ
l_f\ijhp_kk_\ujZ[hldbmkeh\ghck\yabc ⇒ dbihy\e_gbyiheh`bl_evguowfhpbcg_cjhg
c gZqg_l ijbh[j_lZlv k\hckl\Z j_amevlZlZ b h[jZlgZy Znn_j_glZpby Res(dc) gZqg_l h[h]Z
sZlvkymkbeb\Zy aZdhghf_jghklvObc(dc)&dc&Res(dc) ⇒ cdhlhjZyl_i_jvm`_[m^_l³kjZ
[Zlu\Zlv´ g_ ijhklh [_amkeh\gh Z _s_ b k \_jhylghklvx [ebadhc d qlh fu lZd `_ [m^_f
kqblZlv [_amkeh\guf ³kjZ[Zlu\Zgb_f´ g_cjhgZ AZdhghf_jghklv Obc(dc)&dc& Res(dc) ⇒ c,
lZdbf h[jZahf Z\lhfZlbq_kdb \dexqbl \ k_[y \k_ \ha[m`^_gby gZb[he__ ihegh blhqghoZ
jZdl_jbamxsb_ ^hklb`_gb_ wlZigh]h j_amevlZlZ dc b \hafh`ghklv i_j_oh^Z d ke_^mxs_fm
^_ckl\bxMkbeblkyg_lhevdhaZdhghf_jghklvObc(dc)&dc&Res(dc) ⇒ c,ghb\k_aZdhghf_j
ghklb ³[ehdZ´ Obc(dc)&dcti&Res(dcti) ⇒ dcti+1, i = 1,...,k- Mkbe_gb_ wlbo aZdhghf_jghkl_c
[m^_l mlhqgylv h[jZlgu_ Znn_j_glZpbb Res(dcti), i = 1,...,k- dhgljhebjmxsb_ j_amevlZlu
\k_omqZkldh\^_ckl\byGZkZfhf^_e_bf__lf_klh[he__kbevgh_ml\_j`^_gb_
Fha]\k_]^Zklj_fblvky^h[blvkyihegh]hdhgljheygZ^\g_rgbffbjhfbkq_jiu\Zxs_dhgljhebjmy\gmlj_ggbfaZdhghf_jgufdhglmjhfjZ[hlufha]Zkh[ulby\g_r
g_]h dhglmjZ Dh]^Z aZdhghf_jghklb Obc(dcti)&dcti&Res(dcti) ⇒ dcti+1, i = 1,...,k- ihke_ bo
mkbe_gbyiheh`bl_evgufbwfhpbyfbgZqgmlk\_jhylghklvx[ebadhcdg_ij_ju\gh\h\j_
f_gbdhgljhebjh\Zlvh[jZlghcbh[klZgh\hqghcZnn_j_glZpbyfbObc(dcti),Res(dcti), i = 1,...,kkh[ulby\g_rg_ckj_^ulh\gmlj_ggbcdhglmjfha]Z[m^_lagZlv\k_qlh_fmg_h[oh^bfhk
lhqdb aj_gby ij_^kdZaZgby b ^hklb`_gby p_eb h \g_rg_f dhglmj_ l_ h \g_rg_f fbj_
Bf_gghaZkq_lwlh]hbkha^Z_lkylhm^b\bl_evgh_hsms_gb_qlhfu`b\_f\h\g_rg_ffbj_
ohly_klvki_pbZevgu_wdki_jbf_glukgZ^_\Zgb_fbkdZ`ZxsboebgaihdZau\Zxsb_qlhwlh
hsms_gb_y\ey_lkyj_amevlZlhflj_gbjh\db
JZa[b_gb_^_ckl\bygZwlZiu\ijhp_kk_h[mq_gbyijhbkoh^blihkl_i_gghbihklhyggh
DZdm`_]h\hjbehkvi_j\hgZqZevgufwlZihfnhjfbjh\ZgbynmgdpbhgZevguokbkl_fb\lhf
qbke_ wlZiguo j_amevlZlh\ y\ey_lky f_lh^ ³ijh[ b hrb[hd´ b bkke_^h\Zl_evkdZy ^_yl_ev
ghklv?keb\j_amevlZl_lZdhc^_yl_evghklbj_amevlZl[m^_l^hklb]gmllhgZc^_gguckihkh[
^_ckl\byaZdj_iblky\\b^_ihke_^h\Zl_evghklb^_ckl\bcObc(dcti)&dcti&Res(dcti) ⇒ dcti+1, i =
1,...,k-\dhlhjhcg_[m^_lgbdZdbowlZih\H[klZgh\hqghcObc(dcti) bh[jZlghcRes(dcti) Zn
n_j_glZpbyfb\k_oqZkl_c^_ckl\by[m^_l\kyh[klZgh\hqgZybh[jZlgZyZnn_j_glZpbbdhlh
ju_ [ueb ihemq_gu \ khhl\_lkl\mxsb_ fhf_glu \j_f_gb Ijb ih\lhj_gbb wlh]h ^_ckl\by
[m^_lf_gylvkyh[klZgh\dZbh[jZlgZyZnn_j_glZpbyhlmqZkldh\ ^_ckl\byihwlhfm\aZdhgh
f_jghklbObc(dcti)&dcti&Res(dcti) ⇒ dcti+1, i = 1,...,k-gZqg_l\oh^blv[he__lhqgZybg\Zjb
ZglgZy kf jZa^ h[klZgh\hqgZy b h[jZlgZy Znn_j_glZpbb <u^_e_gb_ wlZih\ ^_ckl\bc b
aZdhghf_jghkl_cwlZih\lbiZObc(dc)&dc&Res(dc) ⇒ ck\b^_l_evkl\mxsbohaZ\_jr_gghklb
wlZiZ ^_ckl\by \hafh`gh lhevdh lh]^Z dh]^Z \ j_amevlZl_ hkms_kl\e_gby jZaghh[jZaghc
^_yl_evghklbZg_lhevdh\mkeh\byogZijbf_jh^gh]hbgkljmf_glZevgh]hj_ne_dkZklZg_l
ykghqlhaZ^_ckl\b_fdc fh`_lihke_^h\Zlvfgh`_kl\h^jm]bo^_ckl\bcbagZqblij_^kdZ
19
aZgb_ b Zdlb\Zpby ke_^mxs_]h aZ dc ^_ckl\by ih aZdhghf_jghklyf lbiZ
Obc(dck)&dck&Res(dck) ⇒ ddt1]^_N-ihke_^gbcmqZklhd^_ckl\bydc, hdZ`_lkym`_ijhklh
g_\hafh`gufihlhcijhklhcijbqbg_qlhg_ba\_klghdZdh_^he`gh[ulv^Zevr_^_ckl\b_
Ihwlhfm Zdlb\Zpby ke_^mxs_]h ^_ckl\by [m^_l \hafh`gZ m`_ lhevdh q_j_a aZdhghf_jghklb
lbiZ Obc(dc)&dc& Res(dc) ⇒ kIhgylghqlh_keb\ijhp_kk_kh\_jr_gkl\h\Zgby^_ckl\bc\
b]jZobeb\ijhn_kkbhgZevghc^_yl_evghklb\uykgblvkyqlhbkZfh^_ckl\b_dc _klvdhf[b
gZpbyg_kdhevdbo[he__we_f_glZjguo^_ckl\bcdhlhju_lZd`_ih-jZaghfmfh]mldhf[bgb
jh\Zlvky ijb ^hklb`_gbb jZaguo p_e_c lh ^_ckl\b_ dc lZd `_ Z\lhfZlbq_kdb jZah[v_lky gZ
[he__ f_edb_ wlZiu dc1,...,dclLZd`_dZdb^ey^_ckl\bydc, ^eywlbowlZih\Z\lhfZlbq_kdb
[m^mlgZc^_guaZdhghf_jghklbj_amevlZlh\lbiZObc(dcj)&dcj& Res(dcj) ⇒ cj, j = 1,...,l. Wlh
h[tykgy_ldZdZ\lhfZlbq_kdbnhjfbjmxlkyhl^_evgu_³[ehdb´^_ckl\by (4):
DJWIJWIJFH[kGFDJWIJ DJWIJ-Dhg_qgucWlZiguc
Ijhf_`mlhqguc J_amevlZl
⇑
↓⇓
⇑
... b ⇒
dc
⇒
c...
<== Fha](4)
⇓⇑
⇑
Res(dc)
<== <g_rgbcFbj
]^_WIJwlZigucijhf_`mlhqguc j_amevlZl-^_ckl\b_[he__h[s_]hmjh\gykf^Ze__b
⇒ DJ, c ⇒ DJ -aZdhghf_jghklb \ujZ[hlZggu_g_cjhghfdhg_qgh]hj_amevlZlZDJgZijb
f_jg_cjhghfdWlbaZdhghf_jghklbbf_xl\hajZklZxsb_agZq_gby\_jhylghklbij_^kdZaZ
gby\uau\Zxsb_iheh`bl_evgu_wfhpbbbaZdj_ieyxsb_aZdhghf_jghklb\k_]h[ehdZ?keb
^_ckl\b_dc, \ijhp_kk_kh\_jr_gkl\h\Zgby^_ckl\bcjZah[v_lkygZihke_^h\Zl_evghklv^_c
kl\bc dc1,...,dcl, lh ^hklb`_gb_ ^_ckl\b_f dc k\h_]h j_amevlZlZ c ih aZdhghf_jghklb
Obc(dc)&dc&Res(dc) ⇒ c, c ⇒ d khojZgblk\h_agZq_gb_\lhfblhevdh\lhfkemqZ_dh]^Z
aZdhghf_jghklvc ⇒ d [m^_lbf_lv[hevrmxhp_gdm\_jhylghklbq_faZdhghf_jghklvcl ⇒ d,
³kjZ[hlZ\rZy´ihke_^hklb`_gbyihke_^g_]hwlZigh]hj_amevlZlZObc(dc)&dcl&Res(dcl) ⇒ cl.
Wlh[m^_lijhbkoh^blv\lhfkemqZ_dh]^Z^_ckl\b_cbf__lkZfhklhyl_evgh_agZq_gb_
JZkkfhljbfgZijbf_j^_ckl\b_dc -[_];_]hq_\b^ghy\ey_lkykeh`guf^\b`_gb_f
khklhysbf ba k_jbb [he__ ijhkluo wlZiguo ^_ckl\bc <k_ wlZigu_ ^_ckl\by [_]Z k\yaZgu \
hij_^_e_ggmx ihke_^h\Zl_evghklv \gmljb ^_ckl\by dc Dh]^Z ³[_]´ [m^_l aZ\_jr_g lh ^hk
lb`_gb_ j_amevlZlZ c ih aZdhghf_jghklb c ⇒ d aZdj_ibl wlhl wlZiguc ijhf_`mlhqguc j_
amevlZlb\lhfqbke_\kxihke_^h\Zl_evghklv[he__f_edbowlZiguoj_amevlZlh\ dc1,...,dcl.
Ykgh qlh aZdhghf_jghklv c ⇒ d [m^_l bf_lv [hevrmx hp_gdm \_jhylghklb q_f aZdhghf_j
ghklv cl ⇒ d, \h-i_j\uo ihlhfm qlh ^_ckl\by dc1,...,dcl pbdebq_kdb ih\lhjyxlky \gmljb
^_ckl\byGF -[_]Z\h-\lhjuoihlhfmqlh^eyijZ\bevghchp_gdbaZ\_jr_gghklb³[_]Z´g_
h[oh^bfhhp_gblvijZ\bevghklv\k_cihke_^h\Zl_evghklb^_ckl\bcl_hp_gblv^hklb`_gb_
j_amevlZlZ c ih aZdhghf_jghklb Obc(dc)&dc&Res(dc) ⇒ c, Z g_ ih aZdhghf_jghklb
Obc(dcl)&dcl&Res(dcl) ⇒ clIhwlhfm^ey[he__f_edbowlZiguoj_amevlZlh\ dc1,...,dclgZijb
f_j ih^t_fZ gh]b lheqdZ iju`dZ b l^ wlZiguf j_amevlZlhf \ ³[ehd_´ ijb\h^ysbfd
^hklb`_gbx wlZigh]h ijhf_`mlhqgh]h j_amevlZlZ WIJ \k_]h [ehdZ y\ey_lky g_ kZfuc ih
ke_^gbc dhg_qguc j_amevlZl d - DJ \uau\Zxsbc kZgdpbhgbjmxsmx Znn_j_glZpbx Z lhl
[he__³djmiguc´wlZigucijhf_`mlhqgucj_amevlZl\^ZgghfkemqZ_³[_]´dhlhjuc³k\yau
\Z_l´ \kx ihke_^h\Zl_evghklv [he__ f_edbo wlZiguo j_amevlZlh\ WlZiguc ijhf_`mlhqguc
j_amevlZl c lZd `_ dZd b dhg_qguc j_amevlZl d h[eZ^Z_l kZgdpbhgbjmxsbf ^_ckl\b_f ld
aZdhghf_jghklv c ⇒ d [m^_l \uau\Zlv iheh`bl_evgu_ wfhpbb aZdj_ieyxrb_ aZdhghf_jgh
klbc1 ⇒ c,..., cl ⇒ cGhiheh`bl_evgu_wfhpbbfh]ml\hagbdZlvg_lhevdhihke_aZ\_jr_gby
20
[_]ZWfhpbbdZdbgl_]jZevgZyhp_gdZmki_rghklb^_ckl\bc-ijb[eb`_gbydp_ebiheh`b
l_evgZywfhpbybebm^Ze_gbyhlp_ebhljbpZl_evgZywfhpbyklj_fylkylZd`_g_ij_ju\gh
\h \j_f_gb dhgljhebjh\Zlv ^hklb`_gb_ p_eb Ihkdhevdm dZ`^h_ ba we_f_glZjguo ^_ckl
\bc dc1,...,dcl _keb hgh ohlv kdhevdh-gb[m^v agZqbfh ijb[eb`Z_l p_ev gZijbf_j \ kemqZ_
dh]^Zh[klZgh\hqgZyZnn_j_glZpbyObc(dci) ^_ckl\bydcik\yaZgZkij_h^he_gb_fg_ijhklh]h
ij_iylkl\byyfZdZf_gvij_]jZ^Zbl^bdh]^Zhp_gdZ\_jhylghklb^hklb`_gbyj_amevlZlZ
ihaZdhghf_jghklbObc(dci)&dci&Res(dci) ⇒ ci^eywlh]hij_iylkl\byf_gvr__^bgbpulh]^Z
ij_h^he_gb_ ij_iylkl\by \uah\_l iheh`bl_evgu_ wfhpbb aZdj_ieyxsb_ g_cjhgu \uihe
gb\rb_^_ckl\b_dci, bg_cjhgci. Ihwlhfm[m^ml\ujZ[hlZgug_lhevdhaZdhghf_jghklbc1 ⇒ c
,..., cl ⇒ c, ij_^kdZau\Zxsb_kh\k_[hevr_c\_jhylghklvx^hklb`bfhklvwlZigh]hijhf_`m
lhqgh]hj_amevlZlZc, ghbaZdhghf_jghklbc1&dc ⇒ DJFl&dc ⇒ DJij_^kdZau\Zxsb_
m\_ebq_gb_\_jhylghklb^hklb`bfhklbdhg_qgh]hj_amevlZlZDJihke_hkms_kl\e_gby[he__
f_edbo wlZiguo ^_ckl\bc c1,...,cl, hkms_kl\ey_fuo \ dhgl_dkl_ [he__ djmigh]h wlZigh]h
ijhf_`mlhqgh]h^_ckl\byGF kj_amevlZlhfc. Ihwlhfm\ko_f_ij_^kdZau\Z_fufdhg_q
gufj_amevlZlhfy\ey_lkyg_lhevdhwlZigucijhf_`mlhqgucj_amevlZlWIJghbdhg_qguc
j_amevlZlDJ.
<uiheg_gb_ke_^mxs_]h^_ckl\bydci+1g_fh`_l[ulvaZims_ghg_cjhghfcildg_c
jhgcig_fh`_lagZlvbke_^h\Zl_evghij_^kdZaZlvdZdhc[m^_lke_^mxsbcmqZklhd^_ckl\by
LZdh_ ij_^kdZaZgb_ \hafh`gh lhevdh _keb agZlv qlh \k_ ^_ckl\by dc1,...,dcl \uihegyxlky \
dhgl_dkl_ g_dhlhjh]h [he__ djmigh]h ^_ckl\by dc - [_] Ihwlhfm ³aZimkd´ ^_ckl\by dci+1
^he`_g[ulvhkms_kl\e_gaZdhghf_jghklvxdc&ci ⇒ dci+1hagZqZxs_cqlh\dhgl_dkl_^_c
kl\by dc ^hklb`_gb_ j_amevlZlZ ^ey mqZkldZ ^_ckl\by ci ij_^kdZau\Z_l b \ha[m`^Z_l gZqZeh
ke_^mxs_]hmqZkldZ^_ckl\by dci+1.>_ckl\b_[he__h[s_]hmjh\gyWIJ\wlhb_klv\^Zg
ghfkemqZ_^_ckl\b_dc.
FuhibkZebdZdZ\lhfZlbq_kdbkljhblkyb_jZjoby^_ckl\bc\ijhp_kk_h[mq_gbyb
dZdbfbaZdhghf_jghklyfbb\ha[m`^_gbyfbwlb^_ckl\by\uihegyxlkyGhgZkZfhf\_jog_f
mjh\g_ hj]ZgbaZpbb ^_ckl\bc fu\k_jZ\ghg_agZ_fdZdbfbaZdhghf_jghklyfb^he`ghhkm
s_kl\eylvkyi_j_dexq_gb_kh^gh]h^_ckl\bygZ^jm]h_ldjZagu_wlZiu^_ckl\byg_ij_^
kdZau\Zxl ^jm] ^jm]Z Hj]ZgbaZpby ^_ckl\bc gZ kZfhf \_jog_f mjh\g_ m`_ g_ fh`_l
[ulvhj]Zgbah\ZgZaZdhghf_jghklyfb, ldaZ\bkblg_hlkljmdlmjuij_^kdZaZgbc\g_r
g_ckj_^uZhlp_e_c^hklb]Z_fuohj]ZgbafhfLZddZdp_evklZ\blkyfhlb\Zpbhgguf\ha
[m`^_gb_f><bly_\@lhhgZy\ey_lkykm]m[h\gmlj_gg_cihklZgh\dhc^eyhj]ZgbafZp_eb
H^gZdhihke_ihklZgh\dbp_ebhp_gdZ\_jhylghklb__^hklb`_gbyfh`_l[ulvhkms_kl\e_gZ
ihh[gZjm`_ggufaZdhghf_jghklyfqlhbhkms_kl\ey_lkyi_j_dexqZxs_cnmgdpb_cwfh
pbc gZklZ^bbijbgylbyj_r_gbcGZkZfhf\_jog_fmjh\g_hj]ZgbaZpbb^_ckl\bchgbhj
]ZgbamxlkygZklZ^bbijbgylbyj_r_gbc]^_hgbij_^klZ\eyxlkh[hcdZdijZ\behebg_cgmx
ihke_^h\Zl_evghklvhl^_evguo³[ehdh\´^_ckl\bcLZddZd\wlhcihke_^h\Zl_evghklb^_ckl
\bchp_gdZ\_jhylghklbij_^kdZaZgbydhg_qgh]hj_amevlZlZ\k_]^Zkljh]h\hajZklZ_llhijb
gylb_ j_r_gbc ij_^klZ\ey_l kh[hc k\h_h[jZaguc k_fZglbq_kdbc ³[ehqguc´ \_jhylgh
klguc\u\h^gZbemqr_]hieZgZ^_ckl\bykf[he__ih^jh[gh^Ze__<j_amevlZl_ihemqZ
_lkylZihke_^h\Zl_evghklvbb_jZjobyj_amevlZlh\dhlhjZyhibkZgZ\L_hjbbnmgdpbhgZev
guokbkl_fAZf_lbfqlhwlmihke_^h\Zl_evghklvbb_jZjobxj_amevlZlh\dhlhjZyZ\lhfZlb
q_kdbmlhqgy_lkybkh\_jr_gkl\m_lky\ijhp_kk_^_yl_evghklbfu\u\_ebbaZgZebaZkljmd
lmju ij_^kdZaZgbc kh[ulbc \h \g_rg_c kj_^_ dhlhju_ meZ\eb\Zxlky aZdhghf_jghklyfb ba
{PRFJW`Ko_fulZdbfh[jZahf^ZxlgZfkljmdlmjmbijhp_kknmgdpbhgbjh
\ZgbynhjfZevghcfh^_ebjZ[hlufha]Zhkgh\ZgghcgZijbgpbi_ij_^kdZaZgby
H[tykgbfl_i_jvdZdfh`_lkh\_jr_gkl\h\Zlvky^_yl_evghklv\gmljbhl^_evgh]h³[ehdZ´ ^_ckl\bc <ijhp_kk_b]jbeb ijhn_kkbhgZevghc^_yl_evghklbihke_^h\Zl_evghklvmqZ
kldh\^_ckl\bcbkhhl\_lkl\mxsb_h[jZlgu_Znn_j_glZpbbObc(dc)& dcti&Res(dcti) ⇒ dcti+1,
i = 1,...,k-fh]ml\Zjvbjh\Zlvky?kebihke_lZdbo\ZjbZpbcj_amevlZlc g_[m^_l^hklb]gmllh
21
\hagbdg_lhjb_glbjh\hqgh-bkke_^h\Zl_evkdZyj_ZdpbybhljbpZl_evgu_wfhpbbdhlhju_ih
gbaylhp_gdb\_jhylghklb\k_o³kjZ[hlZ\rbo´aZdhghf_jghkl_cb\ke_^mxsbcjZawlbaZdh
ghf_jghklb\jy^eb[m^mlZdlb\babjh\ZguDZdba\_klghhjb_glbjh\hqgh-bkke_^h\Zl_evkdZy
j_Zdpby \hagbdZ_l \kydbc jZa dh]^Z h`b^Z_fuc Zdp_ilhjhf j_amevlZlh\ ^_ckl\by j_amevlZl
g_ ^hklb]gml Ij_^iheh`bf qlh \ ijhp_kk_ b]ju gZc^_gu lZdb_ \ZjbZpbb dc’ ^_ckl\by dc,
dhlhju_ ih khhl\_lkl\mxsbf aZdhghf_jghklyf Obc(dc’ti)&dc’ti&Res(dc’ti) ⇒ dc’ti+1, i =
1,...,k’- [m^ml ijb\h^blv d ^hklb`_gbx lZdbo j_amevlZlh\ c’, qlh ihke_ hkms_kl\e_gby hk
lZevguo ^_ckl\bc hgb lZd `_ [m^ml ijb\h^blv d dhg_qghfm j_amevlZlm < wlhf kemqZ_ wlb
\ZjbZpbb[m^mlaZdj_ie_gu?kebihke_g_h^ghdjZlgh]hijbf_g_gby\ZjbZpbcdc’ bihemq_
gbydhg_qgh]hj_amevlZlZhdZ`_lkyqlh ihke_^hklb`_gbyj_amevlZlZc’ dhg_qgucj_amevlZl
^hklb]Z_lky k [hevr_c \_jhylghklvx ih aZdhghf_jghklb c’ ⇒ d, q_f ihke_ j_amevlZlZ c ih
aZdhghf_jghklb c ⇒ d, lh \k_ aZdhghf_jghklb ³[ehdZ´ ijb\h^ysb_ d j_amevlZlm c’ klZgml
bf_lv [hevrmx hp_gdm mkeh\ghc \_jhylghklb LZd dZd aZdhghf_jghklb bf_xsb_ [hevrmx
hp_gdm mkeh\ghc \_jhylghklb kjZ[Zlu\Zxl [uklj__ lh aZimkd ^_ckl\by dc’ [m^_l kjZ[Zlu
\Zlv[uklj__ih\j_f_gbq_faZimkd^_ckl\bydc. :dlb\babjh\Z\rbkv^_ckl\b_dc’ \ulhjfh
abl lhjfhagufb aZdhghf_jghklyfb \k_ g_ kh\f_klbfu_ k gbf ^_ckl\by Lhjfhagu_ aZdhgh
f_jghklbbf_xllhqghlZdmx`_ijbjh^mqlhb\ha[m`^Zxsb_gh^eyijhklhlufubojZk
kfZljb\Zlvg_[m^_fIhwlhfmfha]Z\lhfZlbq_kdbi_j_dexqblkygZaZimkd[he__wnn_d
lb\gh]h^_ckl\byGF¶
5.3. H[tykg_gb_ p_e_gZijZ\e_gghc ^_yl_evghklb \ L_hjbb nmgdpbhgZevguo kbk
l_fJZkkfhljbfbh[tykgbfgZhkgh\_ko_fihke_^h\Zl_evgh\k_klZ^bbhj]ZgbaZ
pbbp_e_gZijZ\e_ggh]hih\_^_gby\khhl\_lkl\bbkL_hjb_cnmgdpbhgZevguokbkl_fbBg
nhjfZpbhgghcl_hjb_cwfhpbcZlZd`_g_dhlhju_baijhpblbjh\Zgguo\ur_k\hckl\Zdp_i
lhjZj_amevlZlh\^_ckl\by
:nn_j_glguckbgl_a><bly_\@hkms_kl\ey_lkyZdlb\Zpb_c↓ fhlb\Zpb_cFjZaebq
guoihke_^h\Zl_evghkl_c^_ckl\bcda,db,dc,ddba\e_dZ_fuofhlb\Zpb_cbaiZfylbDZd\b^
ghbako_fbijbwlhfZ\lhfZlbq_kdbmqblu\Z_lky\kyh[klZgh\hqgZyZnn_j_glZpbyb
kZfZfhlb\ZpbydZdklbfme³Ba\e_q_gb_baiZfylb´wlhg_\ha[m`^_gb_^_ckl\bcZlZdZybo
Zdlb\ZpbydhlhjZyijhba\h^blkylhevdhfhlb\Zpbhgguf\ha[m`^_gb_f\\b^m_]hobfbq_kdhc
ki_pbnbqghklb b k\h_h[jZaghc ³iZqdhh[jZaghc´ Zdlb\ghklb ³>hfbgbjmxsZy fhlb\Zpby
hljZ`Z_lky\oZjZdl_jghfjZkij_^_e_gbbf_`bfimevkguobgl_j\Zeh\\g_cjhgZojZaebqguo
hl^_eh\ fha]Z JZkij_^_e_gb_ f_`bfimevkguo bgl_j\Zeh\ ghkbl oZjZdl_j ki_pbnbq_kdbc
^ey jZaebqgh]h [bheh]bq_kdh]h dZq_kl\Z fhlb\Zpbc´ >Km^Zdh\ K @ ³LZdbf h[jZahf
iZqdhh[jZagZyjblfbdZp_gljZevguog_cjhgh\\mkeh\byo^hfbgbjmxs_]hibs_\h]hfhlb
\Zpbhggh]h \ha[m`^_gby hljZ`Z_l ijhp_kku h`b^Zgby ibs_\h]h ih^dj_ie_gby´ >Km^Zdh\
[email protected] LZdZy Zdlb\ghklv _klv dZd [u ³\hh[jZ`_gb_´ iha\heyxs__ fhlb\Zpbb ih bf_x
sbfky aZdhghf_jghklyf nhjfbjh\Zlv dhgdj_lgmx p_ev Zdp_ilhj j_amevlZlh\ ^_ckl\bc b
ieZg ^_ckl\bc Ihemq_gb_ j_Zevguo, Z g_ \ “\hh[jZ`_gbb´ j_amevlZlh\ kjZam `_ kgbfZ_l
ki_pbnbq_kdmx Zdlb\Zpbx ↓ fhlb\Zpb_c wlbo j_amevlZlh\ ³m^Zehkv h[t_dlb\ghaZnbdkbjh
\Zlv ijhp_kkh`b^ZgbyiZjZf_ljh\ibs_\h]hih^dj_ie_gbybke_^h\Zl_evghijyfhhlg_klb
bodZiiZjZlmZdp_ilhjZj_amevlZlh\^_ckl\byLZdbfbhdZaZebkvg_cjhgudhlhju_m]heh^
guo `b\hlguo ijhy\eyxl \ujZ`_ggmx iZqdhh[jZagmx Zdlb\ghklv ;ueh mklZgh\e_gh qlh
ijZdlbq_kdb\k_g_cjhguklZdhcnhjfhc Zdlb\ghklbg_f_^e_gghi_j_oh^ylgZj_]meyjgmx
jZajy^gmx^_yl_evghklvdZdlhevdh`b\hlgu_m^h\e_l\hjyxlk\hx^hfbgbjmxsmxibs_
\mxihlj_[ghklvIjbq_f[uehhlf_q_ghqlhdh]^Z]heh^gh_`b\hlgh_\b^blibsmiZqdh
h[jZagZyZdlb\ghklvaZf_gy_lkygZj_]meyjgmxij_bfms_kl\_gghmg_cjhgh\ajbl_evghch[
eZklbdhjufha]Zijb\\_^_gbbibsb\jhlh\mxihehklv-mg_cjhgh\lZeZfbq_kdhch[eZklb
ijbihklmie_gbbibsb\`_em^hd-mg_cjhgh\]bihlZeZfbq_kdhch[eZklbijb\\_^_gbb]ex
dhau\djh\v-mg_cjhgh\kl\heZfha]Z´>Km^Zdh\[email protected]_f\b^ghqlh\k_
22
wlZiu Znn_j_glgh]h kbgl_aZ - fhlb\Zpby iZfylv h[klZgh\hqgZy b imkdh\Zy Znn_j_glZpbb
_kl_kl\_ggufh[jZahfkeb\Zxlky
IeZg^_ckl\bcFhlb\Zpby³ba\e_dZ_lbaiZfylb´g_ijhklhihke_^h\Zl_evghklb^_ckl
\bc da,db,dc,dd Z ieZgu ^_ckl\bc \uiheg_gb_ dhlhjuo ijb\h^beh jZgvr_ d ^hklb`_gbx
p_eb >Ze__ gZ klZ^bb ijbgylby j_r_gbc ba \k_o ³ba\e_q_gguo ba iZfylb´ ieZgh\ ^_ckl\bc
[m^_l\u[jZgh^bgieZgIhkdhevdmieZg^_ckl\bc³ba\e_dZ_lkybaiZfylb´^h\kydbo^_ckl
\bc lh Zdlb\Zpby aZdhghf_jghkl_c ieZgZ fh`_l hkms_kl\eylvky lhevdh \ ³\hh[jZ`_gbb´
;he__ lhqgh ieZg ^_ckl\bcij_^klZ\ey_l kh[hc ihke_^h\Zl_evghklvaZdhghf_jghkl_c dh
lhju_Zdlb\bjmxlky\³\hh[jZ`_gbb´ih\gmlj_gg_fmdhglmjmjZ[hlufha]Zh[hagZq_gghfm
gZklj_edhc→<wlZihke_^h\Zl_evghklvij_^klZ\e_gZkj_^g_cp_ihqdhcda ⇒ a ⇒ db
⇒ b ⇒ dc ⇒ c ⇒ dd ⇒ d. Ihwlhcp_ihqd_ijhbkoh^bl³hi_j_`_gb_oh^Zkh[ulbc\hlgh
r_gbyof_`^mhj]Zgbafhfb\g_rgbffbjhf´WlZp_ihqdZij_^klZ\ey_lkh[hcihke_^h\Z
l_evgh³kjZ[Zlu\Zxsb_´\³\hh[jZ`_gbb´aZdhghf_jghklbkf
(5)
Obc(da)&da&Res(da) ⇒ a, Obc(db)&db& Res(db) ⇒ b, Obc(dc)&dc&Res(dc) ⇒ c,
Obc(dd)&dd&Res(dd) ⇒ d.
³KjZ[Zlu\Zgb_´\³\hh[jZ`_gbb´hagZqZ_li_j_^ZqmwlbfbaZdhghf_jghklyfbiZqdhh[jZaghc
Zdlb\ghklbghg_j_]meyjgh_\ha[m`^_gb_i_j_oh^gZdhlhjh_hkms_kl\ey_lkylhevdhihke_
ihemq_gby j_Zevguo j_amevlZlh\ b [_amkeh\gh]h bo kjZ[Zlu\Zgby Qlh agZqbl ³kjZ[Zlu\Zgb_´\³\hh[jZ`_gbb´gZijbf_jaZdhghf_jghklbObc(da)&da& Res(da) ⇒ aijbhlkmlkl\bb
j_amevlZlZRes(da)"LZdh_³kjZ[Zlu\Zgb_´hkms_kl\ey_lkyih[he__keZ[ufaZdhghf_jghklyf
kf
(6)
Obc(da)&da ⇒ a, Obc(db)&db ⇒ b, Obc(dc)&dc ⇒ c, Obc(dd)&dd ⇒ d,
dhlhju_\khhl\_lkl\bbknhjfZevghcfh^_evxg_cjhgZbk_fZglbq_kdbf\_jhylghklguf\u
\h^hfjbklZd`_h[gZjm`b\Zxlkyg_cjhgZfba, b, c, dGh³kjZ[Zlu\Zgb_´g_cjhgh\a, b, c,
d ih aZdhghf_jghklyf g_ hagZqZ_l qlh g_ [m^ml h`b^Zlvky h[jZlgu_ Znn_j_glZpbb
Res(da), Res(db), Res(dc), Res(dd) hl j_amevlZlh\ ^_ckl\bc \dexq_ggu_ \ [he__ ³lhqgu_´
aZdhghf_jghklbl_o`_kZfuog_cjhgh\a, b, c, d.;he__³lhqgZy´aZdhghf_jghklv\dexqZ_l
\k_[yf_g__³lhqgmx´dZdgZijbf_jaZdhghf_jghklvObc(da)&da& Res(da) ⇒ a \dexqZ_l\
k_[yaZdhghf_jghklvObc(da)&da ⇒ a;he__³lhqgZy´aZdhghf_jghklvjZkiheh`_gZgZlhc`_
\_ld_ k_fZglbq_kdh]h ]jZnZ jbk qlh b f_g__ lhqgZy b agZqbl _keb g_cjhghf h[gZjm`_gZ
[he__³lhqgZy´aZdhghf_jghklvlh\k_]^Zh[gZjm`_gZbf_g__³lhqgZy´;he__³lhqgZy´aZdh
ghf_jghklv\k_]^Zbf__lkljh]h[hevrmxhp_gdmij_^kdZaZgbyb\wlhfkfuke_mlhqgy_l[h
e__ keZ[mx aZdhghf_jghklv ³KjZ[Zlu\Zgb_´ f_g__ ³lhqghc´ aZdhghf_jghklb ijb gZebqbb
[he__³lhqghc´\k_]^ZhagZqZ_lqlh\[hevrbgkl\_kemqZ_\\ijhrehfq_j_adZdhc-lhfhf_gl
\j_f_gb ijboh^beZ gZ ³\oh^´ g_cjhgZ b ³mlhqgyxsZy´ bgnhjfZpby iha\heyxsZy ³kjZ[h
lZlv´ b [he__ lhqghc aZdhghf_jghklb b l_f kZfuf k^_eZlv [he__ lhqgh_ ij_^kdZaZgb_ dZd
wlZigh]h lZd b dhg_qgh]h j_amevlZlZ \ ijhlb\ghf kemqZ_ [he__ ³lhqgZy´ aZdhghf_jghklv g_
kfh]eZ[u[ulvh[gZjm`_gZgZhkgh\Zgbbijhreh]hhiulZIhwlhfmg_kfhljygZ³kjZ[Zlu
\Zgb_´f_g__lhqghcaZdhghf_jghklbg_cjhgh`b^Z_lihklmie_gb_mlhqgyxs_cbgnhjfZpbb
?]hh`b^Zgb_khklhbl\lhfqlhhg]hlh\g_f_^e_gghkf_gvrbfeZl_glgufi_jbh^hfkjZ
[Zlu\Zgbyg_cjhgZ\\b^m[he__\ukhdhc\_jhylghklbwlhcaZdhghf_jghklb³kjZ[hlZlv´m\_
ebqblvqZklhlmbfimevkZpbc\khhl\_lkl\bbkm\_ebq_gb_f\_jhylghklbij_^kdZaZgbyih[h
e__³kbevghc´aZdhghf_jghklbGhdZd[uehh[tykg_ghjZg__aZdhghf_jghklbg_ijhklh
y\eyxlky[he__³lhqgufb´Zkb]gZebabjmxl[_amkeh\ghk\_jhylghklvx[ebadhcdbebih
[_amkeh\ghfm klbfmem h nZdlbq_kdhf ^hklb`_gbb j_amevlZlZ qlh kgbfZ_l ³iZqdhh[jZagmx´Zdlb\ghklvbi_j_\h^blg_cjhggZj_]meyjgmxZdlb\ghklvl_fkZfufjZaebqZy “\hh[
jZ`_gb_” bnZdlIhdZ`_h[jZlgu_Znn_j_glZpbbhlj_amevlZlh\g_ihemq_gu³iZqdhh[jZagZy´Zdlb\ghklvfhlb\Zpbbi_j_\h^blg_cjhgua, b, c, d \khklhygb_h`b^Zgbywlboj_amevlZ
lh\ldj_]meyjghcZdlb\ghklvx[_amkeh\ghcwlbg_cjhgu³kjZ[hlZlv´g_fh]mlihlhcijb
23
qbg_ qlh mkeh\by wlbo aZdhghf_jghkl_c g_ \uiheg_gu \ kbem lh]h qlh h^gh ba mkeh\bc
Res(da), Res(db), Res(dc), Res(dd) g_\uiheg_ghIhwlhfmg_cjhgua, b, c, dkh^ghcklhjhgu
i_j_^Zxl iZqdhh[jZagmx Zdlb\ghklv \ ³\hh[jZ`_gbb´ ih aZdhghf_jghklyf Z k ^jm]hc
klhjhgu h`b^Zxl h[jZlgmx Znn_j_glZpbx Res(da), Res(db), Res(dc), Res(dd), lj_[m_fmx
[he__kbevgufbaZdhghf_jghklyfbkjZ[Zlu\Zxsbfb[_amkeh\ghihke_q_]hhgbi_j_oh
^yl \ j_]meyjgmx Zdlb\ghklv:dlb\Zpby\ ³\hh[jZ`_gbb´j_amevlZlh\a, b, c, d, Zdlb\bjm_l
ke_^mxsb_^_ckl\byihp_ihqd_aZdhghf_jghkl_c L_fkZfuf\³\hh[jZ`_gbb´Zdlb\bab
jm_lky\_kvieZg^_ckl\bcwnn_dlb\ghklvdhlhjh]h\p_ehfhp_gb\Z_lkygZke_^mxs_fwlZ
i_-wlZi_ijbgylbyj_r_gbc
Ijbgylb_ j_r_gbc hkms_kl\ey_lky ijb jZkkfhlj_gbb ieZgZ ^_ckl\bc k mq_lhf i_j_
dexqZxs_c nmgdpbb wfhpbc l_ gZ hkgh\Zgbb dZq_kl\Z \hagbdr_c wfhpbb b \_jhylghklb
ijh]ghaZ^hklb`_gbyp_ebih^ZgghfmieZgm<_jhylghklvijh]ghaZhp_gb\Z_lkyg_ihieZgm
DZd [ueh kdZaZgh ijbgpbibZevgh g_ kms_kl\m_l ohjhrbo f_lh^h\ i_j_kq_lZ \_jhylgh
kl_c ij_^kdZaZgby ³\^h]hgdm´ eh]bq_kdhfm \u\h^m dhlhjuc ij_^klZ\e_g a^_kv ieZghf Fha]³h[oh^bl´ex[hceh]bq_kdbc\u\h^gZoh^y\k_]hh^gm\_jhylghklgmxaZdhghf_jghklv
ij_^kdZau\Zxsmx dhg_qguc j_amevlZl LZdhc aZdhghf_jghklvx \ ^Zgghf kemqZ_ y\ey_lky
aZdhghf_jghklv
(7)
0GDH[kGDGEH[kGEGFH[kGFGGH[kGG ⇒ d,
\ujZ[hlZggZyg_cjhghfdIhwlhfm\_jhylghklv^hklb`bfhklbdhg_qgh]hj_amevlZlZihieZ
gm hp_gb\Z_lky aZdhghf_jghklvx mqblu\Z_fhc wfhpbyfb Wlh g_ hagZqZ_l qlh ieZg g_
³ijhb]ju\Z_lky´\³\hh[jZ`_gbb´>ey³ijhb]ju\Zgby´ieZgh\^_ckl\bc^hklZlhqgh\³\hh[
jZ`_gbb´fh^_ebjmygZijbf_jf_lh^³ijh[bhrb[hd´\u[jZlvg_dhlhjmxihke_^h\Zl_ev
ghklv ^_ckl\bc da,db,dc,dd, ih dhlhjhc _keb ³ijhb]jZlv´ aZdhghf_jghklyfb ihke_^h\Z
l_evghklvihemqZ_fuowlZiguoj_amevlZlh\lhwlb^_ckl\by\h-i_j\uoijb\_^mld^hklb`_
gbx dhg_qgh]hj_amevlZlZZ\h-\lhjuoihaZdhghf_jghklyf^Z^ml^hklZlhqghohjhrmx
hp_gdm ij_^kdZaZgby ^hklb`bfhklb wlh]h j_amevlZlZ IeZg ^he`_g ijhb]ju\Zlvky k p_evx
h[_ki_q_gby kh]eZkh\Zgghklb \k_o ^_ckl\bc b h[_ki_q_gby _]h g_ijhlb\hj_qb\hklb ld
_klv_s_lhjfhagu_aZdhghf_jghklbLZdbfh[jZahfieZgfh`_l[ulvhp_g_gwfhpbyfbih
dZq_kl\mfhlb\ZpbbbaZdhghf_jghklb^Zxs_c\_jhylghklgmxhp_gdmieZgZGh^eyihe
ghcj_ZebaZpbbi_j_dexqZxs_cnmgdpbbwfhpbc\ijhp_kk_ijbgylbyj_r_gbcg_h[oh^bfh
^himklblv \hafh`ghklvijhba\hevghc \ZjbZpbbieZgZ\ ³\hh[jZ`_gbb´ Wlhhkms_kl\ey_lky
fha]hfdZdk\h_h[jZaguc³[ehqguc´k_fZglbq_kdbc\_jhylghklguc\u\h^
JZkkfhljbf[he__ih^jh[ghdZdfha]hkms_kl\ey_l³[ehqguc´k_fZglbq_kdbc\_jhylgh
klguc\u\h^Wlhh^gh\j_f_gghh[tykgbldZdkh\_jr_gkl\m_lkyieZg^_ckl\bc (3) \
p_ehfiml_f_]hehdZevguobbeb]eh[Zevguobaf_g_gbcWlhijhbkoh^ylaZkq_lbaf_g_
gbc\u\h^Ziml_f\ZjbZpbbieZgZ^_ckl\bc\khhl\_lkl\bbki_j_dexqZxs_cnmgdpb
_cwfhpbcIjbgylb_j_r_gbykhklhbl\lhfqlhijb^Zgghcfhlb\ZpbbFbkhijh\h`^Zx
s_c__hljbpZl_evghcwfhpbbfha]klj_fblkygZclblZdhcieZg^_ckl\bcdhlhjuc^Z\Ze[u
fZdkbfZevgmxiheh`bl_evgmxwfhpbx-ij_^\hkobs_gb_^hklb`_gbyj_amevlZlZhij_
^_e_ggh]hdZq_kl\ZkfZdkbfZevghchp_gdhc\_jhylghklb^hklb`bfhklbwlh]hj_amevlZ
lZ AZ kq_l Zdlb\bjmxs_]h ^_ckl\by fhlb\Zpbb F fha] \ ³\hh[jZ`_gbb´ fh`_l ³ijhb]ju
\Zlv´jZaebqgu_\ZjbZglu^hklb`_gbyp_ebIjbwlhf\k_g_h[oh^bfu_^ey^hklb`_gbydh
g_qghcp_ebwlZigu_j_amevlZlukljh]hm\_ebqb\Zxsb_\_jhylghklv^hklb`_gbydhg_qgh]h
j_amevlZlZ \dexqZxlky \ j_amevlbjmxsbc ieZg ^_ckl\bc Ihwlhfm ijbgylb_ j_r_gbc b
_klv ijhp_kk hj]ZgbaZpbb k_fZglbq_kdh]h ³[ehqgh]h´ \_jhylghklgh]h \u\h^Z (2),(3),
hkms_kl\ey_fh]h fha]hf ³Ijhb]ju\Zy´ jZaebqgu_ ieZgu ^_ckl\bc fha] ijhb]ju\Z_l l_f
kZfuf jZaebqgu_ k_fZglbq_kdb_ \_jhylghklgu_ \u\h^u iulZykv gZclb lZdhc dhlhjuc [u
h[_ki_qbe dZd lj_[m_fh_ dZq_kl\h p_eb lZd b fZdkbfZevgmx hp_gdm \_jhylghklb ij_^kdZaZgbyLZdbfh[jZahfwfhpbbdZdbgl_]jZevgu_hp_gdbj_r_gbcy\eyxlky\lh`_\j_fy
l_fb hp_gdZfb dhlhju_ hj]Zgbamxl k_fZglbq_kdbc \_jhylghklguc \u\h^ dZd hl^_ev
24
guo g_cjhgh\ iml_f ih^dj_ie_gby kf jbk lZd b fha]Z \ p_ehf gZoh^y gZbemqrbc
³[ehqguc´k_fZglbq_kdbc\_jhylghklguc\u\h^. G_cjhghj]Zgbam_lk_fZglbq_kdbc\u\h^
iml_fihkljh_gby³mlhqgyxs_]h´]jZnZjbkZfha]iml_fhj]ZgbaZpbb³[ehqgh]h´
\_jhylghklgh]h \u\h^Z P_ihqdZ ij_^kdZaZgbc hlebqZ_lky hl ³mlhqgyxs_]h´
]jZnZ \h-i_j\uo l_f qlh hgZ ebg_cgZ \ kbem ebg_cghklb ihke_^h\Zl_evghklb ^_ckl\bc Z
\h-\lhjuol_fqlhhgZk\yaZgZk^_yl_evghklvx\h\g_rg_ckj_^_^_ckl\by\dhlhjhcgZ^h
h^gh\j_f_ggh ij_^\hkobsZlv b dhgljhebjh\Zlv Gh p_ev jZ[hlu hl^_evgh]h g_cjhgZ b
fha]Z\p_ehf h^gZ blZ `_-hj]ZgbaZpbyk_fZglbq_kdh]h\_jhylghklgh]h\u\h^Zkp_
evx^hklb`_gbyfZdkbfZevghclhqghklbij_^kdZaZgby.
Dhgdj_lgZy p_ev><bly_\@klZ\blkyZdlb\Zpb_c ↓ fhlb\Zpb_cFihke_^h\Zl_evgh
klb^_ckl\bcda,db,dc,dd,\u[jZgghc\ijhp_kk_ijbgylbyj_r_gby DZdm`_]h\hjbehkvwlZ
Zdlb\Zpby\³\hh[jZ`_gbb´i_j_^Z_lky\k_fg_cjhgZfj_amevlZlh\a, b, c, dihaZdhghf_jgh
klyfLZddZdj_amevlZluRes(da), Res(db), Res(dc), Res(dd) ^_ckl\bc_s_g_ihemq_gulh
g_cjhguj_amevlZlh\a, b, c, d i_j_c^ml\khklhygb_h`b^Zgbywlboj_amevlZlh\\khhl\_lkl
\bbkaZdhghf_jghklyfb.Wlhb_klvihklZgh\dZdhgdj_lghcp_eb- h`b^Zgb_\k_fbg_c
jhgZfb j_amevlZlh\ a, b, c, d - \k_c kh\hdmighklvx h[jZlguo Znn_j_glZpbc h j_amevlZlZo
kh\_jr_gguo^_ckl\bcRes(da), Res(db), Res(dc), Res(dd).
:dp_ilhj j_amevlZlh\ ^_ckl\by b _klv \ky h`b^Z_fZy h[jZlgZy Znn_j_glZpby j_
amevlZlh\Res(da), Res(db), Res(dc), Res(dd). ?kebdhgdj_lgZyp_evklZ\blky\k_ckh\hdmigh
klvxj_amevlZlh\a, b, c, d, dZdh`b^Zgb_^hklb`_gbywlboj_amevlZlh\lhh[jZlgZyZnn_j_g
lZpby hl \k_ckh\hdmighklb^_ckl\bcb _klvZdp_ilhjj_amevlZlh\^_ckl\by Ihke_kh\_jr_
gby dZdh]h-eb[h ^_ckl\by fha] h`b^Z_l ihemq_gb_ j_Zevgh]h j_amevlZlZ hl ^_ckl\bc ih
\g_rg_fm dhglmjm Ihke_ ihemq_gby j_Zevgh]h j_amevlZlZ hkms_kl\ey_lky ³kebq_gb_ ij_^
kdZaZgbykiZjZf_ljZfbj_Zevgh]hj_amevlZlZ´ Wlhkebq_gb_hkms_kl\ey_lkyaZdhghf_j
ghklyfb ³Kebq_gb_´ khklhbl \ lhf qlh \k_ wlb aZdhghf_jghklb g_ kfh]ml ³kjZ[hlZlv´
_keb g_ [m^_l ihemq_gZ bf_ggh lZ h[jZlgZy Znn_j_glZpby dhlhjZy aZibkZgZ \ aZdhghf_jgh
klb ?keb ijb dZdhf-lh ^_ckl\bb [m^_l ihemq_gZ ^jm]Zy Znn_j_glZpby lh g_f_^e_ggh \ha
gbdg_l hjb_glbjh\hqgh-bkke_^h\Zl_evkdZy j_Zdpby ;he__ lhqgh hjb_glbjh\hqghbkke_^h\Zl_evkdZy j_Zdpby \hagbdZ_l lh]^Z b lhevdh lh]^Z dh]^Z l_jy_lky beb j_adh
iZ^Z_lhp_gdZij_^kdZaZgbydhg_qgh]hj_amevlZlZihemq_ggZygZhkgh\ZgbbieZgZ^_c
kl\bc (3).
5.4. NhjfmeZwfhpbcAZf_sZxsZynmgdpbywfhpbc.
<nhjfme_wfhpbcW I>IBi [email protected]\ghcy\ey_lkyjZaghklvBi -Bc) - “hp_gdZ
\_jhylghklb\hafh`ghklbm^h\e_l\hj_gbyihlj_[ghklbgZhkgh\_\jh`^_ggh]hbhglh]_g_
lbq_kdh]hhiulZ´LZdhchp_gdhcke_^m_lkqblZlvhp_gdmmkeh\ghc\_jhylghklbb ⇒ d^hklb
`bfhklbdhg_qgh]hj_amevlZlZd ihke_^hklb`_gbyg_dhlhjh]hwlZigh]hj_amevlZlZbDZdfu
\b^_eb ihke_ ^hklb`_gby dZ`^h]h ijhf_`mlhqgh]h j_amevlZlZ \_^ms_]h d ^hklb`_gbx dh
g_qghc p_eb mkeh\gZy \_jhylghklv lZdbo \_jhylghklguo aZdhghf_jghkl_c kljh]h \hajZklZ_l
bagZqbljZaghklvBi -Bc^Z`__kebhgZhljbpZl_evgZ\k_]^Zm\_ebqb\Z_lkyqlhijb\h^bl
diheh`bl_evgufwfhpbyf
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jhgujZkrbjy_l^bZiZahgba\e_dZ_fuobaiZfylbwg]jZff, Zk^jm]hcklhjhgukgb`Z_l
djbl_jbb“ijbgylbyj_r_gby” ijbkhihklZ\e_gbbwlbowg]jZffkgZebqgufbklbfmeZfb´
Ijhbkoh^blwlhZ\lhfZlbq_kdbiml_fih\ur_gbymjh\gy\ha[m^bfhklbg_cjhgh\ijbmkbe_
gbbfhlb\Zpbbkbevguc]heh^bkhhl\_lkl\mxs_fmkbe_gbbhljbpZl_evguowfhpbc<wlhf
kemqZ_\khhl\_lkl\bbknhjfZevghcfh^_evxg_cjhgZb³mlhqgyxsbf´]jZnhfijhbkoh^bl
Zdlb\Zpbyl_o\_jhylghklguoaZdhghf_jghkl_cdhlhju_[uebh[gZjm`_gugZjZggbowlZiZo
nhjfbjh\ZgbynmgdpbhgZevguokbkl_fbdhlhju_bf_xlg_hq_gv\ukhdmxhp_gdmmkeh\ghc
\_jhylghklbWlb\_jhylghklgu_aZdhghf_jghklbbf_xlf_gvr__qbkehij_^bdZlh\\mkeh\b
25
yo aZdhghf_jghkl_c b agZqbl y\eyxlky [he__ ]_g_jZebah\Zggufb b ijbf_gbfufb \ [he__
rbjhdhf qbke_ kemqZ_\ Wlh \ lhqghklb j_Zebam_l h[jZlguc ih kjZ\g_gbx k jZa\blb_f
nmgdpbhgZevguo kbkl_f f_oZgbaf j_^mdpbb nmgdpbhgZevguo kbkl_f ?keb hjb_glbjh
\hqgh-bkke_^h\Zl_evkdZy j_Zdpby jZa\b\Z_l nmgdpbhgZevgu_ kbkl_fu b m^ebgy_l \_l\b
³mlhqgyxs_]h´ ]jZnZ \ \_jhylghklguo aZdhghf_jghklyo lh ih^gylb_ mjh\gy \ha[m^bfhklb
g_cjhgh\iha\hey_l³kjZ[Zlu\Zlv´klZjuf³keZ[uf´aZdhghf_jghklyfijbg_ijbf_gbfhklb
[he__kbevguo\^Zgghcgh\hcbebg_h`b^Zgghch[klZgh\d_b\ha[m`^Zlvg_cjhgijb\h^y
lZdbfh[jZahfd[he__]_g_jZebah\Zggufkihkh[Zf^_ckl\bc
5.5. <aZbfhk\yav ijbgpbih\ p_e_iheZ]Zgby b ij_^kdZaZgby. NhjfZevgZy fh^_ev
jZ[hlufha]Zkbgl_abjmxsZyh[ZijbgpbiZFZl_fZlbq_kdZyfh^_evjZ[hlufha]Z\ul_
dZxsZy ba ijbgpbiZ p_e_iheZ]Zgby ij_^klZ\ey_l kh[hc b_jZjobx keZ[uo nhjfZevguo kbk
l_fFZl_fZlbq_kdhcfh^_evxjZ[hlufha]Z\ul_dZxs_cbaijbgpbiZij_^kdZaZgbyy\ey_l
ky fgh`_kl\h nmgdpbhgZevguo kbkl_f ^PRFJW`. Ijbgpbi jZ[hlu b kh^_j`Zgb_ dZ`^hc
nmgdpbhgZevghc kbkl_fu hibkZg \ij_^u^msbojZa^_eZoDZdk\yaZguf_`^mkh[hcwlb^\_
fh^_ebjZ[hlufha]Z"
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fu \b^_eb wlb bkoh^gu_ p_eb gZ gZqZevghf wlZi_ nhjfbjh\Zgby nmgdpbhgZevguo kbkl_f
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[hd´ l_ gZbf_g__ ^bnn_j_gpbjh\Zggufb ^_yl_evghklyfb >Zevg_cr__ kh\_jr_gkl\h\Zgb_
nmgdpbhgZevguokbkl_fhj]ZgbafZijhbkoh^blm`_iml_fm\_ebq_gbywlZiguoj_amevlZlh\b
h[h]Zs_gb_f Zdp_ilhjZ j_amevlZlh\ ^_ckl\by ijb mqZklbb hjb_glbjh\hqghbkke_^h\Zl_evkdhc j_Zdpbb H[mq_gguc hj]Zgbaf bf__l m`_ ^h\hevgh keh`gmx ihke_^h\Z
l_evghklvbb_jZjobxp_e_cbih^p_e_c^eydZ`^hcnmgdpbhgZevghckbkl_fuWlbihke_^h
\Zl_evghklbbb_jZjobbp_e_cbih^p_e_cnhjfbjmxlkybakljmdlmjuij_^kdZaZgbc\h\g_r
g_f fbj_ dhlhjmx meZ\eb\Z_l fha] \ \b^_ fgh`_kl\Z \_jhylghklguo aZdhghf_jghkl_c
{PRFJW`
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eyxsZykh[hcb_jZjobxkeZ[uonhjfZevguokbkl_fij_^iheZ]Z_lqlh\k_fgh`_kl\hp_e_c
dZdbf-lhh[jZahfaZ^Zgh.Ijbgpbi`_ij_^kdZaZgbylhevdhgZqbgZ_lkaZ^Zgbyfgh`_kl
\Zbkoh^guop_e_c^FJW!`hklZevgu_p_ebihemqZxlky\j_amevlZl_^ebl_evgh]hijhp_k
kZh[mq_gbyDjhf_lh]hihemq_ggZyihijbgpbimij_^kdZaZgbyb_jZjobyj_amevlZlh\\dex
qZxsZybglmbpbxkfjZa^m`_g_fh`_l[ulviheghklvxhkhagZgZbdZdihdZaZgh\jZa
^_e_^Z`_g_fh`_l[ulv³ba\e_q_gZ´bawdki_jlZdZdagZgb_Ihwlhfmihemq_ggZy\j_
amevlZl_h[mq_gbyihijbgpbimij_^kdZaZgbyb_jZjobyp_e_cijbgpbibZevghg_fh`_l[ulv
dZd-lhbagZqZevgh^ZgZdZdwlhlj_[m_lkyijbgpbihfp_e_iheZ]Zgbybke_^h\Zl_evghijbf_
g_gb_nhjfZevghcfh^_ebhkgh\ZgghcgZb_jZjobbkeZ[uonhjfZevguokbkl_fm`_ijbgpb
ibZevghg_\hafh`gh
Ij_^iheh`bf qlh fu \u\_eb qbklh nhjfZevgh b_jZjobx b ihke_^h\Zl_evghklv p_e_c
baZgZebaZfgh`_kl\Z^PRFJW`DZdmxemqr_\wlhfkemqZ_bkihevah\ZlvnhjfZebaZpbx
jZ[hlufha]Z-hkgh\ZggmxgZkeZ[uonhjfZevguokbkl_fZobebgZfgh`_kl\_^PRFJW`"
DZd[uehkdZaZghfgh`_kl\hPR³kbevg__´ex[h]heh]bq_kdh]h\u\h^Zklhqdbaj_gbyihem
q_gbyij_^kdZaZgbc
G_kfhljy gZ \k_ wlb jZkkm`^_gby ijbgpbi p_e_iheZ]Zgby ijh^he`Z_l b]jZlv \Z`gmx
jhev\fh^_eb^PRFJW`KZfhh[gZjm`_gb_\_jhylghklguoaZdhghf_jghkl_cg_\hafh`gh
[_a p_e_c FJW NZdlbq_kdb \ fh^_eb ^PRFJW` ijbgpbi p_e_iheZ]Zgby b ijbgpbi
ij_^kdZaZgbykbgl_abjh\Zgu\h^gmfh^_evdhlhjmxfub[m^_f\^Zevg_cr_fkqblZlvnhj
fZevghcfh^_evxjZ[hlufha]Z,kbgl_abjmxs_ch[ZijbgpbiZ.
26
H[tykg_gb_ko_f\hkijbylbyMGZck_jZ
6.1. Ko_fZ\hkijbylbyM.GZck_jZ>[email protected] Ijh^he`bfZgZebako_f\hkijbylby
MGZck_jZgZqZluc\><bly_\@GZihfgbf\u\h^k^_eZgguc\jZ[hl_><bly_\@³BlZd
Ko_fu h[jZamxl b_jZjobx \ dhlhjhc fZdkbfZevgufb Ko_fZfb y\eyxlky Ko_fu-fhlb\u
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gbdgh\_gb_ b kh\_jr_gkl\h\Zgb_ kZfbo Ko_f hklZ_lky g_ykguf L_f kZfuf g_l hl\_lZ b gZ
]eZ\guc \hijhk Qlh fu \b^bf" DZdmx qZklv bgnhjfZpbb ba \k_]h ihlhdZ fu h[mqZ_fky
ij_^\hkobsZlv" GZ \hkijbylb_ ba\e_q_gb_ dZdhc bgnhjfZpbb fu gZkljZb\Z_fky k\hbfb
^\b`_gbyfb gZkljhcdhc ajbl_evghc kbkl_fu b l^" GZijbf_j >`=b[khg b \ wlhf k gbf
kheb^Zj_g MGZck_j ml\_j`^Zxl qlh gZ bg\ZjbZglgmx ohly gb hgb gb bo ihke_^h\Zl_eb
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lZhibr_fijhp_kknhjfbjh\ZgbyKo_fjZaj_rbfiZjZ^hdk\hkijbylbyhij_^_ebfbg\Zjb
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g_ljm^ghihgylv qlhdZ`^uc hl^_evguc³[ehd” (4) ^_yl_evghklbb_klvKo_fZGZihfgbf
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y\eyxlky ij_^\hkobsZxsb_ Ko_fu ih^]hlZ\eb\Zxsb_ bg^b\b^Z d ijbgylbx bgnhjfZ
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wlb Ko_fu \f_kl_ k ^hklmighc \ ^Zgguc fhf_gl bgnhjfZpb_c hij_^_eyxl qlh [m^_l \hk
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lb\ghklv gZijZ\ey_lky \k_ l_fb `_ ij_^\hkobsZxsbfb Ko_fZfb ij_^klZ\eyxsbfb kh[hc
k\h_]hjh^ZieZgu^eyi_jp_ilb\guo^_ckl\bclZd`_dZdb]hlh\ghklvd\u^_e_gbxhi
lbq_kdbo kljmdlmj g_dhlhjuo \b^h\ L_jfbg ³\hkijbylb_´ hlghkblky dh \k_fm pbdem i_j
p_ilb\ghfmpbdem-?<Zg_ddZdhc-lhhl^_evghc_]hqZklb´>[email protected]
l_jij_lbjm_f wlh hij_^_e_gb_ \ l_jfbgZo ³[ehdh\´ ^_ckl\bc \ dZ`^uc fhf_gl \hkijb
gbfZxsbf gZ hkgh\Zgbb m`_ ihemq_ggh]h j_amevlZlZ b hl ij_^u^ms_]h ZdlZ \hkijbylby
dhgkljmbjmxlky ij_^\hkobs_gby ih aZdhghf_jghklb H[kGFGF5HVGF ⇒ cihklmie_gby
g_dhlhjhc³hij_^_e_gghcbgnhjfZpbb´Res(dc) h[jZlghcZnn_j_glZpbbhj_amevlZlZoi_j
p_ilb\gh]h^_ckl\bydc, ^_eZxsb_\hafh`guf^eyg_]hijbgylb___³ijbgylb___´hagZqZ_l
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gh_^_ckl\b_dc ^hklb]Z_lk\h_]hj_amevlZlZih\g_rg_fmdhglmjm→ b^_eZ_l klbfmeypbxba
\g_rg_c kj_^u ^hklmighc ^ey \hkijbylby Qlh[u k^_eZlv wlm bgnhjfZpbx ^hklmighc _fm
ijboh^blky Zdlb\gh bkke_^h\Zlv hilbq_kdbc ihlhd ^\b]Zy ]eZaZfb ]heh\hc b \k_f l_ehf
i_jp_ilb\gu_^_ckl\bydc<h[s_fkemqZ_\³[ehd_´P_evx\hkijbylbyy\ey_lkyg_
dhlhjuc wlZiguc j_amevlZl F ij_^klZ\eyxsbc kh[hc g_ ijhklh \hkijbylb_ g_dhlhjhc
³hij_^_e_gghc bgnhjfZpbb´ Res(dc) Z b_s_b__agZq_gb_FP_evklZ\blkyh`b^Zgb_fih
aZdhghf_jghklbH[kGFGF5HVGF⇒ c ihemq_gbybgnhjfZpbb\\b^_h[jZlghcZnn_j_g
lZpbbRes(dc) h^hklb`_gbbj_amevlZlZ- agZq_gby c. I_jp_ilb\gu_^_ckl\bydc ^_eZxl\ha
fh`gufg_ijhklh³ijbgylb_bgnhjfZpbbdh]^ZhgZhdZ`_lky^hklmighc´Zij_^kdZau\Zxl
ihklmie_gb_wlhcbgnhjfZpbbihaZdhghf_jghklbH[kGFGF5HVGF⇒ c.
P_evx \hkijbylby g_dhlhjh]h h[t_dlZ \ j_amevlZl_ g_dhlhjhc p_e_gZijZ\e_gghc ^_y
l_evghklb\dexqZxs_c\k_[yi_jp_ilb\gmx^_yl_evghklvy\ey_lkyagZq_gb_h[t_dlZAgZ
q_gb_ h[t_dlZ b _klv j_amevlZl i_jp_ilb\ghc ^_yl_evghklb ih \hkijbylbx h[t_dlZ Hg
27
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ihemqbebbwfhpbhgZevghhp_gblvijb[eb`Z_lebwlhgZkddhg_qghcp_ebbebg_lGZijbf_j
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:gZeh]bqghagZq_gb_fa\hgdZkh\k_fb_]hk\hckl\ZfblhghfqZklhlhcf_klhfa\mqZgbyb
l^bklmdZdhjfmrdby\eyxlkykhhl\_lkl\_gghj_amevlZlui_jp_ilb\ghc^_yl_evghklba bb.
Ko_fu-fhlb\u_klvnmgdpbhgZevgu_kbkl_fu]^_fhlb\hfy\ey_lkyfhlb\ZpbyLZdb_ko_fu
dZd ijhkljZgkl\_ggh-\j_f_ggu_ ko_fu dZ[bg_lZ d\Zjlbju d\ZjlZeZ ]hjh^Z b l^ y\eyxlky
j_amevlZlZfb hjb_glbjh\hqgh-bkke_^h\Zl_evkdhc^_yl_evghklbihboh[ke_^h\ZgbxdhlhjZy
y\ey_lkykZfhklhyl_evghc^_yl_evghklvxhj]ZgbafZ>:[email protected]
JZkkfhljbfiZjZ^hdk\hkijbylby><bly_\@³Ihkdhevdmfufh`_f\b^_lvlhevdhlh
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lhevdh lh qlh ij_^\hkobsZ_f gh fu fh`_f ij_^\hkobsZlv lhevdh lh qlh gZmqbebkv
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// Kbkl_fgucih^oh^dikbohnbabheh]bq_kdhcijh[e_f_GZmdZFk- 22.
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32
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