Simulation Logic, Applets and Compositional Verification
38
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Simulation Logic, Applets and Compositional Verification Christoph Sprenger — Dilian Gurov — Marieke Huisman. N° 4890 Juillet 2003. ISSN 0249-6399. ISRN INRIA/RR--4896--FR+ENG. THÈME 2. apport de recherche.
(3)
(4)
(5) ! "$#! %& ' ( )* ,+(.-/0 ( 132
(6) 46587:9<;>=(2@? =
(7) 46ACB
(8) DEAC4GFIH 5KJ85KL>B@MON(46;QPRFISTLU4658ACV>AXWN
(9) 5K7:YZLUB []\_^:`3abcedgf:h_ijalknmpoGinqija:k arsqtukvqwxkzy|{}`~>mpknivGwxa mu ary,za:``3all[,x} a:_ah tp_>mpr,_ala6q'\_a'q'\_a@h>
(10) CpG cpw_inkjknarbppplceuxtpopa6y : ¡£¢_¤p p¥§¦ a_a:yahCrltqmp`>mGyi¨rijmGhxtuk
(11) ©pa:ijªUqturinmph«`ar\_mQ&¬mplqmGhGrmGk¯®Um£°~xtpya:Xytu¬ar { x mGUa:|rija6ymu¬y`tp|r±q:tu'²tu__knar'y³!´w_±`3ar\_mQ²a:y|ry±mphµt¶qknmGya«qmGa:y>mphxQa:hxqa/~>ar aa:h rtphxyi¨rijmGh·y{Qy ra`¸`mQQa:knylmG_aa:«~}{·y|in`w_kvt£rijmGh·tphxa:h_h_a:yy{G¹ º/inkjhxalknmpopivq3a»}ra:hxQa6X,ijr\ yin`w_kjrtph_amGwxy,opa:tura6y r]ª_»Qa:/>mpinhCry:³ ¦ ay\_m£¼r\xturgyij`½w_kvt£rinmphOq:tuhO~>aq'\xtu'tpqra:ivy|a6knmpoGinq:tuknkj{ tphx¾u©}ivqa]©pa:yt_<knmpoGinq:tukQyturivy ¬8tGq.rijmGh½qtph½~>a]a:_a:yahCra6~>a\xt<©}inmpw_'tuknkj{ ~}{tg`t£»Qin`tpk}`3mQQa:k}¬mp t oGij©Gah3¬mp`wxkntx³
(12) ¿]tpya:3mGhr\_a6y|aa:yw_kjryItphxa:tpkninaivQa:tGyI~}{3dgw_`~>aotuhUzmphxol0as_a©pa:kjmG t qmG`UmCy|ijrinmphxtpk(©paijªUqturinmph«ra:q'\_hxinCw_aGz,\_aa`t£»Qij`tpk
(13) `mQQa:kny a_kvtpqa½knmpoGinq:tuktpyyw_`Qrinmphxy rm/a6QwxqaqmG`UmCy|ijrinmphxtpk(©paijªUqturinmph«rm y|rtphx_tp&`3mQQa:kRq'\_a6q'ÀCinh_oU³½m£ a©Ga6EijhXr\_aqmphCra»Cr mp¬ tp__knary:¯a6Cw_ijxUa6X,ijr\inhCra¬8tpqa:y:¾r\xiny ra:q'\_hxinCw_ah_a:a:_ygrmO~UaaªUh_a:¾³±Qijhxqa3¬mpt opin©pa:h ~>a\Ut<©Cinmpwxtpk¬mp`w_kvt&tphxÁinhCra¬8tpqa±t«`tu»}in`tuk]tu_xkjar3Qm}a:y½h_mpr3tukn]t<{}ya»Qiny|r: a±xmGUmCy|a±t r mu¹Âkna©pa:ktu__mGtGq'\z¾,\_a:aknmQqtukItGyyw_`QrijmGhxy a6y rivq.r r\_a±qmGhCrmpk
(14) ®xm£ÄÃ'ÅÇÆ.ÈxÉÅKÈQÆÊ3mp¬]tp__knar'y ,\xijknalr\xaopknmp~xtpkz_mp>ar {±a:y|rinqry]r\_aqmphCrmpkE®xm£ÌËÊÍ}ΣÏ6Ð8Ñ£ÈQÆmp¬
(15) r\_ay{Qy ra`/³,¿0{/yaxtpturinh_o r\_artpyÀQymp¬s©pa:ij¬{}ijhxo«opknmp~xtpk tphx¶knmQqtpk0_mp>arina:y½mu¬stp__knar'yImGw_3`3ar\_mQÒy|wx_UmG|r'y½ya:qw_a >mGy|r|¹ÂivyywxtuhUqagkjmCtpQinh_omu¬
(16) h_a*tu_xkjary]mphCrmty`tur,q:tu'¾³ ÓOÔCÕEÖ×Ø ¡£Ù
(17) p¥ Ú _xkjary:y|a6qw_i¨r {G ra`>mp'tukknmpoGinqp qmp`>mGyi¨rijmGhxtuk,©Gai¨ªUq:t£rijmGhz qmphCra»}r|¹Ç¬a:a xmQqa6yya:y:³. ÛzÜ<ÝßÞ(à¾á.â8ãlÝßÞä£å'â8æKÝçå'èßè éÞÇê6ä<äuá.â8æKë ì3íélæÇÜ<ë]îUê<â8á.äuëå'ï3ð ï<Ýßá.ïå'ÞIä£å'âæIá'ñEæKÜ<ë]ò>ë â8Ý ópô¾å'âKìä<â8á'õ8ë|ö÷æRø8ù:Û¾úû.ü.ü.üú û.ý.þ.û.ÿ. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65.
(18) · "
(19) X± ,+
(20) -
(21) %X .
(22) ½ ¥
(23) mpwxy°_f6y|a:hCrmphUy*w_h_a `fr\_mQQa Qa ©Gfi¨ªUq:t£rijmGh qmp`UmCy|ijrinmphxh_aknkja >mpw_ Qa:y xmG_infrf:y½Qa y _arf±~xtGy|f:a:y y|w_3k tphxtukn{Qy|a Qa ®Umur3_a qmphCr pkna Qa6y3tp__knar'y_f:yahCra:yyw_ kna:ysqtura6y_wxqap³
(24) mpral`3fr\_mQQa½y tu_xw_ija½y|w_sw_h_a qmGa:yUmGhx_tphxqa frmGi¨ralahCral`mQQ^kna:y ~Utpya Qa y|{Qy|r^:`3aQa²r'tuhxyijrinmph mp'Qmphxh_f,xtuZy|in`w_kvt£rijmGh ar¶kvtlkjmGopivCw_a Qassah_h_a6yy{C¹÷ºOijknh_a fra:hxQw_at<©Ga:q Qa:y(_knwxy(oGtphx_y
(25) UmGijhCr'y(ª_»Qa:yyij`½w_kjrtuhxf:y:³
(26) mGwxy(`mphCrmphUy
(27) Cw_aZknt yij`½w_kvt£rinmph3>awQr qrmp`ag>q:mptu'rtpaq`rfa:hGivy|r'f:tuaTkna`knmpaoGhCinCrw_Ua:tu`3aw_hCh¶r,a`r:QmQ©}Qiv^qkna a©p`a:tuy»}t_in`kvtutk0yUtumGrw_ivy ½ª>tuwx~_h_ina±kjijr¬f mGkn`½mpoGw_inCkna±w_a@Qmp>hxah_wQfraG³ ra@hÒy a: tu_xf:_yw_a{GhCtprhCf:ar yw_±qa:yf:yw_kjrtury:ÄtuinhxyisCw_a«Qa6yin_fa:ytuhCrf:inawxa6y3_aXdgwx`~>ao·arzmGh_oxÄh_mpwUyQf©GaknmpQ¹ >mphUyXwxh_a,ra6q'\_h_ivCw_aQa²©pf:ijªUqturinmph3qmp`>mGyi¨rijmGh_h_a:kjknapGUmGw_kntGGwxaknkja,kna:y·`mQQ^kna:y`t£»Qin`tuwQ» a`_kvtpqahCrÌkna:y \}{}Umpr\_^6y|a6y kjmGopivGwxa:yÌtuªxhQaf6Qw_inakvt ©pfijªUqturinmphXqmp`>mGyi¨rijmGh_h_aknkna O_w `mQQa:k¨¹÷q'\_a:q'À}inh_o&y|rtphx_tu'¾ ³ 0a>ahx_tphCr:I_tphxyknaqmphCra»}ra_a:y3tu__knar'yR`w_h_ina:y3 ijhCra¬8tpqa6y qarragra6q'\_h_ivGwxagQmGi¨r rag' t h_faG³ 0mp``a>mpw_]w_hxa*¬mp`w_knagqmp`>mpra`a:hGr'tuknasar]wxh_a ijhCra:|¹ ¬8tGqa!_mph_h_f:a:y:Qw_h_altux_kjar,`tu»Qij`tukna !h a»Qiny|ra xtGyµrmpw£ mGw_y:Qh_mGwxy _mGUmCy|mGhxy w_h_altux_mQq'\_" a _awQ»gh_ij©Ga:tpwQ»¾6_tphxy¾kvtpCw_a:kjknakja6y¾\}{}Umpr\_^6y|a6y¾kjmQq:tukna:y3a6y ra:ijoGh_ahCr¾kvt,y rwxqrw_aIQwg®xmpr QaIqmGhCr pkna a:h&` `aCw_a½kvt_mG_ijfrfoGkjmG~xtuknaa:y|rainhCrkna3qmp`>mpra`a:hGr QwX®xmurlqmGhGr GkjaG#³ h·yfUtu'tuhCr kna:y%r $pq'\_a6yQa3©pf:ijªUq:t£rinmph«_a:yg_mp_ijfrf6ysoGkjmG~xtukna:ysarlkjmQq:tukna:ygQa:ygtu_xkjary:¾h_mura3`fr\xm}_a a6y r tG_tu_rfaltpw q'\xtpoGa`ahC'r &QÑ£Ã.)Å (÷ÐvÃ'Ã.Èx Î *EÉÊQa h_mpwx©paknkna:y,tux_kjary,yw_,kvtqtur+a 3_wxqap³ ,!Ø 6 Ö .¤ - ¥ Ú __knar'yQyf:qw_ijrfGGknmpoGinCw_a]ra`>mpaknkjaGC©Gfi¨ª>qt£rijmGhqmp`>mGyi¨rijmGh_h_a:kjknapG_mQqa:yy|wxy qmphCra»}r|¹Ç¬a:a.
(28) Ð ½È nΣÅÇÐ8Ñ * Ñ uÐ8É . . . . '& & jÊÅKÃÎ *.
(29) . . Ñ _& Ñ<Ã.Ð ÅÇÐ8Ñ *EÎ UÊÆ.Ð É'ΣÅÇÐ8Ñ *. . . . #! ½
(30)
(31) :¡ Ø Ù ¤u Ø ³ ´wx Ú __mGtGq'\³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ³ b Qw_``tp{±mu¬,a:yw_kjry ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ³ akvt£ra6 ¦ mGÀ°³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³. -¢Q Ø Ô ¡£ ¯ Ø ¤ b_³ QUa6qijªUqturinmphxy,tphxO}ij`½w_kvt£rinmph ³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ b_³ b Qij`½w_knturinmph/zmGopivq¸³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ b_³ a_a:yahCrturinmph/,a:yw_kjry3³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ b_³ ¦ a:tpÀ}in`w_kvt£rijmGh ³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ Ø Ø Ø ¢ - Ô ¡ (¤p¢_ Ø Ø - Ô : x³ Ú __knar'y³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ x³ b }rwxq.rw_tpkzza:©pakE³l³l³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ x³ ¿ a:\xt<©}ijmGw_tpk>¯a©Gak ³ ³l³ ³l³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ x³ 0mG`UmCy|ijrinmphxtpkz,a:tGy|mGh_inh_o ³ ³l³l³g³l³ ³l³ ³l³l³ ³l³ ³l³g³l³ ³l³l³ ³l³ ³l³ ³l³l³g³l³ ¢ - Ô Ø ¤ - ¯ Ø . . . . . . . !. . ". . #%$. . . )(. '&. * . +. . 10. -/.. . . 32. 4. 5 . . 6. 7080. , . 10. >%.. ?@?. . ï ÿ .ü ACB ED. . . . #9. b. . %;=<. . bp bu b. :" # + -#. .
(32) &UÆÊ* CÊÆ . :. ÈQÆÑ£ÏÈQÐvà Π* . +
(33) "/±R
(34) ½ ¦ ijr\Òr\_aOa`aopa:hxqa mu¬ y|`tpkjkya:qw_a/Qa:©Civqa6y]ywxq'\ÒtGy3mp>ah²_kvt£r|¬mG`y|`turqtu'_ytuhUÒya¹ qw_a`mQQw_kna:yltpyg(tuknkntGQinw_` tphx `½~xtpyy{ p¾i¨r ~>a:qmG`a:ygij`>mprtphGrgrm/yarlqi¨raintrm/Qa:qinQa ,\xar\xaRtphtp__kninq:t£rijmGhq:tuh~>astpq:qa_ra:3mGhtl_a©}inqap³I}inhxqaywxq'\Qa:©Civqa6yItua]r {}_ivqtuknkn{wxya:½rm y|rmGalxin©£tpq{C¹÷y|a:hxyi¨rij©Ga_t£r't__¬mGr\_a½tGqqa:Qrtphxqamu¬(r\_ivyh_aTra6q'\_h_mGkjmGop{±ijrivyij`>mprtuhCrr\xt£r >murahCrivtuk¾wUy|a:y]\xt<©Gas¬wxkjk¯rwxy r,inh r\_al_mura:qrinmph mu¬¯r\_ain_in©<tGq{G³
(35) xmp0r\_a h_a:µopahxa't£rinmph±mu¬¯y`tp|r]qtp_y:}tuh±inhCra:a6y rijh_o½UmCyyin~_ijknijr {3ivy0rm½\xt<©pa &QÑ£Ã'Å (÷ÐvÃ'Ã.Èx Î *>É'Ê knmGtGQinh_omu¬tu__knivqt£rijmGhxy Ktu__knar'y³0[]\_ivy`a6tuhxy]r\xt£rmGhxqa r\_aq:tu'±ivyivyyw_a6 tphx opin©pa:h±rmr\_a wUy|a::>r\xa½wxyalq:tuh«inhxy|rtuknk(h_a tu__knar'ygmph«r\_aqtu'O\_in`y|a:k¨¬¯\_aQm}a:yh_mur \xt<©parm opm~xtpq'À rm r\_aqtpivyyw_a,inh/mp'Qa]rmQmr\_ivy:³÷h r\_ivyqtGy|altpwQrmG`turivq q'\_a:q'ÀQy,tua h_aa6Qa:rm3a:hxyw_a r\xt£r r\_ahxa!tp__knargq:tuhO~>arwUy ra:¾³ []\_a:ya½q'\xa:q'ÀQysq:tuhOinhC©Gmpkn©pal¬mGsa»Qtp`_kjar {}Ua3ytu¬ar {pE`a`mG{ qmphxyw_`QrijmGhz_tuhxinkjkninqi¨rg_t£r't½mG,qmphCrmGkE®xm£l³ ÷h r\_ivy3xtu>a30a¬mQqwxy½mph r\_a kvtpy|r3qtura:opmp{·mu¬_mp>arina:yrm·~Ua/tu~xkja±rmytu¬akn{·inhxy|rtpkjk tphOtu__knarUmCy r¹ÇivyywxtphxqalmGh/ty`tursqtp¾Ui¨rh_aa6_y]rm±a6y|>a:qrsqartpijhOqmphCrmpk¾®Um£¼_mp>arina:y tGyyUa6qijªxa:z³&º/mpa_a:qinyakn{p
(36) 0ay rwxQ{Áy|a6Cw_ahCrivtuk 8yijh_oGkja¹Kr\_a:tp_a:ltp__knar'ytuhU_mGUmCy|at y>a:qijªUq:t£rinmphÁtphx©pa:ijªUqturinmph·`ar\xm}·¬mG½yt£¬ar {&_mp>arina:y mp¬]inhCra:_mQqa6Qw_'tukIqmGhCrmpk®xm£l Ð ÊxmGUa:|rija6yQa6yqin~_inh_o&ya:Cw_ahUqa:y½mu¬`ar\_mQ¶inh}©pmQqturinmphxy,\_inq'\ZtuaQa:a`a:¶yt£¬a±¬mp½r\_a oGij©Gah¶tp__kninq:t£rinmph¯³X}inhxqa0a±tpa±ijhCra:a6y ra:Áinh¶>mGy|r|¹ÂinyywxtuhxqakjmCtpQinh_o«mp¬stu_xkjary:(r\_aij`_kna¹ `a:hGr't£rijmGhÁmu¬tu_xkjary`inop\Crh_mpr~>at<©£tuinkntp~_knat£r©Gai¨ªUq:t£rijmGhXrij`aG³ ¦ a±r\_a:a¬mpa_mGUmCy|at É'Ñ &_Ñ<Ã.Ð ÅÇÐ8 Ñ *>Î 0©Gai¨ª>qt£rijmGh&`ar\_mQ¾¯,\xinq'\·tuknkjm£yr\xa3©Gai¨ª>qt£rijmGh&_mp~xkja:`rm/~Uaa:QwUqa:&rm r\_a ¬mpknknm£,ijh_o½r\xa:a rtpyÀQy i Qa:qmp`>mGyijh_o3r\_alopknmp~xtpk¾~Ua:\xt<©}ijmGw_'tukE_mp>ar {~}{ªxhxQinh_oknmQqtukzy|rwxqrw_'tuk¾_mp>arina:y]mp¬ r\_aqmp`>mph_a:hGr'y \_a:atp__knar'y 8iji _m£©Cinh_olqmGa:qrh_a6yy(mp¬Ur\_ivyRQa6qmp`>mGyi¨rijmGhzur\xt£r0iny:p©Gai¨¬{}inh_o r\xturr\_askjmQqtpkxtux_kjarR_mpQ¹ arina:y Ktpyy|w_`QrijmGhxy ]tuagyw qinahCr,rmoGwxtu'tuhCra:asr\_alopknmp~UtukE_mp>ar { oGwxtu'tuhCra:a}tphx iniji ©pa:ij¬{}ijh_o3r\xt£rstp__knary,yt£riny|¬{r\_ainstpyyw_`Qrinmphxy:³ Ú y(a»Q_kvtuinh_a:½~>aknm£lptpyy|wx`3_rinmphxy(tua]y rwxqrw_'tuk}'t£r\_a(r\xtuh3~Ua:\xt<©}ijmGw_'tukGrmltuknkjm£Ztuknopmpijr\_`ivq q'\xa:q'À}ijhxo±mu¬]qmGa:qrh_a6yysmu¬0xmGUa:|r {«Qa6qmG`3>mGyijrinmphxy:³[]\_ivygxtu>a ¬mQqwUy|a6ymGh«r'tpyÀ! ini"¯,\_inkja ¬mG]rtGy|À 8ijini ]y r'tuhx_tp tuknopmGijr\x`3ivqsra:q'\xh_inCw_a6y,tukna6tpQ{a»Qiny|r:³ []\_aXqmp`>mGyi¨rijmGhxtuks©paijªUqturinmphÒ`3ar\_mQ²_mp>mGya:Ò\_a:a«yw__>mpry±Qi$#EaahCryqa:hxtuinmGy½¬mp ya:qw_aOUmCy r¹Çivyywxtphxqa/knmGtp_ijh_omp¬ltp__knar'y&%'nÆ nÅ(]qmphCrmpk]®Um£ yt£¬ar { _mp>arina:y:³÷h²r\_aOªx'y r yqa:hxtuinmx>r\_aqtp&inyyw_alyUa6qijªxa:yg~>mur\Xr\xa3oGkjmG~xtuk(tuhU«knm}q:tuk(_mp>arina:y tuhU«©pa:ijªxa6y*)Owxyijh_o r\_a,ra:q'\_h_ivCw_a:y0Qa:yqin~Ua6½inhr\xiny0xtu>a+)r\xturRr\xasQa:qmp`>mGyi¨rijmGh3ivyRqmpa6q.r6u`a:tuhxijh_o r\xt£r0r\_a knmQqtpk
(37) yUa6qijªUqturinmph«ivy y|w qija:hCrrma6y r'tu~_kniny\Or\_aopknmp~xtpk yUa6qijªUqturinmphz³ ItGq'\Orin`atuh&tp__knar iny knmGtGQa:X>mGy|r|¹Âinyy|wUtuhxqapztuhÁtpkjoGmpi¨r\_` _m£©CivQa6«~}{«r\_aqtp&inyy|wxaq'\_a6q'À}y ,\xar\xa r\xatu__knar in`_kna`ahCrturinmph/yturivy ªUa:y r\xala6Gwxija: y|>a:qi¨ª>qt£rijmGhz³ Ú hOtpk¨rahxt£rij©Gagyqa:hxtuijm3ivy]r\xtur,r\_aq:tu' ivyy|w_a:mphxkj{·_m£©CivQa6y r\_a±opknmp~xtpkRy|>a:qi¨ª>qt£rijmGh, 8tphxkjmQq:tuk0y>a:qijªUq:t£rinmphUy ¬mp½i¨r'ym£,h¶tux_kjary . : ÜÜæKæKæKæKä/ä/.. 010100àzàzàzàzàà àz2,å<Ýßö|;â8ë á.ÞKÞÇé:á'Þ ñ¨æö á1ö|23á1230æK0ë â8öÂë Ü<ÞÇï<á.á.ê<èßâ8á1ö 5'ë é6Þ400ï6ë2 5.ÞKí£ö|í7å'ÞK0ÞKì<é ë÷ñvÜå'æ=ê<2,è æ è 2,ÞÇä98 . . . ø?> zø @ 8?.
(38) Ð ½È nΣÅÇÐ8Ñ * Ñ uÐ8É . . . . '& & jÊÅKÃÎ *.
(39) . . Ñ _& Ñ<Ã.Ð ÅÇÐ8Ñ *EÎ UÊÆ.Ð É'ΣÅÇÐ8Ñ *. . . . . tphxOkna:t<©Ga:yijrgrmr\_a3tu__knar _m£©}inQa:rmqmG`aw_X,i¨r\Xtuh·tu_xmG_ivt£ralkjmQq:tuk(y|>a:qi¨ªUq:t£rijmGhO¬mp 6a tpq'\Á>mGy|r|¹ÂinyywxtuhxqaknmGtp_a:Átux_kjar:³ Ú y½ijh r\_a_a©}ijmGwxyyqa:hxtuinmx(tuh tpkjoGmpi¨r\_` xm£©}ivQa:~}{ r\_a±q:tu'Xivyy|w_a:q'\_a6q'À}ylr\_a±tp__knar½tpoGtpijhxy|rlr\xakjmQq:tukRyUa6qijªUqturinmphw_>mph¶knmGtGQinh_ox ~_wQr½inhr\xiny yqa:hxtuinm tpknym r\_axmGUa:|r {«Qa6qmG`3>mGyijrinmphh_aa6_y rmO~Ua©Gai¨ªxa6XturkjmCtpQinh_o rin`ap
(40) Umpra:hGrintpkjkn{ mGhQ¹÷qtu'¾³ . .
(41) ÷hÁa6tukjinal mpÀß b (t/xm}mu¬,y{}y|ra:`¸~xtGy|a6tu__mGtGq'\·tur_m£©}ijh_oOqmpa6q.rhxa:yymp¬,_mGUa:|r {XQa¹. q mp`>mGyi¨rijmGhxyRivy ijh}©Ga:y|rinoGt£ra:¾C,\_ivq'\tpij`y t£r,y|a:`3ij¹÷tuwQrmp`t£rinqs©paijªUqturinmphz³(m£ a©Ga6u¬mp]`tuh}{ tp__kninq:t£rijmGhxystphXtuknopmGijr\x`3ivql©Gai¨ªUq:t£rijmGh«`ar\xm}&iny_a¬a:tp~_kjaGEa©pa:h«`mpa½ym±ij¬0ywxq'\Xtq'\_a:q'À ivy rm~>al>a¬mp`3a6¬a:Cw_a:hCrkn{±tpy]inh/mpw_,ya:qmGhx yqahxtpinmx³ []\_a]tux_mCtpq'\lr\xt£r( aRr'tuÀpa0\_aa iny
(42) inhxy|xija:~C{gr\_a]0mGÀ mph`3mQQwxkntp
(43) ©Gai¨ª>qt£rijmGhl~}{dgw_`3¹ ~>aotuhUzmphxo ³[]\_ain¬'tu`a mpÀivyI~xtGy|a63mphtl~>a\xt<©}inmpw_'tukEÃ.Ð 3È jΣÅÇÐ8 Ñ * _amp'Qa:,\_inq'\& 8i" ivy _a:ya©pa:w_hxQa: 8xtu'tuknknak Rqmp`UmCy|ijrinmph¯}tphx 8iji 0_a:ya©pa:y yt£rivy|¬8tpq.rijmGhmu¬
(44) _mp>arina:y y|>a:qi¨¹ ªUa: ijh Ú [,I_r\_alw_hxij©Ga'ytpk¨¹Âxt£r\¬'tuop`a:hGr,mp¬¯r\xa ~_'tuhxq'\xijh_op¹Krij`a6Ira`>mp'tuk¾knmpopivq [, dz []\xinyE wUy ri¨ªxa6yIqmG`UmCy|ijrinmphxtpkQ©pa:ijªUqturinmph3ijhr\_a]¬mpknknm£,ijh_oly|r {}kja zrml©Gai¨¬{r\xturr\_aqmp`>mGyi¨rijmGh mp¬]qmp`>mph_a:hGr'y r\xt£r½iny: ~>a\Ut<©Cinmpwxy tphx yturivy ªUa:ylt/opknmp~Utuk(ra:`UmGtpkI_mp>ar {
(45) mph_a ªUhx_y(tuh3tu~xy|r'tpqrinmphmp¬ X <r\Ut£r(iny:uts~>aX\Ut<©Cinmpwx YX 0 yij`½w_kvt£rinh_o X uy|wUq'\r\Ut£r
(46) r\_a,qmG`UmCy|ijψrinmphmp¬ tphx yturivy ªUa:y ³ 0mp`>mph_a:hGr qtuh±~Uara:tura:y|in`ijkvtukn{p³ ÷htpxQi¨rijmGhz_t Î GÐ Î Ñ GÊ X0 qmphxy|rwxqYrinmph θ ivyIopinψ©pa:hzp,ijr\r\_a_YmGUa:|r {r\xtur X yt£riny|ªxa:y φ a»QtGq.rkj{3,\_ah X ivyRyin`w_kvt£ra:~}{ ³[]\_ivy qmphxy|rwxqrinmphtpkjknm£yI~>a\Ut<©Cinmpwxtpk>tp~xy rtGq.rijmGhxyrm½~>a opin©pahr\_mpw_oG\ra:`UmGtpk>knmpoGinq θ (φ) ¬mG`½w_kvtua 't£r\_aIr\xtphr\_mpwxop\~Ua:\xt<©}ijmGw_'yGyw__>mprinh_ol©pa:ijªUqturinmphinhr\_a¬mpknkjm£,inh_oy|r {Ckna rm ©Gai¨¬{gr\xt£r(r\xa]qmp`>mGyi¨rijmGhmu¬ X tuhx Y yt£riny|ªxa6y ψ umphxaIªxhxxyts_mp>ar { φ mu¬ X uy|wxq'\r\xtur(r\_a qmp`>mGyi¨rijmGhmu¬ tuhx yturivy ªxa6y ³ 0mG`UmGh_ahCry tuhU tuastGyyw_`a:3rm~>aªxh_ijra¹Ây|rtura ~>a\Ut<©Cinmpwxy:ztuknkjm£θ,(φ) inh_or\_aY©Gai¨ª>qt£rijmGh&ψ mp¬0~>mur\a:yw_kjrinh_XoOy|w_~_¹ÇY_mp~xkja:`yrmO~Ua>a¬mp`a:«,ijr\ y|rtphx_tp±`3mQQa:k¨¹÷q'\_a6q'ÀCinh_o½ra6q'\_h_ivGwxa:y:³ ÷hÁqmGhCr'tpy|rgrm/r\_atp~Um£©Gapz atua3¬8tpqa:X,i¨r\ÁUmprahCrintpkjkn{«inhQªxh_ijra±qmphCra»}r|¹Ç¬a:atp__knar~>a¹ \Ut<©Cinmpwxy:<opahxa't£ra6 ¬mp`*ªxh_ijra,tp__knary rwxqrw_a:y:³ ¦ a,qmGhxy|ivQa:
(47) ya:Cw_a:hGrintpkQtu__knar'y
(48) mph_kn{pu,\xaa tp__knar,qmG`3>mGyijrinmph±ivy]y rwUq.rwxtpkKCr\Ut£r]iny:< mpinhxy0r\_a:ij,y|rwxq.rw_a:y:C,ijr\xmpwQr,inhGrmQQwUqinh_o½qmphxqw_|¹ ahUq{²ijh r\_a·~>a\xt<©}inmpw_6³ ÷h r\_ivy/qmphCra»}r:,r\_aQa:qin_tp~_inkjijr {µmu¬lr\_a·qmpa6q.rh_a:yy_mp~xkja:` mp¬ xmGUa:|r { Qa:qmp`UmCy|ijrinmphUy,inytuh/mp>ahOxmG~_kja:`/³ ÷hOmGw_syarw_z>a©pa:hO,\_ahOa:y|rivq.rinh_orm±ytu¬ar { xmGUa:|rija6ytpys`3a:hCrinmph_a6Otu~>m£©papxijh«oGah_a:tpk¾r\xaainysh_m`t£»Qin`tuk tp__knary|rwxqrw_al¬mpgtopin©pa:h ~>a\Ut<©Cinmpwxtpk>xmGUa:|r { ψ ³
(49) _mp]r\_ivy,a6tpymphz} altpQmGQrt3yq'\_a:`3a ,\_a:a i kjmQq:tuk}y|>a:qi¨ªUq:t£rijmGhxy Ktpyy|wx`3_rinmphxy ztpasÃ'ÅÇÆ.ÈxÉÅKÈQÆÎ }_mGUa:|rija6y:r\Ut£r(iny:£a6y rivq.r r\_a]qmGhCrmpkj¹ ®xm£¼y|rwxqrw_a mu¬tu__knar'y_tphx 8iji opknmp~xtpkpyUa6qijªUqturinmphxy+ 8opwxtptphGraa6y>tuasËÊ.ÍQΣÏ6Ð8Ñ£ÈQÆÎ Q_mGUa:|rija6yr\xtur¯ivy6a6y rivq.r¾r\_aRqmphCrmpkj¹ ®xm£ ~>a\Ut<©Cinmpwx,mu¬
(50) tp__knar'y³ [ m3©paij¬{½r\xt£r r\xa qmp`>mGyi¨rijmGhmu¬ tp__knar,y rwUq.rwxa6y tuhx yt£riny|ªxa:yRr\xag~>a\Ut<©Cinmpwxtpkx_mpQ¹ a:|r { ψ
(51) mph_a3ªxhxxytXÃ.ÅKÆ.ÈxÉÅKÈQÆÎ RxmGUa:|r { φ mu¬ X ywxq'X\·r\Ut£rlYr\xa±qmG`3>mGyijrinmph·mu¬ θ (φ) tuhx Y yt£riny|ªxa6y ψ ³ Ú oCtuinhz r\_a&a6y|w_kjrinh_oÁ©Gai¨ªUq:t£rijmGhÒyw_~Q¹Â_mp~_kna`ytpa«tpkjoGmpi¨r\_`inq:tuknkj{ q'\xa:q'À£tu~_kna . . . . . . ?@?. ï ÿ .ü ACB ED. . 9. 5 .
(52) &UÆÊ* CÊÆ !. :. ÈQÆÑ£ÏÈQÐvà Π* . y\_m£,inh_o/r\Ut£r X yt£riny|ªxa:y φ iny½t«y r'tuhxxtu'X`mQQa:k¨¹÷q'\_a:q'À}inh_oO_mp~_kna` ij¬,r\xatux_kjar3y|rwxq.rw_a iny3©}ina a:ÒtpytX in_Àpa y rwxqrw_ap y|a:aaG³ oU³ 0,\xijknaOy|\_m£,inh_o&r\xtur3r\_aOqmG`3>mGyijrinmph mp¬ X tphx yt£riny|ªxa6y q:tuh ~Ualq'\_a6q'Àpa:±~}{±y r'tuhxxtu'ra6q'\_h_ivCw_a:y ¬mG `mQQa:k¨¹÷q'\_a:q'À}inh_o½ra`>mp'tuk θx(φ) mGUa:|rija6y0Ymp¬(qmphCra»}r|¹Çψ¬a:a_mQqa6yya:y ³ [ m~>atu~xkja,rm\xtphxQknastux_kjar0y|rwxq.rw_atuhx~>a\xt<©}inmpw_0ijhtw_h_ij¬mp`]t<{pG0aªxy|r0Qa:©pa:kjmGt oGah_a:tpk>¬tp`3a:0mGÀ¬mGtu~xy|r'tpqr]y>a:qijªUq:t£rinmphUy `mQQakvy,,ijr\OQa:yinophxtura:ahCr{>mpinhCry .³R[]\xahz r\_a±`ar\_mQ¶mGwQrkninh_a:Ztu~>m£©paivymG~Qrtpijhxa:Á~}{ÁqmG`~_inh_inh_o&inhxy|rtuhCrinturinmphxymu¬,r\xiny½¬'tu`a mpÀ&mGh ~>mur\Ár\xay|rwxq.rw_tpk0tphxr\xa±~>a\xt<©}inmpw_'tukIkna©GakÇ(,i¨r\ tp__i¨rijmGhxtuk0a6y|w_kjryrm·qmphxh_a:qrr\xar m kna©Gakvy³ !. ". . .
(53) . Qa:q.rijmGhÒbXQa©Gaknmpxyr\xaoGah_a:tpkR¬'tu`a mpÀ·ijh r\_aOyar|rijhxoXmp¬tu~xy|r'tpqr3yUa6qijªUqturinmphxy:³ Ú ¬ ra r\_ainhCrm}_wxq.rijmGh3mp¬zy|in`w_kvt£rijmGhtuhxtqmpa6y|>mphx_ijh_ogknmpopivquCqtpkjkna:yij`½w_knturinmphknmpopivquG0aqmph_hxa:q.r r\_a:ya¬mG`tuknkn{~}{ Qaªxhxijh_os`tpxyz~>ar aa:hyUa6qijªUqturinmphxyztphxlknmpoGinq:tuk£¬mG`½w_kntpap³ ¦ aIr\_ah_a6y|a:hCr r mq'\xtu'tpqra:ivyturinmpha6y|w_kjry:³R[]\_a ªUy|rinystkjmGopivqtukzq'\Utu'tpq.rainyt£rijmGhmu¬yij`½w_knturinmph r\Ut£rsy|rt£ra:y r\xt£r6Q¬mptph}{ ªxh_ijra6,yUa6qijªUqturinmph T }r\xaaliny,tq'\xtptGq.ra:ivy|rivq¬mG`½w_knt χ(T ) ywxq'\±r\xt£r S ≤ T ⇐⇒ S |= χ(T ) r\xt£rivy: T y|in`wxkntura:y S _a:qinyakn{«ij¬ S yt£riny|ªxa:y χ(T ) ³±[]\_aya:qmGhx¾¯qmp`_kna`ahCr'tu{pza:yw_kjr ivy t&~Ua:\xt<©}ijmGw_'tuk0q'\Utu'tpq.rainyt£rijmGhXmp¬sknmpopivqtpk0yt£riny|¬8tpqrinmphr\Ut£ryt<{Qylr\xt£r6¬mptuh}{X¬mp`w_kvt φ mp¬ yin`w_kvt£rijmGhknmpoGinqpGr\_aalivy,t Î GÐ Î (y|>a:qi¨ª>qt£rijmGh θ(φ) ywxq'\±r\xt£r Kb S |= φ ⇐⇒ S ≤ θ(φ) []\}wxysty|>a:qi¨ªUq:t£rijmGh yt£riny|ªxa:yst3¬mp`w_kvt φ _a:qinyakn{ij¬i¨ryin`w_kvt£ra:y r\xa`t£»Qij`tpkzy|>a:qi¨ªUq:t£rijmGh mG~Qrtpijhxa:¬mp` ³[]\_a`tp ivyIªUy|r Qaªxh_a6mph¬mp`w_kvtpyRijh±ymu¹÷qtpkjkna:yin`w_kvt£rijmGhh_mp`tuk θ(φ) ¬mG`tuhU/r\_a:h«a»}rahxφQa6Orm±tuknk¯¬mGθ`½w_kvtpy~}{/QaªUh_ijhxotuh&a9#Ea:q.rij©Ga½y|ra:C,ivyalr'tuhxy|¬mp`t£rijmGh mp¬ ¬mG`½w_kvtpyinhCrmyij`½w_kvt£rinmphhxmp`tpkQ¬mp`/³[]\_a,r mq'\xtu'tpqra:ivyturinmphxy Itphx& Kb qmG`~_inh_ainhCrmt d tpkjmGiny(qmph_h_a6q.rijmGh~>ar aah½r\xa xa:mp'Qa(mu¬xªxh_ijrayUa6qijªUqturinmphxy
(54) mp'Qa:a6~}{y|in`wxknturinmphtuhxr\_a xa:mp'Qa
(55) mu¬>kjmGopivqtukG¬mp`wxkntpa0mGQa:a6l~}{knmpopivqtpkCqmphxya:Cw_a:hxqaG³ Ú ytuh_mpr\_a:(qmpmpknkntp{G£y|in`w_kvt£rijmGh xa6y|a:©Ga:yRr\_ayt£riny|¬8tpqrinmph mu¬¯¬mG`½w_kvtua mu¬(y|in`w_kvt£rijmGhknmpoGinqp³
(56) a»}r:¾}a:qrinmph&inhxy|rtphGrintura6y,r\xa:yaopa:h_a'tukza:yw_kjryrmr\_ah_mprinmphOmu¬Itp__knary:³ Ú hXtu__knariny _aªxh_a6tpy tqmGkjkna:qrinmphlmp¬_`3ar\_mQy>a:qijªUq:t£rinmphUy6,\_ivq'\tuaa:yy|a:hCrivtuknkj{ qmGhGrmGkuop'tux\y rwxqrw_a:y rmpoGar\xaI,ijr\a:hGr{½UmGijhCr'y³+
(57) _wx|r\_a6urma:tGq'\tp__knarR atpyym}qinturatph3inhCra:|¬8tGqapCQaªUh_ijhxo,\_ivq'\ `ar\_mQ_y i¨r
(58) _m£©CivQa6yztuhx,\_inq'\l`ar\_mQ_y i¨r(wxya:y:³¯[]\_a0~Ua:\xt<©}ijmGw_¯mp¬Qtphtux_kjar ivy¾r\_ahtqmGhGra»}r|¹ ¬aa]yUa6qijªUqturinmphQa:in©pa6l©}intgtsyar(mu¬xr'tuhxyi¨rijmGhw_kna:y:³ ¿ {lijhUy r'tuhCrivt£rijmGhmu¬_r\_a0¬tp`3a:0mGÀ¬mp` Qa:q.rijmGh b_C agmp~Qr'tuinh±tu_xmG_ivt£rash_mprinmphxy0mu¬
(59) y|in`w_kvt£rijmGhtphxknmpoGinqsmph±~>mur\r\_aly rwxqrw_'tukEtuhU r\_al~>a\xt<©}inmpw_'tukEkna©pa:kny:³R´w_,qmG`3>mGyijrinmphxtpk¾a6tpymph_inh_oxinhxqin_kna r\_a:h/kjm}mpÀQy,tGy ¬mpknkjm£y . . . . . A |=s φ. 8 . θI (φ) ] B |=b ψ A ] B |=b ψ. ø?> zø @ 8?.
(60) Ð ½È nΣÅÇÐ8Ñ * Ñ uÐ8É . . . . '& & jÊÅKÃÎ *.
(61) . . Ñ _& Ñ<Ã.Ð ÅÇÐ8Ñ *EÎ UÊÆ.Ð É'ΣÅÇÐ8Ñ *. . . . . ". ,\xaa tuhx tpa3tu__knar'y iny tp__knarlqmp`>mGyi¨rijmGhz ivy tuhXtGyyw_`QrijmGh&inh«r\xay|rwxqrw_'tuk nk mpoGinq½tuhxA ψ ivy Bt~>a\xt<©}inmpw_'tuk ]opwxtptphGraaG³3Âry qmpa6q.rhxa:yφy`tuinh_kn{ a:y|rymph·tuh«inhxy|rtphGrinturinmph«mp¬ r\_aq'\Utu'tpq.rainyt£rijmGh Çb mphr\xay|rwxq.rw_tpkRkna©Gakdz ÷h¶mp'Qa:rm&`tpÀpa±yw_ar\Ut£rr\_a `tu»Qij`tuk y>a:qijªUq:t£rinmph θ(φ) ivysijryakj¬Ituh«tux_kjar:>0aijhCrmQQwxqalr\_a3q'\xtu'tpqra:ivy rinq¬mG`½w_knt φI ¬mpgtopin©pa:h tp__knarRinhCra:|¬8tGqa },\_inq'\ivyRqmph£ mGijhxa:rm ~Ua¬mpastu_xkj{}inh_o ³ smGijhxor\xinyR0amp~Qr'tuinhtl©£tuintphGr mp¬3 Kb ]¬mpgtu_xkjarIy:U,\_a:a θ ivysa_kvtpqa:/~}{ φ θI ¾y|mr\_a3`t£»Qij`θtpk yUa6qijªUqturinmphOivysoGwxtu'tuhCra:a:rm ~>atuh/tux_kjar,i¨r\/ijhCra:|¬8tGqa I ³ []\_aOkninh_À ~>ar aa:h r\_a«y rwUq.rwxtpktuhxZ~Ua:\xt<©}ijmGw_'tuk]kja:©pa:knyivy_m£©}inQa6¶~}{¶r\_a«tpxQi¨rijmGhxtuk a:yw_kjr,r\xtury|rwxq.rw_tpk¯yij`½w_knturinmph/ivyqmGhGr'tuinh_a: inhO~Ua:\xt<©}ijmGw_'tukzyij`½w_knturinmphz³ [¯mGopar\_a:,,i¨r\Or\_a ¬8tGq.r'ylr\Ut£r½yij`½w_kvt£rinmphÁivyxa6y|a:©Ga:·~}{·tp__knar½qmp`UmCy|ijrinmphÁtphxr\Ut£r~>a\xt<©}inmpw_'tuk0y|in`w_kvt£rijmGh xa6y|a:©Ga:y¯yt£riny|¬8tpqrinmph½mu¬x~>a\xt<©}inmpw_'tukG¬mp`wxkntpap<r\xiny> wxy|rijªxa6y(_inhxqij_kna 8 ³(ºOmpam£©pa::6~}{lwxyijh_o r\_aq'\xtptGq.ra:ivy|rivq¬mG`½w_kvt χ(A) tGy r\xakjmQqtpkRtpyyw_`Qrinmphmph φ tuhxinh}©pmpÀ}inh_or\_a±y|rwxqrw_'tuk ©Ga'y|inmphmu¬ _ a tpknyma:y|rtp~_kjivy\±r\_aqmG`3xkjarahxa:yy]mu¬ xinhxqin_kna 8/.³ []\_ivyUtu>al¬mQqwUy|a6ylmphr\_ar\xamparinq:tukw_hUQa_inh_h_inh_o«mu¬]r\_a_mp>mGya:·qmG`3>mGyijrinmphxtpkRtuQ¹ xmCtpq'\z³}a:qrinmphyÀpar'q'\_a:y0\_m£µmGw_Rra:q'\_hxinCw_a6y q:tuh~Ua tu_xkjina:rmtuh±a»_tu`_knap³([]\_iny a»Qtp`_kja ivy
(62) Qiny|rinknkja6¬mp`@tkntpoGa¯q:tpya0y|rwxQ{GpQa6yqin~Ua6lakvya,\_a:a0ijh¬w_kjk__artpijk Âu,\_ivq'\yw__>mpry
(63) mpw_ qkntpij`°r\xturr\_ivyIyarwx3ivyIyw qinahCrrm \xtphxQkna,a:kja:©£tuhCr_tGq.rinq:tuk_tux_kjivqturinmphxy:³
(64)
(65) inhxtuknkn{pCQa:q.rijmGh _t<y]qmGhxqknwxyijmGhxy]tuhx _a:yahCr'y _ija:qrinmphxy ¬mG]¬wQrw_al mpÀ>³ . . . . . Ú y y|rtura6tu~>m£©paG6mGw_ tp__mGtGq'\ rmqmp`>mGyi¨rijmGhxtukG©paijªUqturinmphlmu¬xtp__knar'y¯ivy
(66) ijhxy_ina6l~}{gr\_a00mGÀ mGhO`m}_w_kntp©pa:ijªUq:t£rinmph/~}{Odgw_`½~Ua:otphxOzmGh_o * kvt£ra:Qa:©pa:kjmGUa6±¬wx|r\_ag~}{ w__¬a`tph tphx Itu'Qi ³ ¦ aa»Q_kvtuinh_a6&,\}{«tuhU&\_m£ 0aQa:©Civt£ra3¬mG` i¨r inh·tG_Qijrinmphz¯i¨ry\_mpwxknX~Ua >mpinhCra6«mpw_rgr\xt£rgr\xa3knmpoGinq Ú [,Zmph&,\xinq'\Xr\_a:ijg¬'tu`a mpÀ iny ~xtGy|a6¾ztuknknm£yyt£¬ar {/tGyg0a:kjk tGy kjin©pa:h_a:yyg_mp>arina:ygrm/~>aa»Q_a:yy|a6¾¯tphxXr\xturgr\_a`mQQakvy r\xa{XqmphxyivQalqmGhCrtuinhX¬8tuinh_a6yy qmphxy|r'tuinhCry:¯r\_a:ya~>ainh_oXqwUqivtuk¬mGr\xa±a»Qivy rahxqa±tuhUÁqmphUy rwxqrinmphÁmp¬]`tu»}in`tuk0`3mQQa:kny¬mp knin©pahxa:yyxmGUa:|rija6y³½Qijhxqa3r\_a_mp>arina:y0atpa½`tpijhxkj{«inhCra:a6y ra:«inhtua3yt£¬ar {O_mGUa:|rija6y ywxq'\tpy:uaG³ oU³jpr\_atp~xy|a:hxqa]mp¬EinknkjivqijrRqmGhGrmGk}®xm£l£r\_aa,inyIh_mlh_aa6½rmtpx¬8tpijh_a6yyqmphxy|r'tuinhCry
(67) rm mGw_s`mQQa:kny:³ Ú Uturs¬mp`Är\_a6y|a3Qi$#EaahUqa:yinh&y|arw_¯xr\_a`t£»Qin`tuk
(68) `3mQQa:k
(69) qmphxy|rwxqrinmph/ijh&r\_a Utu>a Iiny topknmp~xtpk mGh_ap¾inh«r\_ay|a:hxy|a½r\Ut£rli¨rly|rturygmGwQrg~}{«qmphxy|rwxq.rijhxotuknk>mGyy|in~_kna½y|rt£ra:y mp¬¯r\_al`t£»Qij`tpk>`mQQa:kK³R}inhxqar\_a:yaly r't£ra:y,tuagmp~Qr'tuinh_a: tpy,yar'y]mu¬
(70) qartpijh y|w_~_¬mp`w_kvtuagmu¬
(71) r\_a xmGUa:|r {Gxr\_a`t£»Qin`tuk
(72) `3mQQa:k ivygtukn t<{Qy,a»}>mphxahCrivtuknkj{/kvtuopa:,r\xtphOr\xa½_mp>ar {¬mp`w_kvt_³÷h qmphCr'tpy|r:xmpw_sqmphxy|rwxqrinmph/ijh}©Gmpkn©pa:y,ty|ra:Q¹Â,inya r'tuhxy|¬mp`t£rijmGh mp¬ r\_axmGUa:|r {¬mG`½w_kvtijhCrm yin`w_kvt£rijmGhÁh_mp`tuk¬mG` ,\_ivq'\Ár\_a:h Qina6q.rkj{qmGa:yUmGhx_ygrmXtO`t£»Qin`tukR`mQQa:kK³&[]\}wxy:(mpw_ tp__mGtGq'\inymu¬
(73) t`mGagkjmQq:tuk¾hxturw_altuhx/t<©pmGinxyRw_hxh_a:qa:yytp{a»}>mphxahCrivtuk¾~_knm£]¹Âw_xy:³ []\_aopahxa'tukEra:tur`ahCrsmp¬Iy|in`w_kvt£rijmGhOtuhx ijryknmpoGinq:tuk¯q'\Utu'tpq.rainyt£rijmGhr\xt£rs atp_mpQr\_a:a ¬mGkjknm£y,r\_a½tp__mGtGq'\±rm±knmpopivqtpk q'\xtptGq.rainyt£rijmGh±mu¬IaªUh_a`ahCrg~C{/¯tpyah«tphx/mur\_a'y Q dz ¦ \xijknamGhmphxas\xtphx atuas`mGaa:y|rivq.rin©pasijhmpw_ h_murijmGhmu¬z~>a\Ut<©Cinmpwx:Cwxyijh_o½kntp~Ua:kjkna:r'tuhxyi¨¹ rijmGh±y{}y|ra:`yI't£r\xar\xtuhr\_as`mGaoGah_a:tpkxh_mprinmphmp¬z`3mQ_tpk_rtphxy|ijrinmphy{Qy ra`y qmphUy|ivQaa:3~}{ r\_a:yastpwQr\_mGy:pwUy|inh_oyij`½w_kvt£rinmphtGyIaªxh_a:`ahCr:CtuhxQmpx_ijhxolr\_aQintp`mphx`mQ_tuknijr {¬mp` r\_a knmpoGinqpGmGh±r\_agmur\xa]\xtuhU aa»Crahx±r\xain a:yw_kjryRrm`mQ_tukEknmpopivq,ijr\ a:qwxyijmGh±tuhUa:qwxyij©Ga xmQqa6yya:y:³ . . ?@?. ï ÿ .ü ACB ED.
(74) &UÆÊ* CÊÆ . :. ÈQÆÑ£ÏÈQÐvà Π* . ´w_¬'tu`a:0mGÀivytukvy|m·ijh_®xw_ahUqa:ÒinhZUtur~}{¶ mpÀÁ~}{Zpahxyah@ÊÅ3Î b Â0,\_m_m£©}in_a t hxmphQ¹÷qmG`3>mGyijrinmphxtpk"stuknopmpijr\_`ivq©Gai¨ªUq:t£rijmGh«`ar\xm}&¬mplqmphCrmpk ®xm£!yt£¬ar { xmGUa:|rija6ymp¬ tp__knar'y³ ÷h/xturivqwxkntp:Cr\xiny, mpÀ`murij©£t£ra: wxy]rma:_a6y|a:hCr]tp__knarystpy]op'tux\xy³ . . : ( ,+
(75) []\xinyIya:qrinmphQa:©paknmpUyy|a:©pa'tuk}oGah_a:tpkQa6y|w_kjrytp~UmGwQrRyij`½w_knturinmphtuhU½ijryIa:knturinmph½rmlknmpopivqu³ Ú ¬ ra r\_a3ijhCrmQQwxqrinmph«mp¬0y|>a:qi¨ª>qt£rijmGhxygtuhxXy|in`w_kvt£rijmGhxy~Uar 0a:ahXy>a:qijªUq:t£rinmphUyE a_a:yahCrgyin`wQ¹ kvt£rijmGh«knmpopivqu>,\_ivq'\«ivyty|w_~Uy|armu¬Rsah_hxa:yy|{C¹ º/ijknh_a:sknmpopivq ,ijr\ Kqmp¹4 a6qw_'y|inmph«tG_Qa6¾³¿ { _aªxh_inh_o `tuxy
(76) ~>ar aa:h3yUa6qijªUqturinmphxy(tphxknmpoGinq:tukG¬mp`w_kvtua a a6y r'tu~_knivy|\3tknmpoGinq:tuk}q'\xtu'tpqra:ivytu¹ rijmGh½mp¬Eyin`w_kvt£rijmGhinh½ra`y(mu¬¾y|in`w_kvt£rijmGhknmpoGinq]tuhU¾u©}inqa]©pa'yt_utg~Ua:\xt<©}ijmGw_'tukQq'\xtu'tpqra:ivyturinmph mp¬¯knmpopivqtpk>yt£riny|¬8tpqrinmphz³[]\_a6y|ar ma:yw_k¨r'y]qmp`½~_inh_ainhCrmt3d tpkjmGiny]qmph_h_a6q.rijmGh±~>ar aah±r\_a _a¹ mG_amu¬zyUa6qijªUqturinmphxyImp'Qaa:½~}{3yij`½w_kvt£rinmphtphx3r\_as_a:mp'Qamp¬¾kjmGopivqtuk}¬mG`½w_kvtua,mp'Qa:a6~}{ knmpoGinq:tuk¯qmphxya:Cw_a:hxqaG³3÷h«Uturivqw_kvtu6_r\_a~>a\xt<©}inmpw_'tuk
(77) q'\xtu'tpqra:ivyturinmph mu¬Ryt£riny|¬8tpqrinmphOinhC©Gmpkn©pa6y r\_a qmphUy rwxqrinmphmp¬¯t`mQQa:kU¬mp` t¬mp`w_kvt_},\_ivq'\ivy Î GÐ Î zinhr\_a y|a:hxy|asr\xtur ijry|in`wxkntura:y tpkjkyUa6qijªUqturinmphxy yt£riny|¬{}ijh_o±r\_a3¬mG`½w_kntx³[]\_ivy ,ijknky|a:©Ga½tpyr\_a~xtpyiny¬mGmGw_lqmp`>mGyi¨rijmGhxtuk ©Gai¨ª>qt£rijmGh±`ar\_mQ¬mptux_kjary]a»}xkntpijh_a6±inh r\_alhxa»}rsy|a6q.rijmGhz³ . =. . . . . . .
(78)
(79) iny|rs alijhCrmQQwxqalr\xaopa:h_a'tukzhxmurinmphOmp¬It`3mQQa:k m£©Gatyarsmp¬kntp~Ua:kny L tuhxOtyarmu¬It£rmp`inq xmGUmCy|ijrinmphxy A ³ Ø
(80) ,°Ø Ù Ô - T`mQQak,ѣϣÊÆ L Î * A ÐvÃÎÃ.ÅÇÆ.ÈxÉÅÇÈQÆÊ M = (S, L, →, A, λ) '%(Í}ÊÆÊ Ô S ÐvÃÎÃÊÅ Ñ lÃ'Å÷ΣÅ÷Êà L ÐvÃÎ *xÐ Å÷Ê ÃÊÅ Ñ jÎGËÊ ßà → ⊆ S × L × S ÐvÃÎÅKÆÎ *_Ã.Ð ÅÇÐ8 Ñ *&ÆÊ jÎuÅKÐ8Ñ * A ÐvÃÎ *xÐ Å÷ÊlÃÊÅ Ñ Î£Å÷Ñ 3Ð8É &>Æ%Ñ &_Ñ<Ã.Ð ÅÇÐ8 Ñ *xà , Î * λ : S → P(A) ÐvÃgνÏ<Î çÈxΣÅÇÐ8 Ñ *&ΣÃ'Ã'Ð .*xÐ * Å÷Ñ3Ê'ÎGÉ.ÍÃ.ÅÂÎuÅÂÊ s Å8ÍQÊgÎuÅÂÑ ½Ð8É &UÆÑ &QÑ£Ã'Ð ÅÇÐ8 Ñ *xÃgÅKÍ}ÎuÅ
(81) Í}Ñ Î£Å s yUa6qijªUqturinmph S ѣϣÊÆ L Î * A Ðvà Π&QÎuÐ Æ (M, E) *%(Í}ÊÆÊ M ÐvÃÎ Ñ GÊ RÑuÏ<ÊÆ L Î * A Î * ÐvÃÎÃÊÅ,Ñ gÃ.Å÷ΣÅ÷Ê.à E⊆S ÷hCrwxi¨rij©Gakn{p_mGh_alqtuhr\xijh_Àmu¬ E tGy r\_ayar,mp¬
(82) a:hGr{y r't£ra6y]mu¬ r\_al`mQQakdz Ú y]wUy|wxtpkKx0a ,inkjk ,ijra s −→a t rm/Qa:h_mura (s, a, t) ∈→ ³
(83) _mGgqmph}©pa:h_ija:hxqaGU a½_aªxh_a ∗ = {s ∈ S | p ∈ λ(s)} ¬mG p ∈ A Ð Êr\xa3yar mu¬0tpkjky|rtura:ygyt£rivy|¬{Cinh_o t£rmG`inq½_mp>mGyi¨rijmGh λ p(p) ³ Ú `3mQQa:k iny *xÐ Å÷Ê ËÆÎ *>ÉÍGÐ * X`mQQakvylij¬]¬mptuknk s ∈ S tuhx a ∈ L r\_ayar {t | s −→a t} ivy ªxhxi¨rap³ Ú M y>a:qijªUq:t£rinmph Ú n i s y x ª _ h j i r : a j k / { _ ~ ' u t x h ' q x \ j i _ h ± o ¨ i ¬ v i , y x ª x h ¨ i r a n k O { _ ~ p t x h ' q _ \ n i _ h o u t U h n i s y x ª _ h j i r G a ³ 3 ` Q m Q : a k ivy *xÐ Å÷Êi¨¬ (M, E) ijryy|armp¬y|rtura6yivy,ªxh_ijraGU,\xijkna½tMy>a:qijªUq:t£rinmphOivy,ªUh_i¨raij¬r\_aEw_hxQa:kn{}ijh_o±`3mQQa:k¯ivy³[]\xah_a»Cr y|ra:ivy]rm_aªxh_a r\_a wUy|wxtpk" hxmurinmph mu¬yij`½w_knturinmph mph `m}_akvy,tuhx/yUa6qijªUqturinmphxy:³ 4. . . . . . . . . . . . . . . C. . . . . . . . 5 . . . . . :. . ø?> zø @ 8?.
(84) Ð ½È nΣÅÇÐ8Ñ * Ñ uÐ8É . . . . '& & jÊÅKÃÎ *.
(85) . . Ñ _& Ñ<Ã.Ð ÅÇÐ8Ñ *EÎ UÊÆ.Ð É'ΣÅÇÐ8Ñ *. . . . . . Ñ * S Ã.ÈxÉ.ÍÅKÍ}ÎuÅ'%(ÍQÊ *EÊÏ£ÊÆ
(86) -¢Q Ø @y|in`w_kvt£rijmGhXÐvÃαËÐ *>ÎuÆ ÆÊ nΣÅÇÐ8Ñ * R K Å } Í Ê * (s, t) ∈ R Ð ]Î * λ(s) = λ(t) Ð Ð Ð a 0 ÅKÍ}Ê*«ÅKÍ}ÊÆÊÐvà ÃÑ Ê 0 Ã'ÈxÉÍÅKÍ}ÎuÅ t −→a t0 Î * (s0 , t0) ∈ R s− →s t ∈S ÊÃÎ «Å8ÍQΣŠt yij`½w_kntura6y s %Æ.Ð ÅÇÅ÷Ê * s ≤ t Ð ÅKÍ}ÊÆÊÐvÃÎOÃ.Ð 3È jΣÅÇÐ8Ñ * R Ã.ÈxÉ.ÍÅ8ÍQΣŠ(s, t) ∈ R ÅÂÎuÅÂÊà s Î * t ÎuÆÊy|in`wxknturinmph a:Cw_in©<tpkja:hCr +%Æ.Ð ÅKÅ÷Ê * s = t IÐ s ≤ t Î * t ≤ s []\_a3h_mprinmph«mp¬0y|in`wxknturinmph«ivysa»}rahUQa:«rmy>a:qijªUq:t£rinmphUy (M, E) tuhx (M, E 0 ) ~}{OQaªxhxijh_o i¨¬(r\_aaivystyij`½w_kvt£rinmph R y|wxq'\ r\xt£r¬mpa6tpq'\ s ∈ E r\_a:aivysymp`a t ∈ E 0 (M, E) ≤ (M, E 0 ) ,ijr\ (s, t) ∈ R ³
(87) a»}r:C0a,a»}rahU3r\_as_aªxh_ijrinmphmp¬zy|in`w_kvt£rijmGh3rm r\xasqtGy|a,,\_a:a, a,\xt<©Ga]r 0myUa6qijªUqturinmphxy tuhx 2, E2 ) C~xtGy|a6½mGhQi$#EaahCrR`mQQa:kny:³ ¦ asQmr\_ivyI~}{ªUy|r0Qaªxh_inh_o r\_a |Qivy8 mpinhGr (M1 , E1 ) wxh_ijmGh M1]M(M mp¬Gr\_aIw_hx_akj{}inh_o,`m}_akvyztpy (S, L, →, A, λ) 6,\xaa S = (S1 ×{1})∪(S2×{2}) 2 tuhU (s, i) −→a (t, j) i¨¬ tuhx mph_kn{Áij¬ i = j tphx L = L1 ∪ L2 A = A1 ∪ A2 λ(s, i) = λi (s) , ³ ] [ _ \ : a O h 0 l a p m ± À , j i r « \ y n i ` _ w v k £ t r j i G m x h , y p m h U~}{ Qaªxhxijh_o (M1, E1 ) ≤ (M2, E2) ij¬ a s− →i t M1 ] M2 ³ (M1 ] M2 , E1 × {1}) ≤ (M1 ] M2 , E2 × {2}) Ô. Ø. 4. . . '#. $. . . . . . . . . . . . . . . . . . . []\xa hxa»}ry raÒiny3rm_aªxh_aOt·knmpopivq±r\xturq'\Utu'tpq.rainya:y3yij`½w_knturinmphz³Ò[]\_ivykjmGopivq±ivyQaªUh_a:Òinh r my|raUy Rªxy|r aQaªUh_at~xtGy|ivq kjmGopivqltuhx r\_ahO atpx/a6qw_'y|inmph ~}{wUy|inh_o`mQ_tuk a:Cwxt£rijmGh y{Qy ra`y:³
(88) []\_asa6y|w_kjrinh_olknmpoGinq]ivyIa6Gwxij©£tuknahCrIrm`mQ_tuk µ¹Âq:tukvqw_knwxy >,i¨r\opa:tura:y|rª_»Qa:>mpinhCry tphx~Um<»±`mQ_tpkjijrina:y,mGh_kn{p³ Ø Ô ËÊ&ζÉ'Ñ£È *UÅÂÎCË ·Ð * *UÐ ÅÂÊOÃÊŽÑ
(89)
(90) ¢_ ¤ -¢Q Ø - Ø 8¤_¥¼ Õ :¢ ÊŠϣΣÆ.Ð8ÎCË nÊ.ÃѣϣÊÆÃÊÅKÃ3Ñ Ã.ÅÂÎuÅÂÊÃ Æ Î * CÊ /ѣϣÊÆË X, Y, Z, . . . ¾VÍQÊ Ñ£Æ 3È jÎGÊÑ ~xtGy|ivqyin`w_kvt£rijmGh knmpoGinqÑuÏ<ÊƽÎÃÊÅ L Ñ jÎCËÊ ßýΠ* ÎÃÊÅ A Ñ Î£Å÷Ñ 3Ð8É &>Æ%Ñ &_Ñ<Ã.Ð ÅÇÐ8 Ñ *xýΣÆÊÐ * uÈxÉÅÇÐ Ï<Ê GÊ *>Ê Ë . 4. . . . . -. . . E. . . * . . :. . <. . E. . E. . . . . . . . . . (% ÍQÊÆÊ Î* zÍ}ʱÃÊÅgÑ 'ÆÊÊÏ<ÎuÆ.Ð8ÎGË jÊà ÑÎ Ñ£Æ 3È jÎ φ Ðvà pÊ *EÊ &Î<à È}Ã.ÈxÎ p Ñ£∈Æ 3AÈ jÎGʽÑla Å8∈ÍQÊlLÃ'ÍQÎ%&_Ê p Ñ£Æ ¬p ÎuÆʽÉ'Î jÊ Okni¨rafv(φ) 'tukvy ⊆ V Ø Ô Ñ
(91)
(92) ¢x ¤Z ) -¢Q Ø - Ø ¤x¥¶ Ô ¢ ¤p zÍ}ÊOya`tuhCrinq:yÑ Î ÑuÆ ½È nÎ φ ËΣÃ'Ð8ÉÃ'Ð 3È jÎuÅKÐ8Ñ * nÑ pÐ8ɶѣϣÊÆ L Î * A %Ð ÅK͵ÆÊ.à &_Ê'ÉÅÅ÷Ñ²Î Ñ pÊ M ѣϣÊÆ L Î * A Î * µ Î * Ê *xÏ6Ð ÆÑ * Ê *UÅ ρ : V → P(S) Ðvà GÊ *>Ê Ð * £ÈxÉÅKÐ Ï£Ê Ë φ ::= p | ¬p | X | φ1 ∧ φ2 | φ1 ∨ φ2 | [a] φ. . . 4. . E. . . . . . . . 5 . . . 5 . . ï ÿ .ü ACB ED. * . . . = = = = = =. . 7. E. . . . . . . kpkρ k¬pkρ kXkρ kφ1 ∧ φ2 kρ kφ1 ∨ φ2 kρ k[a] φkρ. ?@?. 5 . . E. . . . . . . λ∗ (p) S − λ∗ (p) ρ(X) kφ1 kρ ∩ kφ2 kρ kφ1 kρ ∪ kφ2 kρ a {s ∈ S | ∀t ∈ S . s − →t. Ð & çÐ8Êà . . t ∈ kφkρ}. . .
(93) . &UÆÊ* CÊÆ . :. ÈQÆÑ£ÏÈQÐvà Π* . ¦ aOij`_knivqijrkn{Ztpyyw_`ar\_aOa»Qivy rahxqa/mu¬sr\_a/¬8tukvya xmGUmCy|ijrinmph ,ijr\ ∗ = ∅ ijh²tuknk ` mQQa:kny:³ ¦ ar\xah¶Qaªxh_a tt = ¬ ff ³ ¯arwUylijhCrmQQwxqay|mG`awxy|a¬w_kRffhxmurturinmpλhxy:(ff) ³ ¦ amp¬ rahÁwUy|a ªUh_i¨raopa:h_a'tuknivyturinmphxygmu¬]r\_a~>mCmGkja6tuhÁqmGh_h_a6q.rin©pa6yg¬mp½,\_inq'\ awxyah_mur't£rijmGhxyywxq'\Átpy W φi tphx W Φ ¬mGt ªxh_ijra±yar Φ mu¬]¬mG`½w_kntpap³
(94) xmplr\_a±yUa6qivtukRq:tpyamu¬,tuha`Qr {yarmp¬0¬mG`½w_knitpap a`tuÀGalr\xaivQahCrijªUq:t£rinmphUy W tuhx V ³
(95) _mGt`mGaqmp`xtGq.rsa_a:yahCr't£rinmph/mp¬ `mQ_tpk¾¬mp`w_kvtua a,inkjkzwUy|a [K]∅φ=¬mGff K ⊆ L ∅rm=Qa:tth_muralr\xal¬mp`w_kvt V [a] φ ³ ÷h«qmphUqara q:tpya:y( a,,ijknkxmG`i¨rr\_asqwxkn{~_'tpq'ÀGar'ytuhx3,i¨ra [a, b] φ inhxy|ra6tp3mu¬ [{a, b}]a∈K ³ Ú y0tly|>a:qintpkxqtGy|aG φ a ,ijra [−] φ ¬mG [L] φ ³ ÷hOmGQa:]rm`tuÀGagr\_aknmpoGinqga»}xa6yyij©Gaa:h_mpwxop\ rmq'\xtptGq.rainyagtpkjkzªxh_ijra`mQQakvy:_0a ¬mGkjknm£ tu'y|a:h
(96) tuhxijhCrmQQwxqa `3mQ_tpkza:Cwxturinmph/y|{Qy|ra:`y]m£©Ga0¬mp`w_kvtua mp¬ ~xtGy|ivq y|in`w_kvt£rijmGhknmpoGinqp³ Ø
(97) ,°Ø Ù ¢ - Ô ¢Q Ø Õ Ô `m}xtukCa:Cwxt£rijmGhy|{Qy|ra:` Ô ÑuÏ<ÊÆ L Î * A Ðvà Π*UÐ ÅÂÊÃÊÅRÑ Ê ÈxÎuÅKÐ8Ñ *_ÃsÃ.ÈxÉÍÅ8ÍQΣÅIÅKÍ}ÊgϣΣÆ.Ð8ÎCË jÊà Xi ΣÆ'Ê Σ&_Σ=Ð Æ1{X %ÐvÃiÊ =£ÐvφÃ.ÅKiÐ *E| Éi ÅR∈Î I} * Ê'ÎGÉ.Í φi ÐvÃ½Î Ñ£Æ 3È jÎ Ñ ½ËÎ<Ã.Ð8ÉÃ.Ð ½È nΣÅÇÐ8 Ñ * jÑ pÐ8ÉѣϣÊÆ L Î * A zÍ}ÊÃÊÅ,Ñ lϣΣÆ.Ð8ÎCË nÊ.ÃÑ:É'ÉÈQÆ.Æ.Ð * Ð * Ðvà &_ΣÆ.ÅÇÐ ÅÇÐ8 Ñ *>Ê Ð *UÅÂÑ3ÅKÍ}Ê ÃÊÅ0Ñ O~UmGw_hx·Ï£Î£Æ.Ð8ÎGË jÊà pÊ *EÊ Ë bv(Σ) = {Xi | i ∈ I} I Î * ÅKÍ}Ê ÃÊÅ ΣÑ «¬aaÏ<ÎuÆ.Ð8ÎGË jÊ.à fv(Σ) ¦ al,ijknkz\_a:hxqa¬mpr\ mu¬ rah/wxya φX rma¬a rmr\_a ¬mp`wxknt φ inhOtuh a:Cwxt£rijmGh (X = φ) ∈ Σ ³ ¢ - Ô Ú ha»_tp`3xkja]mu¬¾tg`m}xtuk_a6GwUt£rinmphy{}y|ra:`°ivy Σ = {X1 = X2 ∧ X3, X2 = Y, X3 = + ³
(98) _mG]r\_ivyy{Qy ra` a \xt<©pa bv(Σ) = {X1, X2, X3} tphx fv(Σ) = {Y, Z} ³ Z} []\_a/h_a»}ry|ra:Zivy½rmQaªxhxar\_a/y|a:`tphCrivqy3mu¬tX`mQ_tuk]a:CwxturinmphÒy|{Qy|ra`/IinhZra`y3mu¬sijry oGa6t£ra:y|rlympknwQrijmGhz³ Ú y|mGkjwQrijmGhmu¬,t/`3mQ_tpkRa6GwUt£rinmphÁy{Qy ra` Σ ivytO`tu η : bv(Σ) → P(S) tGyyinoph_inh_o,rma6tpq'\©£tuivtu~_kna X ∈ bv(Σ) tsyar(mu¬Uy|rtura6yuywxq'\r\xt£rtuknk}a:Cwxturinmphxy ijh Σ tua0yt£riny|ªxa6¾³ º«tuxy η tpamGQa:a6«~}{«>mpinhCr|¹Â,inya½inhxqkjwxyinmphz³ ¦ aªxy|rQaªUh_ar\_aa:h}©Cinmph_`ahCr w_E_t£ra ρ[η] tGy ρ[η](X) ij¬ tphx ρ[η](X) = ρ(X) mur\_a,inyap³[]\xah·0aQaªUh_ar\_a`tu = η(X) X ∈ bv(Σ) ~}{ ΨΣ,ρ(η)(X) = kφX kρ[η] ³ bv(Σ) bv(Σ) ijhx_wxqa6~}{r\_ala:Cwxturinmphxy]inh ΨΣ,ρ : P(S) → P(S) Σ Ø
(99) Ø - ¯ Ø ²y|mGkjw_rinmph«Ñ Î Ñ pÎ UÊ ÈxÎuÅKÐ8Ñ *à <Ã.ÅÂÊ Σ %Ð ÅKͽÆÊà &QÊ'ÉůÅ÷ÑÎ Ñ GÊ Ô Î * Î */Ê *xÏ6Ð Æ Ñ * Ê *xÅ ÐvÃgÎ Î & η : bv(Σ) → P(S) Ã.ÈxÉ.ÍÅKÍ}ÎuÅ ΨΣ,ρ(η) = η zÍ}Êy|a:`tphCrivqy M Ñ ,Î Ñ GÎ UÊ ÈxΣÅÇÐ8 Ñ *à <Ã.ÅÂÊ ρ %Ð ÅKÍÆÊà &_Ê'ÉÅ ÅÂÑ M Î * ρ pÊ *>ÑuÅÂÊ kΣkρ zÐvÃ]Ð Å8à pÆÊ'ΣÅ÷Ê.Ã.žÃÑ ¨ÈQÅKÐ8Ñ * Σ
(100) muraRr\xtur ~}{r\_a00a:kjkj¹ÇÀ}h_m£,hl hxtGy ra¹Â[
(101) tu'yÀCi6ª_»Qa6lUmGijhCr r\_a:mpa` pr\_aRoGa6t£ra6y r
(102) y|mGkjwQrijmGh mp¬ ΨΣ,ρ tpkj]t<{Qy a»Qivy r'yyijhxqa ΨΣ,ρ iny½tO`mph_mprmGh_a`tuÁmph·r\_a±kvt£rrivqa P(S)bv(Σ) mp'Qa:a6&~}{ >mpinhCr|¹Â,inya ijhUqknwxy|inmph¯³ ¢ - Ô
(103) xmplr\_a±a»_tu`_knatu~>m£©pap r\xaainy½tOw_h_ivCw_a±ympknwQrinmph kΣkρ = {X1 7→ ρ(Y ) ∩ ³ ρ(Z), X2 7→ ρ(Y ), X3 7→ ρ(Z)} ¦ awxya3`mQ_tpkIa:CwxturinmphXy{Qy ra`ygrm«tG_Xa6qw_'y|inmph&rm/~xtGy|ivqy|in`w_kvt£rijmGhXknmpoGinqp³ Ú ¬mG`½w_kvt mu¬Ã'Ð 3È jÎuÅKÐ8Ñ * jÑ uÐ8É3ivylqmp`>mGya:&mu¬0t±¬mp`w_kvt mu¬ ~xtpyinq3yij`½w_knturinmphXkjmGopivq½tphx&t`m}xtuk φ[Σ] a6Cwxt£rijmGh·y{Qy ra` Σ ³/[]\_a¬aa©£tuivtu~_kna:y mp¬ φ tuaijhCφra:xara:·~}{«r\_aoGa6t£ra6y rympknwQrinmphmp¬ Σ ³
(104) xmp`tuknkj{ . 4. . . . 5 . >. . . . E. E. . . . . . . . . . . . . E. . :. . . 10. ;=<. 4. . . . . . 5 . $. . . . . . . . 5 . . 5 . . . @. . . . ". ;=<. 10. #. . . . ø?> zø @ 8?.
(105) Ð ½È nΣÅÇÐ8Ñ * Ñ uÐ8É . . . . '& & jÊÅKÃÎ *.
(106) . . Ñ _& Ñ<Ã.Ð ÅÇÐ8Ñ *EÎ UÊÆ.Ð É'ΣÅÇÐ8Ñ *. . . . . , . Ø
Documents relatifs
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes
cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme
In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe
