Exhaustive enumeration of Kochen-Specker vector systems
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Exhaustive enumeration of Kochen-Specker vector systems M. Paviˇci´c — J-P. Merlet — N.D. Megill. N° 5388 Novembre 2004. ISSN 0249-6399. ISRN INRIA/RR--5388--FR+ENG. Thème SYM. apport de recherche.
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(41) . ¶ÆM¸ _¸ +²Å·T²± +²8¸º·º· . . Þ:Þ:ÞàJIÞ:Þ:ÞàJIÞ:Þ:ÞàJImÞWàMÞ:ÞMI 9I à I ?Þ 9I BÞ IÞ $IMà $I BÞ Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ à IÞBÞBÞ 9IÞà¼Þ IÞ $IMà $I BÞ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞ 9IÞà¼Þ IÞ $IMà $ImÞ:Þ K N Þ:Þ:ÞJ à IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞWà IÞà¼Þ IÞsà $IMà $ImÞ:Þ K :Þ Þ:Þ:ÞJ à IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞWà IÞà¼ÞB$Þ IÞsà $IMàoÞ $ImÞ:Þ K WàÎÞ:Þ:ÞJ à IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞWà IÞà¼ÞB$Þ IÞsà¼ÞBÞMIMàoÞ:Þ $ImÞ:Þ ?Þ K K Þ:Þ:ÞJ à IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞWà IÞà¼ÞB$Þ IÞsà $IMàoÞ $ImÞ:Þ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞWà IÞà¼Þ IÞsà $IMà $ImÞ:Þ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ?ÞWà IÞBÞBÞ 9IÞà¼Þ IÞ $IMà $ImÞ:Þ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ IlÞ:ÞBÞWà IÞ:Þ à IÞBÞBÞ 9IÞà¼Þ IÞ $IMà $I BÞ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWàMÞ:MÞ I 9I à I ?Þ 9I BÞ IÞ $IMà $I BÞ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ:ÞJà ImÞWà $I 9I à I 9I BÞ I $IMà $I BÞ K Þ:Þ:ÞJà IÞ:Þ:ÞJà IÞ:Þ $ImÞWà $I 9I I 9I BÞ I $IMà $I K N Þ:Þ:ÞJ à IÞ:Þ $IÞ:Þ $ImÞWà $I 9I I 9I I $I $I K :Þ MI $I $I $I 9I I 9I I $I $I ] kuvkm`M|kmuTrO5 5qn_rO suTk¥rj__yz|i_¾jsk[z`tTOrO|uvkm[z^ pG?¤Bkm|O¤ji_© ] ¦ºk`_|GO|lkuTOtvtTh%|m`orQ?`_|uvzs¾ k[z`Otv?rO|uÓk[z^i~k|mkikr+pG?¤Bkm|O¤UO?OuvÁkquvkm`_|Qkuvr? Oj¾ÒGGOtvtThÑpGO¤Bkm|O¤:uTz¨tTtkm[z`¿¥¼h kr¨k[z`p`_?uvzGuvzDGÁ`½j[Gysi~kuvzUtTtr?iiluTpztT`?imimuv?z^`_BkiM©DÜH¦k[z`ÏOOÏuvkm`M|kmuTrOGiM¾\Û_GÛ|` psO¤Bkm|O¤jiM© Z\[z`G`½:k6`½z^ztT`il[GrQ¿i km[z`i^`c¨cÂ{Ñjux?|O^é¿uÓk[qk[z`im`Mr?GqO|rOyzn|m`M^rQO`M © ] BuT ¿¥`rO^uvkHilr?^`r¦ km[z`uvkm`M|kmuTrOGi¥¦§r?|pz|`_:uvk~hO©Z\[GuTiHc+cÂ{ juxO|^ _Ïp`Oiimuv?z`M%Q¢Ûi~kQkm` ?i\uTiim[zrQ¿p:h%km[z`txOilkuÓk`_|Qkuvr? © à K MIoà MIoà NP>I<R >I8R I N MI MIQP 2I >I à à¼Þ:ÞBMÞ Ioà $Ioà $I $I 9I I ?Þ 9I IÞ $I K4à¼Þ:ÞBM Þ Ioà¼Þ:ÞBMÞ Ioà $I $I BÞ I I ?Þ 9I IÞ $I ?Þ 4à¼Þ:ÞBMÞ Ioà¼Þ:ÞBMÞ Ioà¼Þ:ÞBMÞ I $I BÞ I OÞ I ?Þ 9IÞ IÞ $I ?Þ à¼Þ:ÞBMÞ Ioà¼Þ:ÞBMÞ Ioà¼Þ:ÞBMÞ IMà¼Þ?Þ:MÞ I_à¼Þ BÞ IÞ:Þ?Þ IÞBÞBÞ 9IÞ IÞ $I ?Þ N ÞWà¼ÞBM Þ IÞWà¼ÞBMÞ IÞWà¼ÞBMÞ I $I BÞ I OÞ I ?Þ 9IÞ IÞ $I ?Þ N:Þ ÞWà¼ÞBM Þ IÞWà¼ÞBMÞ IÞ $I $I BÞ I I ?Þ 9I IÞ $I ?Þ NWàÎÞWà¼ÞBM Þ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ I $I BÞ I Gà I ?Þ 9IÞ IÞ $I ?Þ NK ÞWà¼ÞBM Þ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼Þ BÞ IÞ:Þsà IÞBÞBÞ 9IÞ IÞ $I ?Þ N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà IÞBÞBÞ 9IÞ IÞ $ImÞBÞ N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞBÞ 9IÞBÞ IÞ $ImÞBÞ N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞBÞWà IÞBÞ IÞsà $ImÞBÞ N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞBÞWà IÞBÞ:Þà IÞsà¼Þ $ImÞBÞ Gà N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞBÞWà IÞBÞ:Þà IÞsà¼ÞBMÞ ImÞBÞ:Þsà N ÞWà¼ÞBMÞ IÞWà¼ÞBMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞBÞWà IÞBÞ:Þà IÞsà¼ÞBMÞ ImÞBÞ:Þsà Z\[G`Otv?rO|uÓk[z^fuvkm`M|km`MDOkuv^`MiuvDkm[GuTiMOim`O¾ uTG_tvyGzuvzÏ?psO¤Bkm|O¤jiM©n `orQ?`_|h¦§|rO^Ökm[z` txOilk/pG?¤Bkm|O¤uxi¥il[zrQ¿ilkO|lkuvGQk¥uÓk`_|QkmuTrOGÛO¾:Gnk[z`8tT?i~k/uvkm`M|kmuTrOim[zrQ¿i/qilys_`oimil¦§yztQ¢Û ilkkm`Oiimuv?z^`_BkM© K . . K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(42). . . . . . . . . % . . . . . . . . . . . . . . . . .
(43). . . .
(44). . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(45). . . . +-, +..
(46) ®Q·¹Æo¸º¬®M°Ì:²_¬G¯ ²°Q²_ÅÆQ²°_±£®QÅdÄ»¼Ä±«² Ä. . ] ¨rOjkuvr?Gt ¦§`MQkyz|`r¦-km[G`z|rOO|^ϾGMtTtv`oÁ°·Ó´:ı£²_Å Åm²Ä_®Qűµ¸º¬ O¾Wklk`_^jkikmrim`_`MÏyGÂkm[z` li kkm`nOiiluTOz^`M?k8il`o|[ © ] ilr?|lk`MÂtTuTilkrO¦/O|rOyGGiuxi8_rOGilkm|yGkm`MÂ?i¦§r?tvtTrQ¿iM© ] O|rOyz¨[zrBil`M k[GQkq[GOikm[z`^nrBi~kqO`Mkmr?|iduTÎr?^^nr?Ñ¿uÓk[Àkm[z`|m`M^%uTzuvGÂO|rOyzGiM¾-GÑuvkuxiztxO_`MÑQkqkm[z` p`_?uvGzuvGnrO¦<k[z`tvuxilkM© ] ¦ºk`_|Hn?|mr?yzuxiztxO_`MrOkm[z`tTuTilkM¾zkm[z`d|`_^%uTzuTzO|rOyzGik[GQkHO|m`8zrk h?`kdrO+km[z`ntvuxilkO|m`nimMzG`M)¾)s¦§rO|d`oO[+imyG[+?|mr?yz¨¿¥`n_rO^zyjk`k[z`:yz^p`_|dr¦O`Mkmr?|iuÓk [sOiuT¨r?^^nr?¿uÓk[Âkm[G`O|rOyGGitT|`MOzhuv¨km[z`qtvuxi~ko©Üz`¿uvkm[Âk[z`^rBi~kH?`MkmrO|iuT+r?^^nr? uxiim`_tT`Mk`M¦§rO|GtT?`_^`M?kk¥k[z``_srO¦k[z`tTuTilkM© Ð [z`MÀkm[G`^%uTÎtTOr?|muvkm[G^Ö|yzGiM¾ uvkni_OGidk[z`?|mr?yzGiuTÀkm[G`rO|j`M|km[Gkk[z`_hÀGs`o|r? k[zuxi/tTuTilkM©T©&Z\[:yGi/uvk¿uTtTtsz|rj`oimi/z`½:k/k[z`8O|rOyznkm[sQk\[GOi6km[z`^nrBi~k¥O`okmr?|i/uvrO^^rO%¿uvkm[km[z` ?|mr?yzGiOtv|`M?jh%z|r:_`Miil`o)©/Z\[z`[GrO`uTikm[GkpBhz|r:_`MiiluTznkm[G`^r?ilkHil`MO`_|`drOsi~k|OuvBki¥Òs|ilkM¾ _rO suTkmuTz%OiiluTOz^`M?kikm[Gktv`oOkmr%pG?¤?k|?¤ji/¿uTtvt<ps`|`MimrOtTO`o%`MO|mtThO© ª£À^r?ilk_?il`oi_¾ km[z`_tvysi~k`_|z|`MimrO|mkmuTzÂtTOr?|muvkm[G^f|m`ojyG_`Mi8km[G`:yz^p`_|rO¦¥uvkm`M|kmuTrOGiM©Z\[z` G|m`MBuTrOysi\c+cÂ{juTOO|^ G|mrQ:uxj`Mi\`½zO^nGtv`dr¦ ps`oi~km¢«MOim`dps`M[G¼:uvr?|", à K MIoà MIoà NP>I<R >I8R I N MI MIQP 2I >I à MI $I $IMà¼Þ?Þ:MÞ I_à¼Þ 9IÞ:Þ IÞBÞ 9I I $I K MI ?M Þ I $IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þ IÞBÞ 9I I $ImÞ MI ?M Þ I à $IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞ 9I ?Þ I $ImÞ à $I ?MÞ I à $IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ I ?Þ I OÞ $ImÞ à $I ?MÞ I àoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ I OÞWà $ImÞ OÞ àoMÞ I ?MÞ I àoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ IÞ?ÞWàoMÞ ImÞ BÞ?Þ àoMÞ I àoMÞ I àoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ IÞ?ÞWàoMÞ ImÞà¼Þ?Þ Þ:ÞWàoMÞ IÞ àoMÞ IÞ àoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ IÞ?ÞWàoMÞ ImÞà¼Þ?Þ N Þ:ÞWàoM Þ IÞ:ÞWàoMÞ IÞ àoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ IÞ?ÞWàoMÞ ImÞà¼Þ?Þ à¼Þ Þ:ÞWàoMÞ IÞ:ÞWàoMÞ IÞ:ÞWàoMÞ IMà¼Þ?Þ:MÞ I_à¼ÞBÞ:Þ IÞ:Þsà¼$Þ IÞBÞà¼Þ IÞBÞWào$Þ IÞ?ÞWàoMÞ ImÞà¼Þ?Þ tTyGilkm`M|z|`MimrO|mkmuTzÏ|m`ojyG`oUkm[z`:yz^qps`M|rO¦¥uvkm`M|kmuTrOGid¦§|rO^ OkrÁÛM¦§r?|km[zuxi`_½z^ztT`O¾<¿uvkm[ Gr%pGO¤Bkm|O¤:uTz%QkOtvtµ©¥ª£Ârkm[G`_|HMOim`Mi\k[z`uT^nG|mrQ?`_^`_BkuxitT`Miij|^%QkuTO©ª£Ïk[z``_½jO^ztv`rO¦ ¥Ops`MtvtTr ic+cÂ{Îjux?|O^ OpsrQ?`O¾Okm[z`8:yz^p`_|r¦<uvkm`M|kmuTrOGi/¿¥?i6|`MjyG_`M¦§|rO^ ?dkmr% Bj¾O¿uvkm[ Ûo?pGO¤Bk|?¤:iM© tTyGilkm`_|/z|m`oilr?|lkuvG8uxi&`oi~kuv^%Qk`Mqkmr[s¼O`zG|mr¼½juT^km`Mtvh 3>Õ 5 p`_[s¼BuTrO|o¾¿[z`M|m`oOikm[G`^%uT Otv?rO|uÓk[z^ _OuTÏz|uvG_uvGtv`[G¼?``_½jsr?z`_Bkmuxt)p`_[s¼BuTrO|o© ª£"z|OkuT_`O¾&¦§r?|nkm[z`Âjux?|O^iqr¦uvBkm`M|m`oi~knkmrÑyGiM¾6k[z`ÏrQO`M|m[z`oOÑrO¦Hkm[G`Ï_tvysi~k`_|z|`MimrO|mkmuTz Otv?rO|uÓk[z^#km`MGzi8krp`O¾rOѼO`M|OO`O¾WimtvuTO[BkmtTh¨?|m`oQkm`M|Hk[GDk[z`%im¼:uTz?id WrO|j`o¦§rO|8k[z`%^%uT Otv?rO|uÓk[z^Ï© J¥`o_ysil`8^r?ilkzuTOO|^%i/rO¦<uT?k`_|`Milk¿uvtTt)[G¼O`8O`M|mhnkuv?[?k_rOyzztTuTznkm[z|rOyz?[zrOyzkdÈXu>© `O© ^%OBhO|rOyzGi¥¿uTtvt<[G¼O`8O`okmr?|i¥uTÂrO^^rO¿uvkm[Ïrk[z`_|?|mr?yzGiɾBkm[z`^%OuvÂtTOr?|muvkm[G^ km`_szi\kmr p``½:k|m`M^n`Mtvh¦XOilkOtv|`M?jhO©6cÏrBi~krO¦rOyG||myzsi\¿`M|m`jr?z`d¿uÓk[zrOyjkH_tvysi~k`_|z|`MimrO|mkmuTzn`_GOpztv`o)© ª£Âk[z`¦§yzkmyz|`O¾uÓ¦/zuTOO|^%i\¿uÓk[+imG|il`M|r?yzztTuvz|`i~kyGjuT`M)¾)tTyGilkm`M|Hz|`MimrO|mkmuTz^%¼hp`¢ _rO^`^rO|`yGim`¦§yGt>M© #zr?|imyG[jux?|O^i&km[z`M|m`uTiO|`Mkm`_|/tvuT¤O`MtvuT[zr:rjnkm[Gk`½jrOz`MBkmuxtGp`_[s¼BuTrO| ¿uTtTt-ilkO|lk8kmrp`n`_½j[zuvpGuÓk`M)© ] iiluT^ztv`n`½zO^nGtv`?¾)¿`nuvsil`M|lk`M+[GOuvUr¦/z`M¿4?|mr?yzGiuvUkm[z` ^uxzjtT`r¦6¥p`_tTtvr ic¨c¨{ juTOO|^ ?i/¦§r?tvtTrQ¿"i , à K >IMà K MIMà MI_à NBP>I#)$IB)5&E5MIE"%$,bI,9*-9+MI+#. ST$ILT>/ 2>3I<R >I<R MI N MI >I . . .
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