• Aucun résultat trouvé

Automatic Abstraction Generation : How to Make an Expert Verification Technique for Security Protocols available to Non-expert Users

N/A
N/A
Protected

Academic year: 2021

Partager "Automatic Abstraction Generation : How to Make an Expert Verification Technique for Security Protocols available to Non-expert Users"

Copied!
22
0
0

Texte intégral

(1)

HAL Id: inria-00116918

https://hal.inria.fr/inria-00116918v2

Submitted on 30 Nov 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Automatic Abstraction Generation : How to Make an Expert Verification Technique for Security Protocols

available to Non-expert Users

Yohan Boichut, Pierre-Cyrille Héam, Olga Kouchnarenko

To cite this version:

Yohan Boichut, Pierre-Cyrille Héam, Olga Kouchnarenko. Automatic Abstraction Generation : How to Make an Expert Verification Technique for Security Protocols available to Non-expert Users. [Re- search Report] RR-6039, INRIA. 2006, pp.21. �inria-00116918v2�

(2)

a p p o r t

d e r e c h e r c h e

ISRNINRIA/RR--6039--FR+ENG

Thème SYM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Automatic Abstraction Generation

How to Make an Expert Verification Technique for Security Protocols available to Non-expert Users

Yohan Boichut — Pierre-Cyrille Héam — Olga Kouchnarenko

N° 6039

Novembre 2006

(3)
(4)

#

$ &% (') *+ -,/.102!435!7689 ;:< =>?@BAC"

D E>7GF-H519IJ &KL I "I+MNPOQ9.102!4RS!

TUWVYX[Z]\^UW_a`CVbc

? de _gfihjhkfmlnpohk_aqgqgfr>siX[t

?? du qgvWXxw>UWb`CVZYX[hkfyZz[U

??

{!|Q}~@€iƒ‚„…€‡†‰ˆ‹ŠŒ}j~^kˆˆŒ†i~pŽGy’‘”“i•–jˆ

—˜™mš›Šœ&žLŸ& ¡Šƒ¢9L€–€‰£‹€

¤¥m¦–¦[§˜ŒŠ¨‰"˜™j©ª|–j˜™©ª|–¬«W­®§¯y°§±p„…ž&C²§~pŽ–˜™³§¯§¯§®"„µ´j¶^¦Q¥§·§kˆ

¸¹ºj»¼C½–¾§»§¿ ¤ k¥§©ª|Q¥§Ž–‘À’‘’Š›†¥§«Q¥mÀ†‰ˆ‹‘”ˆ!‘”ˆ&©j«iŠŒ˜ª¥mÁy˜&¨‰k©‘”¨‰‘’«Q·1ŠŒ|–^ˆ‹k©•–˜™‘’Š›†¦–˜™§Ž–À~ÃÁ§˜&¦–˜Œ§ŠŒ‰©yÀˆ

Ä

‘’ŠŒ|Å¥§«•Q«iŽ[§•Q«Q¨‰j¨«‡•–~pŽGj˜ mÁYˆ‹kˆŒˆŒ‘’y«QˆjƖ{!|–‘Àˆ¦–˜ŒyŽ–À~J‘”ˆ ‘À«·y«–j˜™¥§W•–«Q¨‰k©‘”¨–¥mŽ–ÀÁ§˜&‘’«‰ÇG«–‘ÈŠ™É

ˆ‹Š™¥mŠŒˆŒ†‰ˆ›Š™~1ˆÆmÊ&

Ä

j²§j˜jËC¥"ˆŒ§À•‰ŠŒ‘À§«^~1¥Ì†©y«Qˆ‹‘”ˆ‹ŠmÁG¦[˜ŒÁ§˜™~@‘’«Q·ƒ˜™j¥y©ª|Q¥mŽQ‘’À‘ÈŠ›†p¥m«Q¥§’†‰ˆŒ‘Àˆ§«1ˆ™¥CÁŠ›†yÉ

¦Q˜Œkˆ‹j˜Œ²‡‘À«–·^¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«QˆEmÁYˆ‹k©•–˜™‘ÈŠ›†¦–˜Œ§ŠŒ‰©yÀˆjÆ

£Í«p§˜ª¨‰˜ŠŒƒ~1¥mΧϊŒ|–‘”ˆŠŒk©ª|–«–‘”“y•Q9¥Ì²C¥m‘À”¥mŽ–ÀÁy˜|–‘À·§|p’j²§j‡ˆŒ¦[j©‘’ÇG©j¥CŠŒ‘À§«À¥§«–·§•Q¥§·§kˆÀ‘’ÎyƒÐ9щÒÔÓWÑ

¥§«Q¨ÕÒÖ׃ØÙ&ÚWË

Ä

Û¨–ÇQ«–ۈ™¥CÁÂÅ¥§«Q¨/ˆ‹y•–«Q¨Ü¥mŽQˆ‹ŠŒ˜ª¥§©ŠŒ‘À§«Qˆ^mÁ¦–˜™mŠ™‡©§!Š™˜™¥§«Qˆ‹‘’ŠŒ‘À§«/ˆŒ†‡ˆ‹ŠŒj~1ˆ@‘’«iŠŒ

˜™

Ä

˜™‘’ŠŒ‘À«–·ÝˆŒ†‡ˆ‹ŠŒj~1ˆÆ!{!|–jˆŒ2¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«QˆP¥§’À

Ä

ŠŒ|–Þ¥m•‰Š™§~1¥CŠ™j¨¡·y«–j˜™¥mŠŒ‘À§«¡§Á¥m¦–¦–˜™Ì߉‘’~1¥mŠŒ‘À§«

Á•Q«Q©7Š™‘’y«Qˆ"Š™Û«QˆŒ•–˜™Pˆ‹y•–«Q¨‰«Qjˆ™ˆ"mÁ!ŠŒ|QP˜Œk¥§©ª|Q¥§Ž–‘À’‘’Š›†à¥m«G¥mÀ†‡ˆŒ‘”ˆÆ£Í«á¥y¨–¨‰‘’ŠŒ‘À§«Ë

Ä

P¦Q˜Œy¦Giˆ‹1¥Å«–

Ä

˜™¦Q˜Œkˆ‹j«yŠª¥CŠ™‘’y«mÁˆ‹k©˜™j©†1¦–˜Œy¦Gj˜‹Š™‘’kˆË–ˆŒ•–‘’Š™¥§Ž–’ƒŠ™Pˆ‹j~^‘’Éͨ‰j©‘À¨‰ƒŠ™|–ˆ‹k©•–˜™‘’Š›†P¦–˜™§Ž–À~8Æ

Lˆ§•Q˜~1¥m‘À«x¦–•–˜™¦Giˆ‹1‘”ˆ"Š™à¥m•‰Š™§~1¥CŠ™P¥§ˆ"~p•Q©ª|ᥧˆ¦GiˆŒˆŒ‘’ŽQ’1Š™|–¥§«Q¥mÀ†‰ˆ‹‘”ˆmÁ ¦–˜™mŠ™‡©§”ˆƒÁ§˜

¥§«>•Q«iŽ[§•Q«Q¨‰j¨«‡•–~pŽGj˜ mÁˆŒjˆ™ˆŒ‘’y«QˆË‡y•–˜¥mŽQˆ‹ŠŒ˜ª¥§©ŠŒ‘À§«[âm¥m¦–¦Q˜ŒÌ߉‘À~@¥mŠŒ‘À§«@ŽQ¥yˆ‹k¨>¥§¦–¦–˜™y¥§©ª|¦–˜ŒC²‡‘”¨‰jˆ

¥§«áãP©‘’j«yŠ^²§j˜Œ‘’ÇG©¥mŠŒ‘À§«<Š™iyaËä[åYæiÓWÒÆY{!|–‘”ˆ

Ä

¥Ì†§ËŠŒ|–>˜Œk“i•–‘’˜™~@j«yŠ^mÁ&¥§«á߉¦[˜ŒŠp•QˆŒ˜@©¥§«áŽG

˜™~@C²yj¨1Á˜™§~JŠŒ|–"²y˜™‘ÈÇG©j¥CŠ™‘’y«>©ª|Q¥§‘’«Æ

çÅèiéWê™ëì

¼Cíº§¿

€‡k©•–˜™‘’Š›†"¦–˜Œ§ŠŒ‰©yÀˆjËCˆŒ¥mÁ ¥m«Q¨^ˆ‹y•–«Q¨p¥mŽQˆ‹ŠŒ˜ª¥§©ŠŒ‘À§«QˆjË̲§˜™‘’ÇG©¥mŠŒ‘À§«QˆjËk¥§¦–¦–˜™Ì߉‘’~1¥CŠ™‘’y«QˆjË

¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«Qˆ

? îgïÏîÍð§ñ!òïÏóªôyôióªõªöCó™÷øjùûúýü‡þ‰ÿkù 9ù›ùûõ›ø

?? îEôiùÌó›õÍùyó‹øjô yó ÿk÷!jöyó™÷øjùûúýü#"$ió7ø÷&%'kö(Ìÿ) yô‡ø+*,9úûù)iôyù-+ ./™ÿk÷!›ó01

(5)

#

RSS =>?^B9.102!>+K!768E >N01EI >

>

º "!

¿

œ$#¥m«G¥mÀ†‡ˆŒÛ¨%#¥CŠŒŠŒ‘À·§«G¥mŽ–‘À’‘’Š'&2« ˜(&&k©˜™‘ÈŠ™•–˜™à¥)&Š(&2¥y¨–¥m¦‰Š(&+*ᨉ‘-,.&j˜Œj«yŠªˆ>©§«iŠŒ߇ŠŒjˆ

¨–²/&j˜Œ‘’ÇG©j¥CŠŒ‘À§«Ë«–§Š™¥m~@~@«iŠkË©À•–‘9¨–jˆp¦–˜Œ§ŠŒ‰©y’kˆ¨‰ˆ0&k©•–˜™‘’Š'&§Æ—§•–˜@¨‰kˆpˆŒ†‰ˆ›Š™}~@jˆ‘’«‰ÇG«–‘Àˆjː’

¦Q˜ŒyŽ–’}j~@!¨–ˆ0&k©•–˜™‘ÈŠ(&1¨‰kˆY¦–˜™mŠ™‡©§Àjˆ32Ԋ™§•‰Š9©§~@~@!’ ¦Q˜ŒyŽ–’}j~@¨%#¥mŠ‹Š™‘À·§«Q¥§Ž–‘’À‘’Š'&!jˆ‹Š«@·/&j«4&˜ª¥m

‘À«Q¨5&k©‘”¨–¥mŽQ’yÆ[œ6#•‰Š™‘’À‘”ˆŒ¥mŠŒ‘À§«à¨%#¥m¦Q¦–˜ŒÌ߉‘À~1¥CŠŒ‘À§«GˆŠ¨%#¥mŽQˆ‹ŠŒ˜ª¥§©ŠŒ‘À§«Qˆ&jˆ‹Š¥§’y˜™ˆ&•–«–p¥§ÈŠ™˜™«Q¥CŠ™‘’²y¦[§•–˜

ˆŒ~@‘’ɨ4&j©‘”¨‰j˜@©jˆ^¦–˜™§Ž–À}~@kˆÆY‚Û¥§‘Àˆ^À•–˜1¨5&ÇQ«–‘’ŠŒ‘À§«ÜŠ1~1¥m«–‘À¦–•–”¥CŠ™‘’y« «4&k©kˆŒˆŒ‘ÈŠ™«iŠ1ˆ‹y•–²§j«yŠ@•–«–

©˜ŒŠ™¥§‘’«–߇¦[˜ŒŠŒ‘”ˆŒ§Æ

ž&§•Qˆ¦–˜Œy¦Giˆ‹y«Qˆ"¨–¥§«Qˆ©Šp¥m˜ŒŠŒ‘”©ÀP¨‰P©§«–«–k©7Š™˜•–«Q1ŠŒk©ª|–«–‘”“y•Q¨‰P²7&˜™‘ÈÇG©j¥CŠ™‘’y«àÁy«Q¨5&PˆŒ•–˜

¨–jˆ¥m¦–¦Q˜ŒÌ߉‘À~@¥mŠŒ‘À§«Qˆƒ¨‰@˜(&&j©˜Œ‘’ŠŒ•Q˜Œ^ˆ‹•–˜"¨‰@”¥m«–·i¥m·yjˆL˜'&j·§•–À‘’j˜™ˆƒ¨%#¥m˜™Ž–˜™jˆƒ¥m•‰ßà”¥m«Q·y¥m·yjˆL¨‰1ˆ‹¦.&j©‘ÈÉ

Ç[©¥CŠ™‘’y«à¨‰p|Q¥m•‰ŠŒÉg«Q‘’²yj¥m•8Ð9щÒÔÓWÑ1Š@ÒÖ׃ØÙ&ÚWÆÔ¢EŠ‹Š™^©§«iŠŒ˜™‘’ŽQ•‰ŠŒ‘À§«à¥¦Gy•–˜ƒŽ–•‰Š"¨‰Áy•–˜™«–‘’˜ƒ•–«–

¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«©§˜™˜Œk©7Š™¨9#•–«8¦–˜™mŠ™‰©§À1Ð9щÒWÓWÑ@y•ÞÒÖ׃ØÙ&Ú>¦[§•–˜&¥§‘’«Gˆ‹‘¥§¦–¦–À‘À“i•–j˜ À¥@²7&˜™‘ÈÇ[©¥CŠ™‘’y«

“i•–ƒ«–y•QˆE¥Ì²y§«QˆE˜™«Q¨‰•Qƒ¥§•‰ŠŒy~@¥mŠŒ‘”“i•–&•–’Š'&j˜Œ‘À•Q˜Œj~^j«iŠjƉœLŠŒy•‰Š9kˆ›Š ¨5&j²§À§¦Q¦:&¥m•ˆ‹j‘’«¨‰L;#§•‰Š™‘’

¥§•‰ŠŒy~1¥CŠŒ‘”“i•–ä[åYæiÓWÒޓi•–‘aË.<1¦Q¥§˜‹Š™‘’˜¨%#•–«–^ˆ‹¦.&j©‘ÈÇ[©¥CŠ™‘’y«Å¨‰¦–˜™mŠ™‡©§À"¨‰|Q¥§•‰Š‹É«–‘À²§j¥§•8¦Gj•‰Š=&Š™¥CÉ

ŽQ’‘À˜L•Q«2¨‰‘”¥m·y«–yˆ‹ŠŒ‘”©¨‰^ˆ0>Q˜ŒŠ'&¦[§•Q˜LÀjˆƒ¦–˜™§¦–˜(&Š(&jˆL¨‰^ˆŒj©˜ŒŠLŠƒ©^¦[§•–˜ƒ•–«à«Q§~ŽQ˜Œ^“y•Q”©§«G“y•Q

¨9#ß?&k©•‰Š™‘’y«QˆjÆ

@ ì »kº ê ¾/A º¿ —ϘŒ§ŠŒ‰©y’kˆ¨–!ˆ'&j©•–˜™‘ÈŠ(&§ËC²/&j˜Œ‘’ÇG©j¥CŠŒ‘À§«^¥m•‰Š™§~1¥CŠ™‘À“i•–yËC¥mŽQˆ‹ŠŒ˜ª¥§©ŠŒ‘À§«p©§˜™˜Œk©7Š™§ËC¥m¦–¦Q˜ŒÌ߉‘’É

~1¥mŠŒ‘À§«QˆjˉÀ¥§«–·y¥§·§kˆE¨‰"|G¥m•‰ŠŒÉg«–‘À²§k¥m•

(6)

C DE F1GIHKJMLONPFIQRHSE

&•‰ŠŒy~1¥CŠŒk¨1¥m«Q¨1©§~@¦–•‰Š™˜ŒÉ¥yˆŒˆŒ‘”ˆ›Š™j¨p²§˜™‘’ÇG©¥mŠŒ‘À§«@¥m«Q¨@²C¥mÀ‘”¨–¥CŠ™‘’y«1mÁ©˜™†‡¦‰ŠŒy·§˜ª¥m¦–|–‘”©E¦–˜Œ§ŠŒ‰©yÀˆÏ¥m˜™

¥xÁ¥§ˆ‹Š‹É ·§˜™

Ä

‘’«–·x¥§¦–¦–À‘À©j¥CŠŒ‘À§«ÜÇQjÀ¨¡Á§˜PÁy˜Œ~1¥§~@ŠŒ|Q‡¨Qˆ>¥§«Q¨ÜŠŒk©ª|–«–‘”“y•QjˆP‘À« ©y~@¦–•‰ŠŒj˜>ˆ™©‘À«Q©§Æ

{!|Q‘Àˆ9‘”ˆÏŽ[j©j¥m•QˆŒL©˜Œ†‡¦‰Š™§·§˜ª¥m¦Q|–‘À©¦–˜Œ§ŠŒ‰©yÀˆE¥m˜™&«–§Š™¥§Ž–’†@~@§˜™L¨–‘ÈãP©•QÈŠ!ŠŒ^•–«Q¨–˜ªˆ›Šª¥m«Q¨@Áy˜E|‡•–~1¥§«

¨–jˆŒ‘’·y«–˜ªˆ¥m«G¨x•QˆŒ˜ªˆÆ£Í«G¨‰k¨ÔË¥§«‡†2«‡•–~pŽGj˜mÁ&ˆŒjˆ™ˆŒ‘’y«Qˆ 1ˆŒj“i•–j«iŠŒ‘”¥m9§˜¦Q¥§˜™¥§’ÀE߉j©•‰ŠŒ‘À§«Gˆ(2§Á

¦Q˜Œ§ŠŒ‰©yÀˆjËyˆŒjˆ™ˆ‹‘À§«Gˆ‘À«yŠ™˜™’k¥Ì²‡‘’«–·GËy¥§«i†@~@jˆ™ˆ™¥m·§Lˆ‹‘>Tyˇ¥§’·yŽ–˜ª¥m‘”©!¦–˜™§¦[˜ŒŠŒ‘ÀjˆEmÁj«Q©˜™†‡¦‰ŠŒ‘À§«§˜E¨Q¥CŠ™¥

ˆ‹ŠŒ˜™•Q©ŠŒ•–˜™jˆ"·y‘’²yP˜™‘ÀˆŒ@ŠŒ2‘’«‰ÇG«–‘ÈŠ™É͈›Šª¥CŠ™ˆ‹†‰ˆ‹ŠŒj~@ˆjƣͫ<Š™|–‘”ˆp©j¥§ˆŒ§Ë

Ä

|Q«<ŠŒ|Q«‡•–~Ž[˜pmÁˆŒjˆ™ˆ‹‘À§«Qˆ‘Àˆ

•Q«iŽ[§•Q«Q¨‰j¨Ë–ŠŒ|Qˆ‹k©•–˜™‘’Š›†¦–˜™§Ž–À~mÁY©˜™†‡¦‰ŠŒy·§˜ª¥m¦–|Q‘À©ƒ¦–˜™mŠ™‡©§”ˆ ‘”ˆ •–«Q¨‰k©‘”¨–¥mŽQ’yËQ²y«

Ä

|–j«8ŠŒ|–

À«Q·mŠŒ|mÁŠŒ|Q"~^kˆŒˆ™¥m·yjˆ9‘”ˆ!ŽGy•–«Q¨‰k¨VUŸƒ¥§±§±WgÆ

XQ§˜ŒŠŒ•–«Q¥mŠŒj’†yËjŠ™‰¨–¥Ì†ƒŠŒ|–j˜Œ9߉‘”ˆ›Šªˆ¥L²§j˜Œ†"ˆŒ•Q©©jˆ™ˆ›Á•Qi¥§¦–¦–˜™y¥§©ª|Š™ƒ©‘’˜ª©•Q~²§j«iŠŠŒ|Q9‘À«‰ÇQ«Q‘ÈŠ™É͈›Šª¥CŠŒ

ˆŒ†‰ˆ›Š™~ ¥m«Q¥§’†‰ˆŒ‘ÀˆW¦–˜™§ŽQ’j~8ŠŒ ~@¦–ÀC†L¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«‰ÉŽQ¥§ˆŒj¨¥§¦–¦–˜™Ì߉‘’~1¥CŠ™‘’y«L~@ŠŒ|–‰¨–ˆYU‚ŏy«Q±§±‰Ë;Z/["¯§¯WgÆ

£Í«àÁ¥§©ŠjËGŠŒ|–‘”ˆ¥m¦–¦–˜™y¥y©ª|ŕQˆŒjˆL˜Œj·§•–”¥m˜&ŠŒ˜™”¥m«Q·§•Q¥§·§jˆŠŒ¥m¦–¦–˜™Ì߉‘’~1¥mŠŒ"Š™|–^ˆŒŠƒmÁÏ~@kˆŒˆ™¥m·yjˆ Š™|Q¥CŠ

Š™|–‘À«iŠŒ˜™•Q¨‰˜&~^‘À·§|iŠ&|G¥Ì²§¥§©j“i•–‘’˜™j¨8¨‰•Q˜Œ‘À«–·P¥m«Å•Q«iŽ[§•Q«Q¨‰j¨8«‡•–~pŽGj˜&§ÁYˆŒjˆ™ˆŒ‘’y«Qˆ!mÁY¦–˜™mŠ™‡©§”ˆÆQ£Í«

Š™|–‘”ˆ&Á˜ª¥m~@

Ä

y˜ŒÎW˖~@yˆ‹Š¦–˜ŒyŽ–À~1ˆ&§ÁϦ–˜™mŠ™‡©§¥m«Q¥§’†‰ˆŒ‘Àˆ&˜Œk¨‰•Q©ŠŒ²C¥m˜™‘’y•QˆÎ‡‘À«Q¨–ˆƒmÁϘ™j¥y©ª|Q¥mŽQ‘’À‘ÈŠ›†

¦Q˜ŒyŽ–’j~1ˆ!§«>ŠŒ|–kˆ‹~@‰¨‰”ˆÆ

£Í«\U]!¥§¯^_WgË

Ä

¦–˜™§¦[yˆŒj¨ƒ¥m«G¨"ˆ›Š™•Q¨‰‘Àj¨"¥m«"¥§ŽQˆ›Š™˜™¥y©7ŠÔÁy˜Œ~1¥m§~^‰¨‰jmÁy˜¦–˜™mŠŒ‰©§”ˆ

Ä

|–‘À©ª|¥§’À

Ä

ˆW•Qˆ

Š™^ˆŒ~@‘’ɨ–j©‘”¨‰&ŠŒ|–"ˆŒj©˜™j©†@¦–˜ŒyŽ–À~ •QˆŒ‘’«–·@¥m•–ŠŒ§~1¥mŠŒ‘”©¥mÀÀ†^·y«–j˜™¥mŠŒk¨P¥m¦–¦Q˜ŒÌ߉‘À~@¥mŠŒ‘À§«@Á•–«G©7ŠŒ‘À§«GˆÆ

£Í«^¦–˜ª¥§©ŠŒ‘”©§ËC©˜Œ†‡¦‰Š™§·§˜ª¥m¦Q|–‘À©¦–˜Œ§ŠŒ‰©yÀˆ¥m˜™9mÁýŠŒj«^ˆŒ¦[j©‘’ÇQk¨•QˆŒ‘À«–·L|Q‘’·y|pÀ²y‡¦–˜™mŠŒ‰©§‡ˆ‹¦[j©‘ÈÇG©j¥CŠ™‘’y«

”¥m«Q·§•Q¥§·§jˆjˉÁy˜L߉¥§~@¦–’>ÒÖ׃ØÙ&Ú`U["¥y¯^WY¥m«Q¨ÝÐEщÒÔÓWÑaUû¢9¥§¯@b_WgÆ¢Ey«Qˆ‹k“i•–«iŠŒÀ†§Ë[¥mÀ

Ä

§˜™Î‰ˆŽQ¥yˆ‹k¨

y«Û˜™·§•QÀ¥§˜ ŠŒ˜™pÀ¥§«–·§•Q¥§·§kˆ ˜Œk“i•–‘’˜™"Š™|–p¦Q˜Œkˆ‹j«Q©§ÁÏ¥m«Û߉¦Gj˜‹Šƒ‘’«Ûy˜™¨–˜&j‘ÈŠ™|–˜LŠŒ©y~^¦Q•‰ŠŒpŠŒ|–

¥§¦–¦–˜™Ì߉‘’~1¥CŠ™‘’y«QˆW§˜ŠŒL«Q©‡¨–YŠŒ|–E¦–˜™mŠŒ‰©§yˆŒ¦[j©‘’ÇG©j¥CŠŒ‘À§«"‘À«iŠŒ&ŠŒ˜™Ï¥§•‰ŠŒy~@¥mŠ™¥¥§«Q¨ƒŠŒj˜Œ~5˜™

Ä

˜™‘ÈŠ™‘’«Q·

ˆŒ†‰ˆ›Š™~1ˆjÆ

ž&

Ä

¥LŽ–˜Œ‘”¨‰·yE~p•Qˆ›ŠYŽ[!Ž–•–‘ÀÈŠkËm’‘À«–·‘À«–·L˜™j¥§‡¦–˜Œ§ŠŒ‰©yÀˆˆŒ¦Gk©‘’ÇG©¥mŠŒ‘À§«Qˆ¥m«G¨Š™|–y˜ŒŠŒ‘”©¥m‡¦–˜™§ŽQ’j~@ˆ

y«<ŠŒ|–j‘’˜@ˆŒ§•–«Q¨x¥§ŽQˆ‹ŠŒ˜ª¥§©7Š™‘’y«QˆjÆ{!|–P~1¥m‘À«Ý©§«iŠŒ˜™‘’ŽQ•‰ŠŒ‘À§«x§Á9Š™|–‘”ˆ¦Q¥§¦Gj˜p©§«QˆŒ‘Àˆ‹Š™ˆmÁˆŒ|–

Ä

‘’«Q·ÅŠŒ|–

ÁÂk¥§ˆŒ‘’ŽQ‘’À‘ÈŠ›†>mÁŠŒ|Q¥m•‰Š™§~1¥CŠ™‘À©"¥§«Q¥mÀ†‰ˆ‹‘”ˆ!mÁˆŒj©˜Œk©†¦Q˜Œy¦Gj˜‹Š™‘’kˆ!mÁY¦–˜™mŠŒ‰©§”ˆ

Ä

|–˜™ŠŒ|–p«‡•–~Ž[˜§Á

ˆŒjˆ™ˆŒ‘’y«Qˆ ‘”ˆ&•–«‡Ž[§•–«G¨‰j¨Û¥§«Q¨

Ä

|–j«ÅŠŒ|Q¦–˜™mŠ™‡©§‘Àˆ&·§‘À²§«Å‘À«à¥|–‘’·y|ېÀ²§j¦–˜™mŠ™‰©§ˆ‹¦[j©‘ÈÇG©j¥CŠ™‘’y«

”¥m«Q·§•Q¥§·§§Æ{!|QPŠŒ‡yEä[åYæiÓWÒ Éƒ{˜™&•‰ŠŒy~@¥mŠ™¥ÅŽG¥§ˆŒj¨Þ§«á&•‰ŠŒy~@¥mŠŒ‘”©&¦–¦–˜™Ì߇‘À~1¥CŠ™‘’y«QˆÁ§˜ŠŒ|–

&«Q¥mÀ†‰ˆ‹‘”ˆ§Áƒ€‡k©•–˜™‘ÈŠ›†Þ—˜™mŠ™‡©§”ˆ"ɦ–˜™C²i‘”¨‰kˆ«–y«‰Ég߉¦Gj˜‹Š•Gˆ‹j˜^¥

Ä

¥Ì†2ŠŒ2¦–˜™¥y©7Š™‘À©j¥mÀ’†<¥m«Q¨áj¥§ˆŒ‘À’†

²y˜™‘ÈÁ†>ˆ‹k©•–˜™‘ÈŠ›†1¦Q˜Œ§ŠŒ‰©yÀˆ9‘À«8¥§«>•Q«iŽ[§•Q«Q¨‰j¨8©§«iŠŒßiŠkÆ

c ½ é[ì » ìPd »e è\f ½ fÏè ¼ {!|– ¦Q¥§¦Gj˜‘”ˆY§˜™·y¥§«–‘ATjj¨p¥§ˆÁ§ÀÀ

Ä

ˆÆm{

Ä

"|Q‘’·y|^À²y‰¦–˜™mŠ™‰©§–ˆŒ¦[j©‘’Ç–É

©j¥CŠ™‘’y«1À¥§«–·§•Q¥§·§kˆ&Ð9щÒWÓÔÑ¥m«Q¨ÅÒÖ׃ØÙ&Ú1¥§˜ŒÇQ˜™ˆ‹ŠE‘À«iŠŒ˜™‰¨‰•Q©k¨1‘À«>€‡j©ŠŒ‘À§«8³‰Æ‡{!|–«Ë‡ˆŒ§~@&«–§ŠŒ‘À§«Qˆ

¥§«Q¨«–mŠª¥CŠ™‘’y«Qˆ ¥m˜™‘’«iŠŒ˜™‰¨‰•Q©j¨>‘’«à€‡k©7Š™‘’y«°QƖ£Í«Û€‡j©ŠŒ‘À§«bQË

Ä

"ˆ‹|Q

Ä

|–

Ä

§•–˜ ²y˜™‘ÈÇ[©¥CŠ™‘’y«PŠ™j©ª|‰É

«Q‘À“i•–^‘ÀˆL¦–À•–·§·yj¨Åy«àŽ[mŠ™|à”¥m«–·y•Q¥m·yjˆ&¥§«Q¨Û¥>«–

Ä

|G¥m«Q¨‰À‘À«–·>§Áψ‹k©˜™j©†¦Q˜Œy¦Gj˜‹Š™‘’kˆL¥yˆ

Ä

ÀÁy˜ƒ¥

Š™j©ª|–«Q‘À“i•–9ŽQ¥§ˆŒj¨§«gU;Z/["¯§¯W

Ä

|Q˜™ŠŒ|Q†¥§˜Œ9ˆ‹¦[j©‘ÈÇQk¨¥yˆ¥&ŠŒ˜™9¥m•‰Š™§~1¥CŠ™§«”¥m«–·y•Q¥m·y§Æk£Í«^€‡k©7Š™‘’y«

^–Ë–Š™|–pˆŒ§•–«G¨‰«–jˆ™ˆ §ÁYŠŒ|–"Š™˜™¥§«QˆŒÀ¥mŠŒ‘À§«8mÁÏ¥§«ihAjˆ‹¦[j©‘ÈÇG©j¥CŠ™‘’y«Å‘’«iŠŒ§•–˜ƒ¥mŽQˆ‹ŠŒ˜ª¥§©Š~^‰¨‰j‘”ˆLˆŒ|–

Ä

«Æ

X‘À«Q¥mÀÀ†§ËQŽ[Áy˜Œ©§«Q©’•G¨‰‘’«Q·Q˖Š™|–߇¦[˜™‘À~^j«iŠ™ˆj˖¦Gj˜‹Áy˜Œ~@k¨

Ä

‘ÈŠ™|8ŠŒ|–ä[åYæ‡ÓWÒàŠ™‡§gËG¥m˜™"¦–˜™jˆŒ«iŠŒk¨

‘À«Û€‡j©ŠŒ‘À§«8®–Æ

k lmQRnSoqpsr0t rvu wGIHYF1HKNxHSuzy-{|rvN0QR}~Nx€FIQRHSEqpsYEMnSL‚nrvƒ

„ލ©y«QˆŒ‘À¨‰j˜Y©˜™†i¦–ŠŒ§·y˜™¥§¦–|–‘”©¦–˜™mŠ™‰©§”ˆˆ‹¦[j©‘ÈÇGj¨^‘’ŠŒ|–j˜‘À«Ð9щÒÔÓWÑUû¢9¥§¯@b_WQ§˜Y‘À«ÒÖ׃ØÙ&ÚgU["¥§¯…^WgË

Š Ä  Ä

j’’Ég·«–

Ä

«|–‘’·y|pÀ²y‡¦–˜™mŠ™‡©§‡ˆ‹¦[j©‘ÈÇ[©¥CŠ™‘’y«p”¥m«Q·§•Q¥§·§jˆjÆj{!|Q9¦Q•–˜Œ¦[yˆŒ9mÁQŠ™|–ÒÖ׃ØÙ&ڐ”¥m«‰É

(7)

·y•Q¥m·y‘”ˆŠ™·§‘À²§~^k¥m«Qˆ&ŠŒ¨‰jˆ™©˜™‘ÀŽGŽ[mŠ™|খ˜™mŠ™‰©§”ˆ&¥§«Q¨8Š™|–p©§«iŠŒßiŠƒ‘’«

Ä

|–‘À©ª|ۊŒ|–j†Û¥m˜™•QˆŒj¨ÔÆ

{!|Qˆ‹•–Ž–Ég”¥m«–·y•Q¥m·yE•Gˆ‹k¨^ŠŒ¨‰ÇQ«–¦–˜™mŠ™‰©§”ˆ‘ÀˆÏ§˜™‘’j«iŠŒj¨p§«iŠ™"߉‘Àˆ‹ŠŒ‘À«–·"‘À~@¦Gj˜™¥mŠŒ‘À²§!¦–˜™§·§˜ª¥m~@~@‘À«–·

”¥m«Q·§•Q¥§·§jˆ¥§«Q¨1¨‰jˆ™©˜™‘ÀŽGkˆ˜Œy’kˆ

Ä

|–‘”©ª|@¥§˜Œ9Š™|–¦–˜™§·y˜™¥§~@ˆ߇k©•‰Š™j¨@Ž‡†1’j·§‘’ŠŒ‘À~1¥CŠŒ 2¦–˜™mŠ™‡©§‰¦Q¥§˜‹É

Š™‘À©‘’¦G¥m«iŠ™ˆjÆm¤ §ÀjˆÏ¥m˜™!©§~@¦[yˆŒj¨p‘’«1ˆŒmÉÍ©¥mÀÀj¨ˆ™©j«Q¥m˜™‘ÀyˆjÆÌ{!|Qˆ‹•–Ž–Ég”¥m«–·y•Q¥m·yÏÁy˜ˆŒ©«Q¥§˜Œ‘Àyˆ©§«iŠ™¥§‘’«Qˆ

©§«Qˆ‹ŠŒ˜™•Q©Š™ˆÔÁy˜¦G¥m˜ª¥mÀ’jy¥m«G¨ˆ‹k“i•–«iŠŒ‘”¥mi©y~^¦[yˆŒ‘’ŠŒ‘À§«ËÌ¥m«Q¨"Á§˜«Q§«‰Éͨ‰Š™˜™~@‘’«–‘”ˆ‹ŠŒ‘”©Ï©ª|–y‘À©mÁ–²C¥mÀ•–kˆÆ

£Š|G¥§ˆ¥§ˆ™ˆ‹‘À·§«Q~^j«iŠ"ˆ‹Š™¥mŠŒj~^j«iŠ™ˆjË¥m«Q¨Þ¥mÀ’

Ä

ˆLŠ™|–1‘’«Gˆ›Šª¥m«iŠŒ‘”¥CŠ™‘’y«QˆƒmÁ!˜Œy’kˆ&Š™|Q¥CŠ|G¥Ì²§^ŽGj«<¦–˜™²‡‘ÈÉ

y•QˆŒ’†¨–ÇQ«–k¨ÔÆQ{!|–¥y©©§~@¦Q¥m«‡†‡‘À«–·^¥yˆŒˆŒ˜ŒŠŒ‘À§«>À¥§«–·§•G¥m·§"¥§’À

Ä

ˆ9§«–Š™@ˆŒ¦[j©‘’Á†8ˆŒ¥mÁŠ›†P¦–˜™§¦[˜ŒŠŒ‘Àjˆ

y«>߉j©•–ŠŒ‘À§«>ŠŒ˜ª¥§©kˆ!mÁ¦–˜Œ§ŠŒ‰©yˆŒ©«Q¥§˜Œ‘ÀyˆjÆ

{!|–ϐÀ¥§«–·§•Q¥§·§!Ð9щÒWÓWщËk¨‰²yÀ§¦[j¨L‘’«Š™|–YÁ˜ª¥m~@

Ä

§˜™Î mÁiŠŒ|Q •–˜™§¦[j¥§«&«–‘À§«"¦–˜™mš›k©7ŠL£‹€‡—ԝCË

‘”ˆ~@‰¨‰•–”¥m˜L¥m«Q¨Å¥§’À

Ä

ˆ!ŠŒ|Qˆ‹¦[j©‘ÈÇ[©¥CŠ™‘’y«ÅmÁY©y«yŠ™˜ŒyÈÉQ

Ä

¦Q¥CŠŒŠŒ˜™«QˆjËG¨–¥mŠ™¥1ˆ‹ŠŒ˜™•Q©7Š™•–˜™jˆ¥§«Q¨Å¨‰‘-,[j˜‹É

j«iŠ^‘À«iŠŒ˜™•Q¨‰˜^~@‰¨‰”ˆÆ£Šªˆ^ˆŒ~1¥§«yŠ™‘À©jˆp¥§˜Œ>ŽQ¥§ˆŒj¨á§« œ¥m~@¦[§˜ŒŠ #ˆp{ œ 1a{j~^¦[§˜ª¥m œ§·§‘”©1§ÁL ©7É

Š™‘’y«Qˆ Uœ¥m~1±"bW2 Ä

|Q‘À©ª| ~@¥§Î§kˆ¥m«ÕÐEщÒÔÓWÑۈŒ¦Gk©‘’ÇG©¥mŠŒ‘À§«ák¥§ˆŒ‘’À†ÞŠŒ˜ª¥m«QˆŒ”¥CŠ™¥§Ž–ÀP‘’«iŠ™2¥à¨–j©”¥m˜ª¥CŠ™‘’²y

À

Ä

˜ŒÉgÀ²yŠŒ˜™~˜™

Ä

˜™‘’ŠŒ‘À«–·>ŽG¥§ˆŒj¨2À¥§«–·§•Q¥§·§ hAj.1++\$v""aËU &£›¯§°"W2 Ä

À’ɈŒ•–‘’ŠŒj¨àŠŒ

¥§•‰ŠŒy~1¥CŠŒk¨>¥§«Q¥mÀ†‰ˆ‹‘”ˆEŠŒ‡§”ˆ/U&¥§¯…^8WÆ

£Í«VU]!¥§¯y®mŽ…WËi¥ŠŒ˜ª¥m«QˆŒÀ¥mŠŒ‘À§«1§Á¥PÒÖÔ×ØÙ&Ú1ˆŒ¦Gk©‘’ÇG©¥mŠŒ‘À§«1‘À«yŠ™p¥§«ahAj@ˆŒ¦Gk©‘’ÇG©¥mŠŒ‘À§«1‘”ˆE¨‰kˆŒ©˜Œ‘ÀŽ[j¨ÔÆ

LˆYŠ™|–<h>j”¥m«–·y•Q¥m·y ‘Àˆ9©y«–«–k©7ŠŒk¨^ŠŒŠŒ|–L|–‘’·y|1’j²§jQ”¥m«–·y•Q¥m·yjˆ ÒÖ׃ØÙ&Ú@¥m«G¨ÅÐEщÒÔÓWщË

Ä

L©ª|–‡yˆŒ

Š™|–"”¥m«–·y•Q¥m·yh>jP¥§ˆEŠŒ|Q"‘’«–¦Q•‰Š&”¥m«–·y•Q¥m·yL§Á§•Q˜ ²§˜™‘’ÇG©¥mŠŒ‘À§«PŠ™j©ª|–«Q‘À“i•–yÆ

! wGrvu Q#" Q6E‚GQ rvƒ

{!|Q‘Àˆ9ˆ‹k©7Š™‘’y«1˜Œk©¥mÀ”ˆÏˆŒ§~@•QˆŒ•Q¥mG«–mŠ™‘’y«QˆE§«@ŠŒj˜Œ~1ˆj˧Š™˜Œj&¥m•–ŠŒ§~1¥mŠ™¥¥§«Q¨@ŠŒj˜Œ~ ˜™

Ä

˜™‘ÈŠ™‘’«Q·ˆ‹†‰ˆ‹ŠŒ~1ˆ

1a{ ¤&€‰ˆÁ§˜EˆŒ|–y˜‹Š2˜Œk“i•–‘’˜™j¨pŠ™¨‰jˆ™©˜™‘ÀŽGy•–˜Ï²y˜™‘ÈÇ[©¥CŠ™‘’y«^ŠŒj©ª|Q«–‘À“i•–yÆyÕ©§~@¦–˜™|Q«QˆŒ‘’²y ˆ‹•–˜™²§j†y«

{ ¤L€‰ˆ ¥m«Q¨>Š™˜Œj¥§•‰ŠŒy~1¥CŠ™¥^©¥§«8ŽGÁy•–«Q¨Á§˜߉¥§~@¦–’‘À«VUû¢9¥§¯i³8WÆ

$%& ' è ¼ !áº)(

' è ¼ ! èië

¼*»+*, -/.

é

º»

è

!ݺp½0,í

' ¼ èiè

¸ »

ì

!Ὁ»j½

œŠ F Ž[L¥ÇQ«Q‘ÈŠ™LˆŒŠE§Áˆ‹†‡~Ž[§”ˆj˧j¥y©ª|1§«–

Ä

‘ÈŠ™|¥m«P¥§˜Œ‘’Š›†§Ëi¨‰«–§ŠŒk¨

Arity(f)Á§˜ f ∈ FËi¥m«Q¨P’Š

X Ž[¥@©§•Q«yŠª¥mŽ–À"ˆ‹Š mÁ²Ì¥§˜Œ‘”¥mŽQ’kˆÆ

T(F,X)¨‰«–§ŠŒkˆ!ŠŒ|–"ˆŒŠmÁŠŒj˜Œ~1ˆjËQ¥m«Q¨

T(F) ¨‰j«–mŠ™jˆ!Š™|–

ˆŒŠ"§ÁE·§˜™§•Q«Q¨ÅŠ™˜™~@ˆ 1ŠŒ˜™~1ˆ

Ä

‘ÈŠ™|–§•–Š²C¥§˜Œ‘”¥mŽ–Àjˆ327ÆÔ{!|–1ˆŒŠ"mÁ9²C¥m˜™‘À¥§Ž–’kˆƒmÁ9¥ŠŒj˜Œ~

t ‘”ˆ"¨‰«–§ŠŒk¨

Ž‡† Var(t)Æ! ˆ‹•QŽQˆ›Š™‘ÈŠ™•‰ŠŒ‘À§«¡‘”ˆ¥ÞÁ•Q«Q©7Š™‘’y«

σ Á˜™§~ X ‘’«iŠ™ T(F,X)Ë Ä |–‘”©ª| ©¥§«/ŽGەQ«–‘À“i•–j’†

߇ŠŒ«G¨‰j¨>ŠŒP¥§«8«Q¨‰y~@§˜™¦–|–‘”ˆ‹~J§Á

T(F,X)ÆQ¬¦[yˆŒ‘ÈŠ™‘’y«

pÁ§˜L¥^ŠŒ˜™~

t ‘”ˆ¥ Ä y˜™¨C²§j˜

N

ÆQ{!|–

j~@¦‰Š›†ˆŒj“i•–j«Q©

¨‰j«–mŠ™jˆŠŒ|–ŠŒ§¦–Ég~@yˆ‹Š&¦[yˆŒ‘ÈŠ™‘’y«ÆG{!|Qˆ‹Š

Pos(t)§ÁY¦Giˆ‹‘’ŠŒ‘À§«Qˆ&mÁ¥@Š™˜™~

t ‘”ˆ

‘À«Q¨‰•G©7ŠŒ‘À²§j’†>¨‰ÇQ«Qj¨Ž‡†.8

1 Pos(t) ={}‘ÈÁ t∈ X

1 Pos(f(t1, . . . , tn)) ={} ∪ {i.p|1in=Arity(f) ¥§«Q¨ p∈ Pos(ti)}

£Á

p ∈ Pos(t)˃ŠŒ|–j« t|p

¨‰«–§ŠŒkˆÛŠ™|– ˆŒ•–Ž‰Š™˜™~…§Á

t ¥CŠÞ¦Giˆ‹‘’ŠŒ‘À§«

p ¥m«Q¨ t[s]p

¨‰j«–mŠ™jˆàŠŒ|–

Š™˜™~§Ž‰Šª¥m‘À«–j¨/Ž‡†/˜Œj¦–”¥§©j~@«iŠmÁŠ™|–ވŒ•–Ž‰Š™˜™~

t|p

¥CŠ¦Giˆ‹‘’ŠŒ‘À§«

p Ži†ÜŠ™|–ۊ™˜™~

sÆ X–§˜¥m«‡†

Š™˜™~

s ∈ T(F,X)Ë Ä 8¨‰j«–mŠ™Ŏi†

PosF(s) Š™|–ۈ‹Š1mÁ&Á•Q«Q©7Š™‘’y«Q¥m¦[yˆŒ‘’ŠŒ‘À§«Qˆ^‘À«

sËY‘gÆyÆ {p Pos(s)| Root(s|p)∈ F}Ä |–j˜Œ Root(t)¨‰«QmŠŒkˆŠŒ|Q&ˆ‹†‡~pŽGy–¥CŠÏ¦[yˆŒ‘ÈŠ™‘’y«

‘À« tÆi‚ŏ§˜™!·§j«–˜ª¥mÀ’†yË

2

+ %Güòjò435353 ø$§ùûõ%iø, %›ÿ46ó $ÿ,87Cò

(8)

Ä

¨‰j«–mŠ™

t(p) ŠŒ|Q"Á•–«Q©ŠŒ‘À§«Q¥§ˆŒ†‡~Ž[§§Á

t À‰©¥mŠŒj¨Å¥mŠL¦[yˆŒ‘ÈŠ™‘’y«

pƄÞp¨–«–§ŠŒŽ‡†

Posx(s) ŠŒ|–

ˆŒŠ §Á¦[yˆŒ‘ÈŠ™‘’y«Qˆ!mÁ²C¥m˜™‘À¥§Ž–’

x∈ X ‡©j©•–˜™˜™‘’«–·^‘À«

sˉ‘gÆyƉŠŒ|Qˆ‹Š

{p∈ Pos(s)|s|p=x}Æ

/{ ¤&€

R‘”ˆY¥LˆŒŠY§Áv6Y27M*19A+:

l→rË Ä |–j˜Œ l, r∈ T(F,X)Ë l6∈ XËm¥m«Q¨ Var(l)⊇ Var(r)Æ

˜™

Ä

˜™‘’ŠŒ8˜Œ•Q’

l→r ‘”ˆ 9A#,!92P! 1˜Œkˆ‹¦ÆM8'192x!021‘’Áj¥§©ª|ܲC¥m˜™‘À¥§Ž–À§Á

l 1˜Œkˆ‹¦Æ r2@‰©©•Q˜™ˆ

y«–À†á§«Q©ő’«

l 1˜Œkˆ‹¦ÆY‘À«

r27Æ9˜Œ•–Àő”ˆ1’‘À«–k¥m˜1‘’Á‘’ŠP‘”ˆ1ŽG§ŠŒ|/ÀÁýŠ>¥§«Q¨Ü˜Œ‘À·§|iŠ‹ÉÀ‘’«–k¥m˜kÆY { ¤&€

R

‘”ˆÀ‘À«–j¥§˜ 1˜™jˆŒ¦ÆÀÁýŠŒÉgÀ‘’«Qj¥m˜k˘™‘À·§|iŠ‹É’‘À«–k¥m˜2&‘’Á ²y˜™†à˜™

Ä

˜™‘ÈŠ™1˜Œ•–À

l→r mÁ R ‘Àˆ’‘À«–j¥§˜ 1˜™jˆŒ¦Æ’ÁýŠ‹É

À‘À«–j¥§˜j˖˜™‘À·§|iŠ‹É’‘À«–k¥m˜27Ɩ{!|–{ ¤L€

R‘’«Q¨–•Q©kˆ¥1˜™

Ä

˜™‘ÈŠ™‘’«–·1˜™”¥CŠ™‘’y«

R

y«>Š™˜™~1ˆ

Ä

|–iˆ‹"˜™4Q߉‘’²y

Š™˜™¥§«QˆŒ‘ÈŠ™‘’²y©ÀyˆŒ•–˜Œ‘Àˆƒ¨‰«QmŠŒk¨8Ž‡†

?RÆW{!|–ˆŒŠƒmÁ

RÉͨ‰jˆ™©j«Q¨–¥m«iŠªˆmÁ¥PˆŒŠƒmÁ·y˜Œy•–«Q¨>ŠŒj˜Œ~1ˆ

E

‘”ˆ R(E) ={t∈ T(F)| ∃sE ˆÆŠjÆ s→?Rt}Æ

œŠ QŽ[¥^¦[yˆ™ˆ‹‘ÀŽ–À†P‘À«‰ÇQ«–‘’ŠŒˆŒŠ mÁˆ‹†‡~pŽGyÀˆ!§Á¥m˜™‘’Š›†

0˖©¥§’Àj¨:7"7+:EˆŒ•Q©ª|Š™|Q¥CŠ

Q ∩ F =Æ T(F ∪ Q)‘”ˆ©j¥mÀ’k¨PŠ™|–ˆ‹Š mÁ""*16"#$"I:7Æ

è , *» *ì ,

& '

¼C½0,º *»+* ì , ½0,í , ì ¼ !á½4A* è í5»j¼Ì½ *» *ì ,

%

# I:24$ :z6Y27g*19A

c→qS '+6 c : !8@*164$V$B2B

c∈ T(F ∪ Q) q∈ QB x\98 #6"I:24$ :s 46"I:2#$"

c→q 'I6 c=f(q1, . . . , qn) f ∈ F Arity(f) =n q1, . . . , qn∈ Q c∈ F0

]9mŠŒŠŒy~pɕ–¦«–§«–É ¨‰ŠŒj˜Œ~@‘À«–‘Àˆ‹ŠŒ‘”©LÇQ«–‘’ŠŒ"Š™˜Œj"¥m•‰Š™§~1¥CŠª¥p¥§˜ŒƒŠŒ|Q«Å¨‰ÇG«–j¨8¥§ˆ9Áy’À

Ä

ˆjÆ

è , *» *ì ,

%

?!"# *8 P @7 2:#$z2V# i"*17 "7"446!i*1\i,+"

:6'`:&)+*)*8x9A

A = hF,Q,Qf, ∆i 'I6 Qf ⊆ Q :ai:+\R, x\98

46"I:2#$"I:B

{!|–O6Y2#2/69A4$ƒ§«

T(F ∪ Q)‘’«G¨‰•Q©k¨Ž‡†LŠŒ|–ϊŒ˜ª¥m«QˆŒ‘ÈŠ™‘’y«Qˆ§Á

A1ýŠ™|–9ˆŒŠ

2ԑ”ˆ¨‰j«–mŠ™j¨

Ž‡†

ÆP„¡|–j«

‘Àˆƒ©Àj¥§˜ Á˜Œy~ŠŒ|–^©§«iŠ™߇ŠjË

Ä

‘À’¥m”ˆŒ1ŽG^¨‰«–§ŠŒk¨ÅŽ‡†

A

ÆԀ‡‘À~@‘’”¥m˜™’†yËQŽ‡†

«QmŠ™¥mŠŒ‘À§«8¥mŽ–•Gˆ‹yË

Ä

mÁýŠ™«8«–§ŠŒ

q∈ A¥m«Q¨ t→q∈ A ˜™jˆŒ¦[j©7Š™‘’²yÀ†@Á§˜

q∈ Q ¥m«Q¨ t→qÆ

è , *» *ì ,

$

è ¾ ì - , * è íA½0, -:½0- è %

%x'I# <9A"@*…< !"8 ?+3

A 2`\:! q :

L(A, q) ={t∈ T(F)|t→?Aq}B~%x'Iz9A"*\6! @8a?+3

A : L(A) =S

q∈QfL(A, q)B

46!|9>@*…<:s6"*19A"/,< g93\,|2K!V?!<6! @8g?3 \46!<"*17 "7"PB

$%

. è ¾7¼*» é ¼ ì » ì ¾ ì Aº! è ¼ * ¾y½‰»+*ì , ì"[è ¼ è ½–¾_e½‰¹ *A*» é ¸ ,½4Aé º+*aº

{!|Q‘Àˆƒˆ‹k©7Š™‘’y«Å˜Œk©¥mÀ”ˆ ŠŒ|Qp¥m¦Q¦–˜ŒÌ߉‘À~1¥CŠŒ‘À§«–ÉgŽQ¥yˆ‹k¨PÁ˜ª¥m~@

Ä

y˜ŒÎ

Ä

|G¥Ì²§Ž[j«à¨‰²yÀ§¦–‘À«–·GÆPZƒ‘À²§«Û¥

Š™˜Œj9¥§•‰ŠŒy~1¥CŠŒy«

A¥m«Q¨^¥L{ ¤L€

RË̊Œ|QEŠ™˜Œj9¥§•‰ŠŒy~1¥CŠ™¥L©y~^¦Q’ŠŒ‘À§«@¥mÀ·§§˜™‘’ŠŒ|–~8Ëk‘’«–‘’ŠŒ‘”¥mÀÀ†¦–˜™jˆŒ«iŠŒk¨

‘À« U;Z/["¯§¯_WL¥§«Q¨ÜŠŒ|Q«¡•QˆŒj¨/‘À« UXG¥§¯@bWgË9©y~^¦Q•‰ŠŒkˆP¥<ŠŒ˜™Û¥§•‰ŠŒy~1¥CŠŒy«

Ak

ˆ‹•G©ª|/ŠŒ|Q¥mŠ

L(Ak) = R(L(A))Ä |Q«‘’Š!‘Àˆ9¦[yˆ™ˆ‹‘ÀŽ–À 1ýÁy˜9ŠŒ|–©”¥§ˆ™ˆ‹kˆÏ§Á{ ¤&€‰ˆ!©C²y˜™j¨@Ž‡†@ŠŒ|Q‘Àˆ!¥mÀ·§y˜Œ‘’ŠŒ|Q~ ˆŒ UXG¥§¯@b_W

¥§«Q¨ˆ‹•Q©ª|>ŠŒ|G¥CŠ

L(Ak)⊇ R(L(A))§ŠŒ|–j˜ Ä ‘”ˆŒ§Æ

{!|–ŠŒ˜™¥m•–ŠŒ§~1¥mŠ™¥@©y~^¦Q’ŠŒ‘À§«

Ä

y˜ŒÎ‰ˆ ¥yˆ9Á§À’

Ä

ˆjÆX–˜™§~

A=A0

˖ŠŒ|–©§~@¦–ÀŠ™‘’y«ŽQ•–‘’”¨–ˆ¥

ˆŒj“i•–j«Q©

A0,A1, . . . ,Ak

§ÁE¥m•‰Š™§~1¥CŠª¥PˆŒ•Q©ª|ۊ™|Q¥CŠ‘ÈÁ

s∈ L(Ai)¥§«Q¨ s→Rt Š™|–« t ∈ L(Ai+1)Æ

£Á Ä

LÇG«Q¨8¥ÇQßiɦ[§‘À«yŠ¥§•‰ŠŒy~@¥mŠŒy«

Ak

ˆŒ•Q©ª|ŠŒ|Q¥mŠ

R(L(Ak)) =L(Ak)ˉŠŒ|Q« Ä |Q¥Ì²y L(Ak) = R(L(A0))1§˜ L(Ak)⊇ R(L(A))‘ÈÁ R‘”ˆY«–§Š‘À«1¥m«‡†©”¥§ˆ™ˆmÁ€UXG¥§¯@bW2Ƨ{ƒŽQ•–‘’”¨

Ai+1

Á˜™§~

Ai

Ë

Ä

¥§©ª|–‘À²yL¥ !MP9A#$"a:7

Ä

|–‘”©ª|©§«QˆŒ‘”ˆ›ŠªˆE§ÁÇQ«Q¨–‘’«–·a2#$!"9(I"2!:"ŽGŠ

Ä

j« R

¥m«Q¨

Ai

Æ

XQ§˜ ¥@ˆ‹•QŽQˆ›Š™‘ÈŠ™•‰ŠŒ‘À§«

σ:X 7→ Q ¥m«Q¨¥^˜Œ•Q’

l→r∈ RËQ¥@©˜™‘ÈŠ™‘À©j¥mW¦Q¥§‘’˜!‘”ˆ ¥m«‘’«Qˆ‹Š™¥§«Q©

mÁ l ˆŒ•Q©ª|

Š™|Q¥CŠÏŠŒ|–j˜Œ ߇‘”ˆ‹Š™ˆ

q∈ QˆŒ¥mŠŒ‘”ˆ›Á†‡‘À«–·

lσ→Aiq¥m«Q¨ 6 →AiqÆXQ§˜j²§j˜Œ†©˜Œ‘’ŠŒ‘”©¥§–¦Q¥§‘’˜

lσ→Aiq¥m«G¨

(9)

6 →Aiq ¨‰ŠŒk©7ŠŒk¨PŽ[Š

Ä

j« R¥§«Q¨ Ai

Ë Ai+1

‘Àˆ!©§«Qˆ‹ŠŒ˜™•Q©7Š™j¨1Ž‡†P¥y¨–¨‰‘À«–·«–

Ä

ŠŒ˜ª¥m«Gˆ‹‘’ŠŒ‘À§«QˆÏŠŒ

Ai

ˆŒ•Q©ª|>ŠŒ|Q¥mŠ‘ÈŠ˜™j©§·y«–‘ATjjˆ

‘À« q˖‘aÆ§Æ rσ→Ai+1qÆ

Ai

R

q

Ai+1

Ê&

Ä

j²§j˜j˧ŠŒ|–LŠŒ˜ª¥m«QˆŒ‘’ŠŒ‘À§«

rσ→q ‘Àˆ9«–§Š9«Qj©kˆŒˆ™¥m˜™‘À’†@¥«Q§˜™~@¥§’‘>Tk¨@ŠŒ˜ª¥m«Gˆ‹‘’ŠŒ‘À§«Æ‡{!|–ƒ«–§˜™~1¥mÀ‘Àˆ™¥CŠ™‘’y«

§Áˆ‹•Q©ª|Å¥@Š™˜™¥§«QˆŒ‘ÈŠ™‘’y«‘”ˆ¦[˜ŒÁ§˜™~@j¨Ž‡†¥§«Å¥m¦–¦–˜™Ì߉‘’~1¥mŠŒ‘À§«>Á•–«Q©7Š™‘’y«

ᥧ«Q¨ŠŒ|Q‘Àˆ&~@¥Ì†Àj¥§¨j‘ÈŠ™|–˜

Š™1¥m«ߖ¥§©Š&©§~@¦–•–Š™¥CŠ™‘’y«>§Á

R(A)˖§˜!Š™1¥m«8C²§j˜‹ÉÍ¥m¦–¦Q˜ŒÌ߉‘À~@¥mŠŒ‘À§«@mÁ

R(A)Æ

{!|–~^ŠŒ|–‰¨8¦–˜™jˆŒ«iŠ™j¨‘’«`U;Z/["¯§¯_W˜Œk“i•–‘’˜™jˆ ¥yˆ ‘À«–¦–•‰ŠL¥^Š™˜Œj¥m•‰Š™§~1¥CŠ™§«

A0

ËQ¥1{ ¤&€

R¥m«G¨

¥pŠ™˜Œj¥§•‰ŠŒy~1¥CŠŒy«

Asecret

Ä

|Q˜™/8

1

ŠŒ|–"”¥m«–·y•Q¥m·ymÁ

A0

˜Œj¦–˜™jˆŒ«iŠ™ˆ9Ž[mŠŒ|8Š™|–"‘À«–‘ÈŠ™‘À¥§Î‡«–

Ä

Àj¨‰·yƒ§ÁŠ™|–"‘À«yŠ™˜Œ•G¨‰˜&¥§«Q¨ŠŒ|–‘À«–‘’ŠŒ‘”¥m

©§«–ÇQ·§•–˜ª¥CŠ™‘’y«§ÁŠŒ|Q"«–Š

Ä

§˜™Î

1 R ˆŒ¦Gk©‘’ÇQjˆƒŠ™|–1‘’«iŠ™˜Œ•Q¨–˜"¥mŽ–‘ÀÀ‘ÈŠ™‘’kˆƒŠŒÅ©y~^¦[yˆŒ1¥m«Q¨Þ¥m«G¥mÀ†…Tjp~@kˆŒˆ™¥m·yjˆLŽ–˜Œi¥§¨–©j¥§ˆ‹ŠLC²y˜ƒŠŒ|–

«–Š

Ä

§˜™ÎWˇ¥§«Q¨>j¥§©ª|8ˆ‹ŠŒ¦8§ÁŠŒ|Qˆ›Š™•Q¨‰‘Àj¨¦–˜™mŠŒ‰©§¥m”ˆŒ

1

ŠŒ|–2À¥§«–·§•Q¥§·§8mÁ

Asecret

˜Œj¦–˜Œkˆ‹j«iŠ™ˆ^ŠŒ|Q2ˆŒŠ§Á"ŠŒ˜™~1ˆˆŒ•–¦–¦[yˆŒj¨ÜŠ™á˜Œj~1¥m‘À«/ˆŒj©˜ŒŠ

Ä

|–‘À’

߉j©•‰ŠŒ‘À«–·^ŠŒ|–"¦Q˜Œ§ŠŒ‰©yaÆ

£Í«ÅŠ™|–p©§«iŠŒ߇ŠmÁYŠŒ|Q²§j˜Œ‘’ÇG©¥mŠŒ‘À§«8mÁ¦Q˜Œ§ŠŒ‰©yÀˆjˇŠŒ|–^ˆ‹k©•–˜™‘’Š›†>¦–˜™§ŽQ’j~éy«QˆŒ‘Àˆ‹Š™ˆ&mÁ¨‰j©‘À¨–‘’«–·

Ä

|QŠŒ|Q˜¥¦–˜™mŠ™‰©§¦–˜™jˆŒ˜™²§jˆLˆ‹k©˜™j©†¥§·y¥m‘À«Qˆ‹Šƒ¥§«Û‘’«iŠ™˜Œ•Q¨–˜kËGy˜L«–§ŠjÆÔ{!|–ÇQ«–‘’ŠŒ^ŠŒ˜™^¥m•‰Š™§~1¥CŠª¥

¦[˜™~@‘ÈŠE•QˆŠŒ«QˆŒ•–˜™EŠ™|Q¥CŠ9ˆ‹y~^ˆ‹Š™¥mŠŒkˆ¥m˜™ •–«–˜™j¥y©ª|Q¥mŽ–À§Ëm¥§«Q¨^|–«G© Š™|Q¥CŠYŠ™|–‘À«yŠ™˜Œ•G¨‰˜

Ä

‘ÀÀQ«–j²§˜

Ž[¥mŽQ’ƒŠŒ@·«–

Ä

©˜ŒŠ™¥§‘’«>ŠŒj˜Œ~1ˆjÆ

•–˜¦–˜Œj²‡‘’y•Qˆ

Ä

y˜ŒÎ<U]!¥§¯…^Wi¨‰kˆŒ©˜Œ‘ÀŽ[jˆ¥§«¥§•‰ŠŒy~1¥CŠŒk¨&~@ŠŒ|–‰¨ƒÁ§˜©§~@¦–•–ŠŒ‘À«–· C²§j˜‹ÉÍ¥m¦–¦Q˜ŒÌ߉‘À~@¥mŠŒ‘À§«Qˆ

y˜L•Q«Q¨‰˜ŒÉÍ¥m¦–¦–˜™Ì߉‘’~1¥mŠŒ‘À§«Qˆ §ÁŠŒ|Qp‘À«iŠŒ˜™•Q¨‰˜ƒÎ‡«–

Ä

Àj¨‰·yÁ˜™§~S¥1Š™˜Œj^¥§•‰ŠŒy~1¥CŠŒy«

A0

¥m«Q¨2¥>{ ¤L€

RÆ{8«Gˆ‹•–˜™^ŠŒ|–PˆŒ§•Q«Q¨‰«–kˆŒˆ§ÁEŠ™|–1²§j˜Œ‘’ÇG©¥mŠŒ‘À§«ËԈŒ§~@1©˜™‘ÈŠ™˜™‘À¥8¥§˜Œ1¨‰ÇQ«–j¨2Áy˜"ŽG§ŠŒ|

A0

¥m«G¨

RË¥m«Q¨ÞŠÄ Å©”¥§ˆ™ˆ‹kˆmÁ ¥m¦–¦–˜™Ì߉‘’~1¥mŠŒ‘À§«Qˆ¥m˜™1¨‰ÇG«–j¨x¥§ÀˆŒÅˆ‹•Q©ª|ފ™|Q¥CŠ"Š™|–©˜™‘’ŠŒ˜™‘”¥>Îyj¦2|–yÀ¨–‘’«–·

¨–•–˜Œ‘À«–·^ŠŒ|Q"²§˜™‘’ÇG©¥mŠŒ‘À§«Æ

{!|–kˆ‹ ©˜Œ‘’ŠŒj˜Œ‘”¥&©§«Q©˜™«p¥L¦Q¥m˜ŒŠŒ‘”©•–”¥m˜©”¥§ˆ™ˆmÁGŠŒ˜™~1ˆ

Ä

|–‘À©ª|@¥m˜™E©j¥mÀ’k¨ "7 $M+:§˜ $

£Í«&U]!¥y¯^WËWŠŒ|–1ˆŒŠ"mÁE©§«Qˆ‹Š™¥§«iŠ™ˆ¥m«Q¨à²C¥m˜™‘À¥§Ž–’kˆ¥m˜™ÇQ«–‘’ŠŒyË¥m«G¨Ûj¥y©ª|2©§«Qˆ‹Š™¥§«yŠ"¥m«G¨Û²C¥m˜™‘À¥§Ž–À

‘”ˆƒ¥§ˆ™ˆ‹‰©‘”¥CŠ™j¨Š™>y«–gh>jmÉgŠ›†‡¦G

Ä

|–‘”©ª|à©¥§«àŽ[ WË [Ë WË WË [Ë

!"ÔË""–Ë GË WË1§˜#$!

è , *» *ì

,&%

%#'

F(*),+ ? MY27-: R,-:4!+$"9,!*1P#$"P"9(:!3\?!9;: *(:‚,+ @"7@?+:!46+4$xB

$ + $ @"7V: 2'I`!:!s V=$?+9A 'I_:43 : -M6

,! . ` " +

f(t1, . . . , tn) 6P :42|,!6+:6' @"7a ,<'I\#3:/

0 v '+6

t1, . . . , tn "6 R,|43I/ V"0 S

f ∈ F(*)1+ B

]9†8¨‰ÇQ«Q‘ÈŠ™‘’y«Û¥m«Q¨Ž‡†>|‡†‡¦[mŠŒ|QjˆŒ‘Àˆ y«ŠŒ|–"ÇG«–‘ÈŠ™«–kˆŒˆ&mÁŠŒ|Qˆ‹Š™ˆ §ÁY²Ì¥§˜Œ‘”¥mŽQ’kˆ ¥m«Q¨Å©§«Qˆ‹Š™¥§«yŠªˆË

Š™|–ˆŒŠ&§Á¥CŠŒy~@‘À©¨Q¥CŠ™¥@‘”ˆ ÇG«–‘ÈŠ™Š™iGÆQ Ï¥y©ª|Û¥CŠ™§~@‘À©ƒŠ›†‡¦[‘”ˆ&¥yˆŒˆŒ‰©‘”¥CŠŒk¨PŠ™P§«Q¦Q¥m˜ŒŠŒ‘”©•QÀ¥§˜&ˆŒ¥mÁŠ›†

Á•Q«Q©7Š™‘’y«Q¥mˆŒ†‡~Ž[§gÆ1„2¨‰j«–mŠ™

Fprtct Š™|–ˆŒŠ mÁYˆŒ¥mÁŠ›†ˆŒ†‡~Ž[§”ˆË–¥§«Q¨

F24365 ∩ Fprtct =ÆIXQ§˜¥

Š™˜™~

t∈ T(F,X)ËGŠŒ|–^«–mŠ™‘’y«ÛmÁ "6!"7+:M $ @"71#ZLŸ 2ËÔ·§‘À²§j«Å‘’«ÞŸ&ÇQ«–‘’ŠŒ‘À§« ^–Ë[¥§’À

Ä ˆ

y«–ƒŠŒ@À‡©j¥CŠ™ƒk¥§©ª|8¥CŠ™§~@‘À©¨–¥mŠŒ•–~ђ«Š™|–ŠŒj˜Œ~

tÆ

(10)

è , *» *ì ,

%#'

t ?!\ + R, T(F,X) :*''IK'I6\ :!#: s_:2#$"

p :*!'2' t|p

:" $ @4* \B,<2'+6:

p0 ∈ Pos(t) :*!' 'I" p=p0.i Y2' iN t|p0

:<x

"7 $ 4* 2'+

t|p

: !@6!: $ @"#* R,

tBM%x'I:K , _:24$I:R,s'I @6!:

"7 $ @"7 R,s2'|+

t : +x PosGAD(t)B

{Å‘’ÀÀ•Qˆ›Š™˜™¥mŠŒ^ŠŒ|Q¥mŽ[C²§@¨‰ÇG«–‘ÈŠ™‘’y«ËÀŠ•Gˆ©y«Qˆ‹‘”¨‰j˜¥ÅˆŒ‘À~^¦Q’1߉¥§~@¦–’yƜŠ

t Ž[1ŠŒ|Q@ŠŒ˜™~

pair(a, n(a, b))Ä |–˜™ aË b ¥m«G¨ n(a, b)¥§˜Œƒ¥CŠŒy~@‘À©L¨–¥CŠª¥–Ƈ{!|i•GˆË

PosGAD(t) ={1,2}Ä |Q˜™&Š™|–

¦[yˆŒ‘’ŠŒ‘À§«

1‘”ˆ ˜™”¥CŠ™j¨ŠŒ^ŠŒ|–

GAD aËQ¥§«Q¨ 2‘”ˆ ˜™”¥CŠŒk¨PŠ™^ŠŒ|–

GAD n(a, b)Æ

ž&

Ä

ËmŠŒ|Q&‘À«yŠ™•–‘’ŠŒ‘À§«1Ž[|–‘À«Q¨@Š™|–L©˜Œ‘’ŠŒj˜Œ‘”¥~@«iŠŒ‘À§«–k¨1¥mŽ[C²§¥§«Q¨@•QˆŒj¨@‘À«1ŠŒ|–&˜Œj~@¥§‘’«G¨‰˜§ÁԊŒ|–

¦G¥m¦[˜ ‘”ˆ8

1

«x¥CŠ™§~@‘À©pŠ™˜™~©¥§«2Ž[1˜Œ

Ä

˜Œ‘’Š‹Š™«Þ‘’«iŠ™8¥•–«Q‘À“i•–PˆŒ¦Gk©‘”¥m¥§’ÀmŠ™j¨Þˆ›Šª¥CŠŒ

Ä

‘’ŠŒ|–‘À«ÞŠŒ|–1‘À«–‘’ŠŒ‘”¥m

ŠŒ˜™"¥m•‰Š™§~1¥CŠ™§«1©§«Q¨‰‘’ŠŒ‘À§«Gˆ!§«

A0

2*

1

«P¥CŠ™§~@‘”©!ŠŒj˜Œ~ ~•Qˆ‹ŠÏŽ[&¦–˜™mŠ™j©ŠŒj¨^Ž‡†@¥ˆ‹¦[j©‘À¥§Q¥mÀÀmŠŒk¨^Á•–«Q©ŠŒ‘À§«Q¥§GˆŒ†i~pŽGy1©§«Q¨–‘ÈŠ™‘’y«Qˆy«

RË A0

¥m«G¨Š™|–¥m¦Q¦–˜ŒÌ߉‘À~1¥CŠŒ‘À§«PÁ•–«Q©7Š™‘’y«:27Æ

XQ§˜™~@¥§’À†§ËYÀŠ

tatomic

Ž[à¥m«/¥CŠ™§~@‘”©Å¨–¥CŠ™•–~ §ÁLŠ›†‡¦[

ty Ä |–iˆ‹ň™¥CÁŠ›† ˆ‹†‡~Ž[§&‘ÀˆP¨–«–§ŠŒj¨

sfty(∈ Fprtct)ƜŠ qtatomic

ŽG^ŠŒ|Q@¥§’ÀmŠ™j¨Þˆ›Šª¥CŠ™p§Á

tatomic

Ä

|Q«

tatomic ∈ T(F)Æ{!|–˜™^¥§˜Œ

Áy•–˜©˜™‘’ŠŒ˜™‘”¥y«

A0

Ɩ£ Á

tatomic∈ T(F)Ë

U ɪ´VW

L(A0, qtatomic) ={tatomic}

U ɛ³ W X–y˜¥mÀ

q∈ A0

˖‘ÈÁ

tatomic∈ L(A0, q)ŠŒ|Q« q=qtatomic

Æ

U ÉÍ° WYXQ§˜¥mÀ

q∈ A0

Ë

t∈ L(A0, q) ¥m«Q¨ p∈ {p0 ∈ Pos(t) | p0 ∈ PosGAD(t)t|p0 =tatomic}

‘’ŠŒ|–j˜

p=¥§«Q¨ q=qtatomic

ˉ§˜

p=s.1Ë t(s) =sfty

Æ

U É7b W XQ§˜@¥mÀ

q ∈ A0

Ë t ∈ L(A0, q)ˑ’ÁŠ™|–˜™߇‘”ˆ‹Š™ˆ

p ∈ Pos(t) ˆ‹•G©ª|xŠŒ|Q¥mŠ

t(p) = sfty Š™|–«

p.1∈ PosGAD(t)¥m«Q¨ŠŒ|–Š›†‡¦["mÁ

t|p.1

‘”ˆ

tyÆ

¢Ey«Q©j˜Œ«–‘À«–·

RˊŒ|–Å©˜™‘’ŠŒ˜™‘”¥à¥m˜™8¥§ˆÁ§À’

Ä

ˆ 8Á§˜1¥mÀ

l→r ∈ RË t ∈ {l, r} ¥m«Q¨ p ∈ {p0 Pos(t)|p0 ∈ PosGAD(t)t|p0 =tatomic}Ë

U¤!ɪ´VW

p6=Ë

U¤!ɛ³ W

t(s) =sfty

¥m«G¨

p=s.1Æ

„¡|–j«ÝŠ™|–8©§«G¨‰‘ÈŠ™‘’y«Qˆ UÉ™´W’É!UÉ4b@W!¥§«Q¨ U¤!ɪ´+WÀÉ U¤!ɛ³_W ¥m˜™ˆ™¥CŠŒ‘”ˆ‹ÇQj¨Ý§«ÝŽ[mŠ™|

A0

¥§«Q¨

Rˊ Ä 

·‘À«Q¨–ˆmÁQ¥§¦–¦–˜™Ì߉‘’~1¥CŠ™‘’y«Á•–«Q©ŠŒ‘À§«Qˆ©¥§«Ž[E·y«–j˜™¥mŠŒk¨ÔË

Ä

|Q‘À©ª|Àj¥y¨"Š™

Ä

¥§˜™¨–ˆ‘’ŠŒ|–j˜Y¥&ˆŒ§•–«Q¨•–«Q¨‰j˜‹É

¥§¦–¦–˜™Ì߉‘’~1¥CŠ™‘’y«P§˜¥@ˆŒ§•–«G¨C²y˜ŒÉ¥§¦–¦–˜™Ì߇‘À~1¥CŠ™‘’y«1mÁŠ™|–"‘À«yŠ™˜Œ•G¨‰˜ ·«–

Ä

Àj¨‰·y§Æ

l H F1HVr GQ y-rvN0LMGQFqwVGIHYF1HKNxHSu ƒ!GIH " l Q nSo p<r0tSrvugwGIHYF1HKNxHSu6ƒ

y-{|r N0Q}~Nx€FIQRH E p<‚EMnSL‚nr ƒ

Lˆ!~@«iŠŒ‘À§«–k¨P‘À«8€‰j©7Š™‘’y«8³–ËxhAj@‘”ˆ ¨‰‘’˜™j©ŠŒÀ†©y«–«–k©7ŠŒk¨1Š™pŠ™|–|–‘À·§|À²yˆŒ¦Gk©‘’ÇG©¥mŠŒ‘À§«>À¥§«–·§•Q¥§·§kˆ

Ð9щÒÔÓWÑP¥m«G¨<ÒÖ׃ØÙ&ÚWÆ[{!|–p~@ŠŒ|Q‡¨Û¦–˜Œkˆ‹j«iŠŒj¨8‘À« U;Z/["¯§¯‡ËXQ¥y¯"bWY¥m«G¨iU]!¥y¯^W˜Œk“y•Q‘’˜™jˆL¥m«Å‘À«–¦–•‰Š

‘À«ŠŒ|–Áy˜Œ~4mÁ¥pŠ™˜Œj¥m•‰Š™§~1¥CŠ™§«

A0

ËQ¥@{ ¤&€

R¥m«Q¨¥pŠŒ˜™"¥m•–ŠŒ§~1¥mŠŒ§«

Asecret

Æ

{8’‘À«–ÎŊ™|–‘Àˆ²§˜™‘’ÇG©¥mŠŒ‘À§«à~@ŠŒ|–‰¨àŠŒ`hAjGË

Ä

^߉¦–À¥§‘’«Þ‘À«àŠ™|–‘Àˆˆ‹k©7ŠŒ‘À§«Þ|–

Ä

Š™Å¥m•‰Š™§~1¥CŠ™‘À©j¥mÀ’†

·y«–j˜™¥mŠŒ>ŠŒ|–8Š™˜ŒjÅ¥m•‰Š™§~1¥CŠ™§«

A0

¥m«Q¨ Š™|–Û{ ¤&€

R Á˜™§~ ¥m«mhAjሌ¦Gk©‘’ÇG©¥mŠŒ‘À§«Æ{!|Q‘Àˆ

Ä

¥Ì†§ËY¥§«

¥§ŽQˆ‹ŠŒ˜ª¥§©7Š9~@‡¨–WmÁŠ™|–ƒ¦–˜Œ§ŠŒ‰©yQŠ™pŽ[©ª|–j©ªÎyj¨P©j¥m«Ž[ƒŽ–•–‘ÀÈŠ¥m•–ŠŒ§~1¥mŠŒ‘”©¥mÀÀ†§Æ‡‚ŏ§˜™C²y˜kËm‘’«>§˜ª¨‰˜

Š™߇¦Q˜ŒkˆŒˆ9ˆ‹k©˜™j©†p¦–˜™§¦[˜ŒŠŒ‘Àjˆjˇ¥«–

Ä

ŠŒk©ª|–«–‘”“y•QL‘”ˆE¨–²§j’y¦Gk¨P¥m«G¨¥«Q

Ä

~@j¥§«QˆÏŠŒ@©ª|–j©ªÎpŠŒ|–j~

‘”ˆ!·§‘À²§j«Æ

Références

Documents relatifs

Second, we make their approach more efficient by developing a number of dedicated optimizations including the usage of freshness of generated nonces and secrecy of certain terms

Design and Evaluation of Shared Prosodic Annotation for Spontaneous French Speech: From Expert Knowledge to Non-Expert Annotation.. Linguistic Annotation Workshop, 2010,

The three contributions of this work are the following: (i) we propose guidelines to add contextual information in interfaces pre- senting local explanations of ML predictions

Contributions We present an abstraction technique for the parameterized ver- ification of distributed protocols with unique identifiers and apply it for model checking the

– les reformulations avec trois marqueurs très fréquents dans les corpus c’est-à-dire, autrement dit, encore appelé (section 4.2.2), dans la structure concept marqueur

We remark that each new parameter is added to the parameters set once used and the goals set is initialized with the goal locations corresponding to the translation of

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Our approach to query suggestion – generating can- didate query terms from the set of retrieved docu- ments – is related to pseudo-relevance feedback [3], a method for query