No free lunch in search and optimization: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Chetvorno
Cleanup from previous edit
changed pays to might pay. The prices are randomly shuffled, and by saying pays we are implying that the price of vegan is always inversely higher when compared to carnivore.
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
'''Language identification in the limit''' is a formal model for [[inductive inference]]. It was introduced by [[E. Mark Gold]] in his paper with the same title
== Straight burst into young woman came out of a belly came. ==
<ref>{{Citation
  | last=Gold | first=E. Mark
  | title=Language Identification in the Limit
  | volume=10
  | pages=447–474
  | url=http://www.isrl.uiuc.edu/~amag/langev/paper/gold67limit.html
  | url=http://web.mit.edu/~6.863/www/spring2009/readings/gold67limit.pdf
  | publisher=[[Information and Control]] | year=1967}}</ref>
In this model, a [[learner]] is provided with presentation (i.e. strings) of some [[formal language]]. The learning is seen as an infinite process. Each time an element of the presentation is read the learner should provide a representation (e.g. a [[formal grammar]]) for the language. It is said that a learner can identify in the limit a class of languages if given any presentation of any language in the class the learner will produce only a finite number of wrong representations, and therefore converge on the correct representation in a finite number of steps, without however necessarily being able to announce its correctness since a counterexample to that representation could appear as an element arbitrarily long after.


Gold defined two types of presentations:
Straight burst into young woman ケイトスペード バッグ 激安 came ケイトスペード かごバッグ out of a belly came.<br><br>'small Liao ...... fast access case to come, are coming!' Mouse invited the people, the police report to the pull of into the house, ケイトスペード 財布 新作 sat down and began weeping much more than that if you No strokes fell great oaks patience, I am afraid not heard that the nose a tear, and speak out the merits of what it is.<br><br>mouse can not this patient, it is estimated is a simple case, but it will bring out much complicated story, I am afraid it will take time to cracked.<br><br>Fortunately, this is not a police officer surnamed Yan deceived, as officers of the ケイトスペードのバッグ surname Yan.<br><br>mouse Chouchou that lesbians pulling runny nose, and do not feel their feelings deserved sympathy, really Nima little Blame, he would wonder. kate spade マザーズバッグ Now this woman more than rape it, how could there are so pure, accompany people liar sleep sleep, also give people the money.<br><br>'talent na, na ...... me how wonderful encounter no idiot girl, Qugelaopo Nima wages of all confiscated.'<br><br>mouse secretly
* Text (positive information): an enumeration of all strings the language consists of.
相关的主题文章：
* Complete presentation (positive and negative information): an enumeration of all possible strings, each with a label indicating if the string belongs to the language or not.
<ul>
 
  <li>http://www.japanprinter.co.jp/cgi-bin/jpbbs/jp_regi.cgi</li>
 
  <li>?mod=space&uid=55019</li>
 
  <li>?mod=viewthread&tid=53616</li>
 
</ul>


==Learnability==
== am facing the mess left by the previous captain daze. ==
This model is an early attempt to formally capture the notion of [[learnability]].
Gold's paper<ref>p.457</ref> introduces for contrast the stronger models
* ''Finite identification'' (where the learner has to announce correctness after a finite number of steps), and
* ''Fixed-time identification'' (where correctness has to be reached after an apriori-specified number of steps).
A weaker formal model of learnability is the ''[[Probably approximately correct learning]] (PAC)'' model, introduced by [[Leslie Valiant]] in 1984.


==Examples==
Qi nodded, but kate spade トートバッグ they all laughed, obviously cheap relative thing like this<br>One<br>rest II, III standard Columbia is the day before work, which the day before and the captain sat ケイトスペード バッグ sit, pour tea and a cigarette lighter in person, from the captain's Office came out, the two have been fraternizing.<br><br>mine was a brigade vice squad, sixty people, both will brigade is understaffed instructor volunteered after noon, and the captain together to clean up the backlog of cases, the transfer of residence of the suspects escorted to this day not been finished, according to a new instructor had to face Interpol names are written down, and to the evening shift home Interpol sooner arrived home, rear ケイトスペード 財布 店舗 instructor to come knock on the door, ouch, and captain together, festivals condolences Jiafu Li personally sent home.<br>within<br>day, new instructors bursting with popularity, ah .........<br><br>This day is the third day I took office sin, am facing the mess left by the previous captain daze.<br><br>invoices, meal kate spade ハンドバッグ tickets, gas vouchers of various open check, the shortest time is two months ago, the longest ケイトスペード 財布 ゴールド a year, Interpol investigators are going out all kinds of flowers
相关的主题文章：
<ul>
 
  <li>?mod=viewthread&tid=2498329&extra=</li>
 
  <li>?mod=space&uid=6762818</li>
 
  <li>?site=guestbook</li>
 
</ul>


{| class="wikitable" style="float: right"
== can not let the brother ==
|+ Example 4
|-
! !! Teacher
! colspan="2" | Learner's
|-
! !! !! Guess !! Query
|-
! 0.
|  ||  || ''abab''
|-
! 1.
| {{color|green|yes}}  || ''abab'' || ''baba''
|-
! 2.
| {{color|green|yes}} || ''a''<sup>*</sup>(''ba'')<sup>*</sup>''b''<sup>*</sup> || ''aa''
|-
! 3.
| {{color|red|no}} || (''ab'')<sup>*</sup>(''ba'')<sup>*</sup>(''ab'')<sup>*</sup>(''ba'')<sup>*</sup> || ''bababa''
|-
! 4.
| {{color|green|yes}}  || (''ab''+''ba'')<sup>*</sup> || ''babb''
|-
! 5.
| {{color|red|no}}  || (''ab''+''ba'')<sup>*</sup> || ''baaa''
|-
!
| ...  || ...
|}
{| class="wikitable" style="float: right"
|+ Example 3
|-
! !! Teacher !! Learner
|-
! 1.
| {{color|green|''abab''}}  || ''abab''
|-
! 2.
| {{color|green|''baba''}}  || ''a''<sup>*</sup>(''ba'')<sup>*</sup>''b''<sup>*</sup>
|-
! 3.
| {{color|red|<s>''aa''</s>}} || (''ab'')<sup>*</sup>(''ba'')<sup>*</sup>(''ab'')<sup>*</sup>(''ba'')<sup>*</sup>
|-
! 4.
| {{color|green|''bababa''}} || (''ab''+''ba'')<sup>*</sup>
|-
! 5.
| {{color|red|<s>''babb''</s>}}  || (''ab''+''ba'')<sup>*</sup>
|-
! 6.
| {{color|red|<s>''baaa''</s>}}  || (''ab''+''ba'')<sup>*</sup>
|-
! 7.
| {{color|green|''ε''}}  || (''ab''+''ba'')<sup>*</sup>
|-
!
| ...  || ...
|}
{| class="wikitable" style="float: right"
|+ Example 2
|-
! !! Teacher !! Learner
|-
! 1.
| ''abab''  || ''abab''
|-
! 2.
| ''ba''  || ''abab''+''ba''
|-
! 3.
| ''baba'' || ''abab''+''ba''+''baba''
|-
! 4.
| ''ba''  || ''abab''+''ba''+''baba''
|-
! 5.
| ''baba'' || ''abab''+''ba''+''baba''
|-
! 6.
| ''abab''  || ''abab''+''ba''+''baba''
|-
! 7.
| ε    || ''abab''+''ba''+''baba''+ε
|-
!
| ...  || ...
|}
{| class="wikitable" style="float: right"
|+ Example 1
|-
! !! Teacher !! Learner
|-
! 1.
| ''abab''  || ''abab''
|-
! 2.
| ''baba''  || ''abab''+''baba''
|-
! 3.
| ''baabab'' || (''b''+ε)(''ab'')<sup>*</sup>
|-
! 4.
| ''baabab''  || (''b''+ε)(''ab'')<sup>*</sup>+''baabab''
|-
! 5.
| ''abbaabba''  || (''ab'')<sup>*</sup>(''ba'')<sup>*</sup>(''ab'')<sup>*</sup>(''ba'')<sup>*</sup>
|-
! 6.
| ''baabbaab''  || (''ab''+''ba'')<sup>*</sup>
|-
! 7.
| ''bababa''  || (''ab''+''ba'')<sup>*</sup>
|-
!
| ...  || ...
|}


It is instructive to look at concrete examples of learning sessions the definition of identification in the limit speaks about.
.<br><br>'Interpol arrested several gambling, [http://www.dmwai.com/webalizer/kate-spade-9.html kate spade 財布 ゴールド] not afraid of people joke? say that sections of the ring road, we are not blind to what area you mix? Who told you caught?' Guo instructor for several asked all police shouted down, and then he understand: '? Oh, is it nonsense captain, is simply nonsense.'<br><br>hands [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード ママバッグ] behind, you can do this [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード 財布 通販] thing was still distraught member, spanned law enforcement, gamblers, and a one-time catch back eight individuals, inside small business [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード バッグ 通販] owners, small contractors, small civil what people have, it should not mess with if provoked man, let others tugging 'offside' excuse, I'm afraid the bad good, and he took a few steps, then returned, grabbing Gou Sheng Yang direct channel with: 'Sheng Yang, you are old Interpol, how do you No organization can and principled? such a thing is an Interpol that in it? '<br><br>'instructors, we [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード時計人気] have no way ah, poor team like this, field reimbursement list put for a year, let the old captain difficulties at home, the team perks support him, we have no opinion on the face ...... can not we matter asked funds to implement or not, can not let the brother
* '''Example 1''': fictitious session to learn a [[regular language]] ''L'' over the [[Formal language#Words over an alphabet|alphabet]] {''a'',''b''} from text presentation. In each step, the teacher gives a string belonging to ''L'', and the learner answers a guess for ''L'', encoded as a [[regular expression]]. In step '''3''', the learner's guess is not consistent with the strings seen so far; in step '''4''', the teacher gives a string repeatedly. After step '''6''', the learner sticks to the regular expression (''ab''+''ba'')<sup>*</sup>. If this happens to be a description of the language ''L'' the teacher has in mind, it is said that the learner has learned that language. If a computer program for the learner's role would exist that was able to successfully learn each regular language, that class of languages would be ''identifiable in the limit''. Gold has shown that this is not the case.<ref>Theorem I.8,I.9, p.470-471</ref>
相关的主题文章：
* '''Example 2:''' a particular learning algorithm always guessing ''L'' to be just the union of all strings seen so far. If ''L'' is a finite language, the learner will eventually guess it correctly, however, without being able to tell when. Although the guess didn't change during step '''3''' to '''6''', the learner couldn't be sure to be correct. Gold has shown that the class of finite languages is identifibale in the limit.;<ref>Theorem I.6, p.469</ref> however, this class is neither finitely nor fixed-time identifiable.
<ul>
* '''Example 3''': learning from complete presentation by telling. In each step, the teacher gives a string and tells whether it belongs to ''L'' ({{color|green|green}}) or not ({{color|red|<s>red, striked-out</s>}}). Each possible string is eventually classified in this way by the teacher.
 
* '''Example 4''': learning from complete presentation by request. The learner gives a query string, the teacher tell whether it belongs to ''L'' ({{color|green|yes}}) or not ({{color|red|no}}); the learner then gives a guess for ''L'', followed by the next query string. In this example, the learner happens to query in each step just the same string as given by the teacher in example 3. In general, Gold has shown that each language class identifiable  in the request-presentation setting is also identifiable in the telling-presentation setting,<ref>Theorem I.3, p.467</ref> since the learner, instead of querying a string, just needs to wait until it is eventually given by the teacher.
  <li>[http://data.webmasterhome.cn/indexed/history.asp?domain=69.5.26.147/cgi-bin/portal/index.cgi http://data.webmasterhome.cn/indexed/history.asp?domain=69.5.26.147/cgi-bin/portal/index.cgi]</li>
 
  <li>[http://seireihamamatsu.jp/cgi-bin/smileserver/mt/mt-search.cgi http://seireihamamatsu.jp/cgi-bin/smileserver/mt/mt-search.cgi]</li>
 
  <li>[http://www.durschloescher.de/cgi-bin/gb/guestbook.cgi http://www.durschloescher.de/cgi-bin/gb/guestbook.cgi]</li>
 
</ul>


==Learnability characterization==
== for example ==
[[Dana Angluin]] gave the characterizations of learnability from text (positive information) in a 1980 paper.
<ref>{{cite journal| author=Dana Angluin| title=Inductive Inference of Formal Languages from Positive Data| journal=Information and Control| year=1980| volume=45| pages=117–135| url=http://citeseer.ist.psu.edu/context/14508/0|url=http://www-personal.umich.edu/~yinw/papers/Angluin80.pdf}}</ref>
If a learner is required to be [[effective]], then an indexed class of [[recursive language]]s is learnable in the limit if there is an effective procedure that uniformly enumerates [[tell-tale#Formal language theory|tell-tales]] for each language in the class (Condition 1).<ref name="Angluin.1980a.Cond1">p.121 top</ref> It is not hard to see that if we allow an ideal learner (i.e., an arbitrary function), then an indexed class of languages is learnable in the limit if each language in the class has a tell-tale (Condition 2).<ref>p.123 top</ref>


==Language classes learnable in the limit==
Most of the time, and society plays a robber, for example, inflation is printing money, you're a big tycoons also turn you into a pauper; such as social change, it is likely that you will become bandits from tyrannical overnight money ...... to measure a person's wealth, it would be too shallow a. '<br><br>than sin laugh, whenever you meet different people can always find some rare in bizarre idea, Wei Jincheng is even worse, and perhaps the reason a super-rich, more than sin against him extra attention [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペードバッグセール] a few, wondering authentic: 'What do you What is considered a rich feel? '<br><br>'you feel rich to the rich, according to the survey, living [http://www.dmwai.com/webalizer/kate-spade-4.html kate spade バッグ] in the United [http://www.dmwai.com/webalizer/kate-spade-4.html ケイトスペード バッグ 新作] States [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード ハンドバッグ] of paradise, and residents of small African country warlord, the difference is not large compared to the happiness index.' Wei Jincheng laughed.<br><br>'you ignore a problem.' over sin, and he was eating explaining: 'You talk about the spirit of the rich, I am talking about is material wealth, the material is the basis of the spirit of the ah, you can talk, but I did not so no room money is not the girl without a [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード マザーズバッグ] home, talk about the rich that not a joke? '<br><br>'No, no, the mentality of the rich
 
相关的主题文章：
{| class="wikitable" style="float: right"
<ul>
|+ Dividing lines between identifiable and nonidentifiable language classes<ref>Table 1, p.452, in (Gold 1967)</ref>
 
|-
  <li>[http://crown.s333.xrea.com/softbank/softbank.cgi http://crown.s333.xrea.com/softbank/softbank.cgi]</li>
! Learnability model !! Class of languages
 
|-
  <li>[http://hnwzbl.com/plus/feedback.php?aid=392 http://hnwzbl.com/plus/feedback.php?aid=392]</li>
| colspan="2" | Anomalous text presentation<ref group=note name="anomalous text">i.e. text presentation, where the string given by the teacher is a [[primitive recursive function]] of the current step number, and the learner encodes a language guess as a [[Recursively enumerable|program that enumerates the language]]</ref>
 
|-
  <li>[http://www.centralcoastliving.net/realty/exec/search.cgi http://www.centralcoastliving.net/realty/exec/search.cgi]</li>
| || [[Recursively enumerable]]
 
|-
</ul>
| || [[Recursive set|Recursive]]
|-
| colspan="2" | Complete presentation
|-
| || Primitive recursive<ref group=note>i.e. the class of languages that are [[decision problem|decidable]] by [[primitive recursive]] functions</ref>
|-
| || [[Context-sensitive language|Context-sensitive]]
|-
| || [[Context-free]]
|-
| || [[Regular language|Regular]]
|-
| || Superfinite<ref group=note>i.e. containing all finite languages and at least one infinite one</ref>
|-
| colspan="2" | Normal text presentation<ref group=note>i.e. text presentation, expect for the anomalous text presentation setting</ref>
|-
| || Finite
|-
| || Singleton<ref group=note>i.e. the class of languages consisting of a single string (they are mentioned here only as a common lower bound to finite languages and pattern languages)</ref>
|}
 
The table shows which language classes are identifiable in the limit in which learning model. On the right hand side, each language class is a super class of all lower classes. Each learning model (i.e. type of presentation) can identify in the limit all classes below it. In particular, the class of finite languages is identifiable in the limit by text presentation (cf. Example 2 [[#Examples|above]]), while the class of regular languages is not.
 
''[[Pattern language (formal languages)|Pattern Languages]]'', introduced by Dana Angluin in another 1980 paper,
<ref>{{cite journal| author=Dana Angluin| title=Finding Patterns Common to a Set of Strings| journal=Journal of Computer and System Sciences| year=1980| volume=21| pages=46–62| url=http://www.sciencedirect.com/science/article/pii/0022000080900410/pdf?md5=c3534f6c086df22fbf814b12984fab5e&pid=1-s2.0-0022000080900410-main.pdf}}</ref>
are also identifiable by normal text presentation; they are omitted in the table, since they are above the singleton and below the primitive recursive language class, but incomparable to the classes in between.<ref group=note>incomparable to regular and to context-free language class: Theorem 3.10, p.53</ref>{{clarify|reason=I'm not quite sure about context-sensitive and primitive recursive languages; please cross-check.|date=October 2013}}
 
==Sufficient conditions for learnability==
Condition 1 in Angluin's paper<ref name="Angluin.1980a.Cond1"/> is not always easy to verify. Therefore, people come up with various sufficient conditions for the learnability of a language class. See also ''[[Induction of regular languages]]'' for learnable subclasses of regular languages.
 
===Finite thickness===
A class of languages has '''finite thickness''' if every non-empty set of strings is contained in at most finitely many languages of the class. This is exactly Condition 3 in Angluin's paper.<ref>p.123 mid</ref> Angluin showed that if a class of [[recursive language]]s has finite thickness, then it is learnable in the limit.<ref>p.123 bot, Corollary 2</ref>
 
A class with finite thickness certainly satisfies [[MEF-condition]] and [[MFF-condition]]; in other words, finite thickness implies [[M-finite thickness]].<ref name="Ambainis.Jain.Sharma.1997.Cor29">{{cite book| author=Andris Ambainis, Sanjay Jain, Arun Sharma| chapter=Ordinal mind change complexity of language identification| title=Computational Learning Theory| year=1997| volume=1208| pages=301-315| publisher=Springer| series=LNCS| url=http://www.comp.nus.edu.sg/~sanjay/paps/efs2.pdf}}; here: Proof of Corollary 29</ref>
 
===Finite elasticity===
A class of languages is said to have '''finite elasticity''' if for every infinite sequence of strings <math>s_0, s_1, ...</math> and every infinite sequence of languages in the class <math>L_1, L_2, ...</math>, there exists a finite number n such that <math>s_n\not\in L_n</math> implies <math>L_n</math> is inconsistent with <math>\{s_1,...,s_{n-1}\}</math>. [http://www.acm.org/pubs/citations/proceedings/colt/114836/p375-motoki/]
 
It is shown that a class of [[recursively enumerable]] languages is learnable in the limit if it has finite elasticity.
 
==Mind change bound==
{{Empty section|date=July 2010}}
 
==Other concepts==
 
===Infinite cross property===
A language L has '''infinite cross property''' within a class of languages <math>\mathcal{L}</math> if there is an infinite sequence <math>L_i</math> of distinct languages in <math>\mathcal{L}</math> and a sequence of finite subset <math>T_i</math> such that:
*<math>T_1 \sub T_2\sub ...</math>,
*<math>T_i \in L_i</math>,
*<math>T_{i+1}\not\in L_i</math>, and
*<math>\lim_{n=\infty}T_i=L</math>.
 
Note that L is not necessarily a member of the class of language.
 
It is not hard to see that if there is a language with infinite cross property within a class of languages, then that class of languages has infinite elasticity.
 
==Relations between concepts==
*Finite thickness implies finite elasticity;<ref name="Ambainis.Jain.Sharma.1997.Cor29"/><ref>Wright, Keith (1989) "Identification of Unions of Languages Drawn from an Identifiable Class". Proc. 2nd Workwhop on Computational Learning Theory, 328-333; with correction in: Motoki, Shinohara, and Wright (1991) "The correct definition of finite elasiticity: corrigendum to identification of unions", Proc. 4th Workshop on Computational Learing Theory, 375-375</ref> the converse is not true.
*Finite elasticity and [[conservatively learnable]] implies the existence of a mind change bound. [http://citeseer.ist.psu.edu/context/1042497/0]
*Finite elasticity and [[M-finite thickness]] implies the existence of a mind change bound. However, [[M-finite thickness]] alone does not imply the existence of a mind change bound; neither does the existence of a mind change bound imply [[M-finite thickness]]. [http://citeseer.ist.psu.edu/context/1042497/0]
*Existence of a mind change bound implies learnability; the converse is not true.
*If we allow for noncomputable learners, then finite elasticity implies the existence of a mind change bound; the converse is not true.
*If there is no [[accumulation order]] for a class of languages, then there is a language (not necessarily in the class) that has infinite cross property within the class, which in turn implies infinite elasticity of the class.
 
==Open questions==
*If a countable class of recursive languages has a mind change bound for noncomputable learners, does the class also have a mind change bound for computable learners, or is the class unlearnable by a computable learner?
 
== Notes ==
{{reflist|group=note}}
 
==References==
{{reflist}}
 
 
[[Category:Formal languages]]
[[Category:Computational learning theory]]

Latest revision as of 12:26, 7 January 2015

Straight burst into young woman came out of a belly came.

Straight burst into young woman ケイトスペード バッグ 激安 came ケイトスペード かごバッグ out of a belly came.

'small Liao ...... fast access case to come, are coming!' Mouse invited the people, the police report to the pull of into the house, ケイトスペード 財布 新作 sat down and began weeping much more than that if you No strokes fell great oaks patience, I am afraid not heard that the nose a tear, and speak out the merits of what it is.

mouse can not this patient, it is estimated is a simple case, but it will bring out much complicated story, I am afraid it will take time to cracked.

Fortunately, this is not a police officer surnamed Yan deceived, as officers of the ケイトスペードのバッグ surname Yan.

mouse Chouchou that lesbians pulling runny nose, and do not feel their feelings deserved sympathy, really Nima little Blame, he would wonder. kate spade マザーズバッグ Now this woman more than rape it, how could there are so pure, accompany people liar sleep sleep, also give people the money.

'talent na, na ...... me how wonderful encounter no idiot girl, Qugelaopo Nima wages of all confiscated.'

mouse secretly 相关的主题文章：

am facing the mess left by the previous captain daze.

Qi nodded, but kate spade トートバッグ they all laughed, obviously cheap relative thing like this
One
rest II, III standard Columbia is the day before work, which the day before and the captain sat ケイトスペード バッグ sit, pour tea and a cigarette lighter in person, from the captain's Office came out, the two have been fraternizing.

mine was a brigade vice squad, sixty people, both will brigade is understaffed instructor volunteered after noon, and the captain together to clean up the backlog of cases, the transfer of residence of the suspects escorted to this day not been finished, according to a new instructor had to face Interpol names are written down, and to the evening shift home Interpol sooner arrived home, rear ケイトスペード 財布 店舗 instructor to come knock on the door, ouch, and captain together, festivals condolences Jiafu Li personally sent home.
within
day, new instructors bursting with popularity, ah .........

This day is the third day I took office sin, am facing the mess left by the previous captain daze.

invoices, meal kate spade ハンドバッグ tickets, gas vouchers of various open check, the shortest time is two months ago, the longest ケイトスペード 財布 ゴールド a year, Interpol investigators are going out all kinds of flowers 相关的主题文章：

  • ?mod=viewthread&tid=2498329&extra=
  • ?mod=space&uid=6762818
  • ?site=guestbook

can not let the brother

.

'Interpol arrested several gambling, kate spade 財布 ゴールド not afraid of people joke? say that sections of the ring road, we are not blind to what area you mix? Who told you caught?' Guo instructor for several asked all police shouted down, and then he understand: '? Oh, is it nonsense captain, is simply nonsense.'

hands ケイトスペード ママバッグ behind, you can do this ケイトスペード 財布 通販 thing was still distraught member, spanned law enforcement, gamblers, and a one-time catch back eight individuals, inside small business ケイトスペード バッグ 通販 owners, small contractors, small civil what people have, it should not mess with if provoked man, let others tugging 'offside' excuse, I'm afraid the bad good, and he took a few steps, then returned, grabbing Gou Sheng Yang direct channel with: 'Sheng Yang, you are old Interpol, how do you No organization can and principled? such a thing is an Interpol that in it? '

'instructors, we ケイトスペード時計人気 have no way ah, poor team like this, field reimbursement list put for a year, let the old captain difficulties at home, the team perks support him, we have no opinion on the face ...... can not we matter asked funds to implement or not, can not let the brother 相关的主题文章：

for example

Most of the time, and society plays a robber, for example, inflation is printing money, you're a big tycoons also turn you into a pauper; such as social change, it is likely that you will become bandits from tyrannical overnight money ...... to measure a person's wealth, it would be too shallow a. '

than sin laugh, whenever you meet different people can always find some rare in bizarre idea, Wei Jincheng is even worse, and perhaps the reason a super-rich, more than sin against him extra attention ケイトスペードバッグセール a few, wondering authentic: 'What do you What is considered a rich feel? '

'you feel rich to the rich, according to the survey, living kate spade バッグ in the United ケイトスペード バッグ 新作 States ケイトスペード ハンドバッグ of paradise, and residents of small African country warlord, the difference is not large compared to the happiness index.' Wei Jincheng laughed.

'you ignore a problem.' over sin, and he was eating explaining: 'You talk about the spirit of the rich, I am talking about is material wealth, the material is the basis of the spirit of the ah, you can talk, but I did not so no room money is not the girl without a ケイトスペード マザーズバッグ home, talk about the rich that not a joke? '

'No, no, the mentality of the rich 相关的主题文章：

Retrieved from "https://en.formulasearchengine.com/index.php?title=No_free_lunch_in_search_and_optimization&oldid=237534"