25,161
edits
Changes
Created page with "'''Home * Search * Conspiracy Numbers''' border|right|thumb|link=Advances in Computer Chess 5| [[Jonathan Schaeffer on ''Conspira..."
'''[[Main Page|Home]] * [[Search]] * Conspiracy Numbers'''
[[FILE:ACC5Schaeffer.jpg|border|right|thumb|link=Advances in Computer Chess 5| [[Jonathan Schaeffer]] on ''Conspiracy Numbers.'' <ref>Photo from [[Advances in Computer Chess 5]] by [[László Lindner]], [[ICGA Journal#10_3|ICCA Journal, Vol. 10, No. 3]], pp. 138</ref> ]]
'''Conspiracy Numbers''' of the [[Root|root]] or [[Interior Node|interior nodes]] of a [[Search Tree|search tree]] for some value '''v''' are defined as the least number of conspirators, that are [[Leaf Node|leaves]] that must change their evaluation value to '''v''' in order to change the minimax value of the interior node or root <ref>Definition, Sample, and Pseudo code taken from [[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]</ref>. Conspiracy Numbers and their possible application for [[Minimax]] search within a [[Best-First|best-first search]] algorithm was first described by [[David McAllester]] <ref>[[David McAllester]] ('''1988'''). ''Conspiracy Numbers for Min-Max Search''. Artificial Intelligence, Vol. 35, No. 1, pp. 287-310. ISSN 0004-3702</ref>.
=Sample=
==Minimax Tree==
A sample minimax tree T with some arbitrary values of the leaves <ref>due to [[Jonathan Schaeffer]] ('''1989'''). ''Conspiracy Numbers.'' [[Advances in Computer Chess 5]]</ref>
</ref>:
<pre>
root ┌───────┐
max node │ 1 │
└───────┘
/ 3 \
┌───────┐ ┌───────┐
min nodes │ 1.1 │ │ 1.2 │
└───────┘ └───────┘
/ 2 \ / 3 \
┌───────┐ ┌───────┐ ┌───────┐ ┌───────┐
│ 1.1.1 │ │ 1.1.2 │ │ 1.2.1 │ │ 1.2.2 │
└───────┘ └───────┘ └───────┘ └───────┘
5 2 3 4
</pre>
==Conspiracy Numbers==
The conspiracy numbers for all possible value of the root of tree T
{| class="wikitable"
|-
! v
! cn(root, v)
! conspirators
|-
| style="text-align:center;" | <= 1
! 2
| style="text-align:center;" | (1.1.1 or 1.1.2) and (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 2
! 1
| style="text-align:center;" | (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 3
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 4
! 1
| style="text-align:center;" | (1.1.2 or 1.2.1)
|-
| style="text-align:center;" | 5
! 1
| style="text-align:center;" | 1.1.2
|-
| style="text-align:center;" | >= 6
! 2
| style="text-align:center;" | (1.1.1 and 1.1.2) or (1.2.1 and 1.2.2)
|}
The conspiracy numbers for all possible value of node 1.1 of tree T
{| class="wikitable"
|-
! v
! cn(1.1, v)
! conspirators
|-
| style="text-align:center;" | <= 1
! 1
| style="text-align:center;" | (1.1.1 or 1.1.2)
|-
| style="text-align:center;" | 2
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 3,4,5
! 1
| style="text-align:center;" | 1.1.2
|-
| style="text-align:center;" | >= 6
! 2
| style="text-align:center;" | (1.1.1 and 1.1.2)
|}
The conspiracy numbers for all possible value of node 1.2 of tree T
{| class="wikitable"
|-
! v
! cn(1.2, v)
! conspirators
|-
| style="text-align:center;" | <= 2
! 1
| style="text-align:center;" | (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 3
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 4
! 1
| style="text-align:center;" | 1.2.1
|-
| style="text-align:center;" | >= 5
! 2
| style="text-align:center;" | (1.2.1 and 1.2.2)
|}
=Recursive Definition=
Following [[Recursion|recursive]] definition in pseudo [[C]] is based on [[Maarten van der Meulen|Van der Meulen's]] code <ref>[[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]</ref>. '''V(J)''' represents the minimaxed value of node J. Opposed to McAllester's original definition which deals with pure game theoretic values, Van der Meulen's distinguished non terminal leaves with cn = 1 for values different of '''v''' from game theoretic terminal nodes to assign +oo, since it is impossible to change their value, independently been arrived at by [[Norbert Klingbeil]] and [[Jonathan Schaeffer]] <ref>[[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1988'''). ''Search Strategies for Conspiracy Numbers.'' Canadian Artificial Intelligence Conference, pp. 133-139</ref>:
<pre>
int cn(CNode J, int v) {
int c;
if ( V(J) == v ) {
c = 0;
} else if ( isTerminal(J) ) {
c = +oo; /* checkmate, stalemate, tablebase score, etc. */
} else if ( isLeaf(J) ) {
c = 1;
} else if (isMaxNode(J) && v < V(J) ) {
c = 0;
for (all childs J.j)
if (v < V(J.j) ) c += cn(J.j, v); /* sum */
} else if (isMinNode(J) && v > V(J) ) {
c = 0;
for (all childs J.j)
if (v > V(J.j) ) c += cn(J.j, v); /* sum */
} else {
c = +oo;
for (all childs J.j)
c = min( cn(J.j, v), c);
}
return c;
}
</pre>
=Search Algorithms=
[[David McAllester|McAllester's]] aim was related to some drawbacks of [[Alpha-Beta|alpha-beta]], at the worst, the decision at the root is based on a single evaluation of one leaf. If that leaf has assigned an erroneous value, the decision may be disastrous <ref>[[Ulf Lorenz]], [[Valentin Rottmann]] ('''1996'''). ''Parallel Controlled Conspiracy-Number Search.'' [[Advances in Computer Chess 8]]</ref>. The idea of [[Conspiracy Number Search]] (cn-search) and its variants is to continue until it is unlikely that the minimax value at the root will change.
* [[Alpha-Beta Conspiracy Search]]
* [[Conspiracy Number Search]]
* [[Controlled Conspiracy Number Search]]
* [[Parallel Controlled Conspiracy Number Search]]
* [[Proof-Number Search]]
=Chess Programs=
* [[Arachne]]
* [[P.ConNerS]]
* [[Ulysses]]
=Publications=
<ref>[http://ilk.uvt.nl/icga/journal/docs/References.pdf ICGA Reference Database](pdf)</ref>
==1985 ...==
* [[David McAllester]] ('''1985'''). ''A New Procedure for Growing Minimax Trees''. Technical Report, Artificial Intelligence Laboratory, MIT
* [[David McAllester]] ('''1988'''). ''Conspiracy Numbers for Min-Max Search''. Artificial Intelligence, Vol. 35, No. 1, pp. 287-310. ISSN 0004-3702
* [[Ingo Althöfer]] ('''1988'''). ''Root Evaluation Errors: How they Arise and Propagate''. [[ICGA Journal#11_23|ICCA Journal, Vol. 11, Nos. 2/3]]
* [[Maarten van der Meulen]] ('''1988'''). ''Parallel Conspiracy-Number Search''. M.Sc. thesis, Faculty of Mathematics and Computer Science, [https://en.wikipedia.org/wiki/Vrije_Universiteit Vrije Universteit, Amsterdam]
* [[Norbert Klingbeil]] ('''1988'''). ''Search Strategies for Conspiracy Numbers''. M.Sc. thesis
* [[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1988'''). ''Search Strategies for Conspiracy Numbers.'' Canadian Artificial Intelligence Conference, pp. 133-139
* [[Jonathan Schaeffer]] ('''1989'''). ''Conspiracy Numbers.'' [[Advances in Computer Chess 5]]. » [[Conspiracy Numbers#AI|also published]]
* [[Charles Elkan]] ('''1989'''). ''Conspiracy Numbers and Caching for Searching And/Or Trees and Theorem-Proving''. [[Conferences#IJCAI|IJCAI 1989]], [http://ijcai.org/Past%20Proceedings/IJCAI-89-VOL1/PDF/054.pdf pdf]
==1990 ...==
* [[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]
* [[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1990'''). ''Empirical Results with Conspiracy Numbers.'' Computational Intelligence, Vol. 6, pp. 1-11, [http://webdocs.cs.ualberta.ca/%7Ejonathan/Papers/Papers/compi.ps ps]
* <span id="AI"></span>[[Jonathan Schaeffer]] ('''1990'''). ''Conspiracy Numbers''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_(journal) Artificial Intelligence], Vol. 43, No. 1, pp. 67-84
* [[Maarten van der Meulen]], [[Victor Allis]], [[Jaap van den Herik]] ('''1990'''). ''A Comment on `Conspiracy-Number Search'''. [[ICGA Journal#13_2|ICCA Journal, Vol. 13, No. 2]]
* [[Victor Allis]], [[Maarten van der Meulen]], [[Jaap van den Herik]] ('''1991'''). ''Conspiracy-Number Search.'' [[Advances in Computer Chess 6]]
* [[David McAllester]], [[Deniz Yuret]] ('''1993'''). ''[[Alpha-Beta Conspiracy Search]]''. [http://ttic.uchicago.edu/%7Edmcallester/abc.ps ps (draft)]
* [[Lisa Lister]], [[Jonathan Schaeffer]] ('''1994'''). ''An Analysis of the Conspiracy Numbers Algorithm''. [https://en.wikipedia.org/wiki/Computers_and_Mathematics_with_Applications Computers & Mathematics with Applications] Vol. 27, No. 1, [https://en.wikipedia.org/wiki/Elsevier Elsevier], [http://webdocs.cs.ualberta.ca/%7Ejonathan/publications/ai_publications/icn.pdf pdf]
* [[Deniz Yuret]] ('''1994'''). ''[https://scholar.google.com/citations?view_op=view_citation&hl=en&user=EJurXJ4AAAAJ&cstart=40&citation_for_view=EJurXJ4AAAAJ:TQgYirikUcIC The Principle of Pressure in Chess]''. TAINN 1994
==1995 ...==
* [[Ulf Lorenz]], [[Valentin Rottmann]], [[Rainer Feldmann]], [[Peter Mysliwietz]] ('''1995'''). ''Controlled Conspiracy-Number Search.'' [[ICGA Journal#18_3|ICCA Journal, Vol. 18, No. 3]]
* [[Ulf Lorenz]], [[Valentin Rottmann]] ('''1996'''). ''Parallel Controlled Conspiracy-Number Search.'' [[Advances in Computer Chess 8]]
* [[Ulf Lorenz]] ('''1999'''). ''Controlled Conspiracy-2 Search''. Technical Report, [[University of Paderborn]], [http://www2.cs.upb.de/cs/ag-monien/PUBLICATIONS/POSTSCRIPTS/Falgo.ps ps]
* [[Robin Upton]] ('''1999'''). ''[http://www.robinupton.com/research/phd/ Dynamic Stochastic Control - A New Approach to Game Tree Searching]''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Warwick University of Warwick]
==2000 ...==
* [[Ulf Lorenz]] ('''2000'''). ''Controlled Conspiracy-2 Search''. Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS)
* [[David McAllester]], [[Deniz Yuret]] ('''2002'''). ''[[Alpha-Beta Conspiracy Search]]''. [[ICGA Journal#25_1|ICGA Journal, Vol. 25, No. 1]]
==2010 ...==
* [[Mohd Nor Akmal Khalid]], [[Umi Kalsom Yusof]], [[Hiroyuki Iida]], [[Taichi Ishitobi]] ('''2015'''). ''[https://www.researchgate.net/publication/281152992_Critical_Position_Identification_in_Games_and_Its_Application_to_Speculative_Play Critical Position Identification in Games and Its Application to Speculative Play]''. [http://www.scitepress.org/DigitalLibrary/ProceedingsDetails.aspx?ID=+mGlly8Sp00=&t=1 ICAART 2015]
* [[Mohd Nor Akmal Khalid]], [[E. Mei Ang]], [[Umi Kalsom Yusof]], [[Hiroyuki Iida]], [[Taichi Ishitobi]] ('''2015'''). ''[http://link.springer.com/chapter/10.1007%2F978-3-319-27947-3_6 Identifying Critical Positions Based on Conspiracy Numbers]''. [http://link.springer.com/book/10.1007/978-3-319-27947-3 Agents and Artificial Intelligence], [http://dblp.uni-trier.de/db/conf/icaart/icaart2015s.html#KhalidAYII15 ICAART 2015 - Revised Selected Papers]
* [[Jakub Pawlewicz]], [[Ryan Hayward]] ('''2015'''). ''[https://www.aaai.org/ocs/index.php/SOCS/SOCS15/paper/view/11040 Sibling Conspiracy Number Search]''. [https://en.wikipedia.org/wiki/Symposium_on_Combinatorial_Search SoCS 2015]
=External Links=
==Conspiracy Numbers==
* [http://www.robinupton.com/research/phd/cp_intro.html Conspiracy Numbers, Conspiracy Probailities & PCN* Search] by [[Robin Upton]]
* [http://www.cs.duke.edu/brd/Teaching/Previous/AI/Lectures/conspiracy.txt Reading: McAllister paper on "Consipracy Theory"?] by [http://www.cs.duke.edu/brd/ Bruce Donald]
==Conspiracy==
* [https://en.wikipedia.org/wiki/Conspiracy Conspiracy (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Conspiracy_theory Conspiracy theory from Wikipedia]
* [https://en.wikipedia.org/wiki/List_of_conspiracy_theories List of conspiracy theories from Wikipedia]
* [https://en.wikipedia.org/wiki/Conspiracy_theory_%28disambiguation%29 Conspiracy theory (disambiguation) from Wikipedia]
* [[Videos#JeanneLee|Jeanne Lee]] - Sundance, [https://www.discogs.com/de/Jeanne-Lee-Conspiracy/release/687632 Conspiracy] (1975), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: feat.: [https://fr.wikipedia.org/wiki/Jack_Gregg Jack Gregg], [https://en.wikipedia.org/wiki/Mark_Whitecage Mark Whitecage], [https://en.wikipedia.org/wiki/Steve_McCall_(drummer) Steve McCall], [[Videos#GunterHampel|Gunter Hampel]], [https://en.wikipedia.org/wiki/Sam_Rivers Sam Rivers], [https://en.wikipedia.org/wiki/Marty_Cook Marty Cook]
: {{#evu:https://www.youtube.com/watch?v=CRqGVLEYbUc|alignment=left|valignment=top}}
* [[Videos#ChrisSquire|Squire]] & [https://en.wikipedia.org/wiki/Billy_Sherwood Sherwood], [https://en.wikipedia.org/wiki/Conspiracy_%28band%29 Conspiracy] - [https://en.wikipedia.org/wiki/Conspiracy_(band)#Conspiracy Conspiracy], [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=af-8Of_uBxw|alignment=left|valignment=top}}
=References=
<references />
'''[[Search|Up one Level]]'''
[[FILE:ACC5Schaeffer.jpg|border|right|thumb|link=Advances in Computer Chess 5| [[Jonathan Schaeffer]] on ''Conspiracy Numbers.'' <ref>Photo from [[Advances in Computer Chess 5]] by [[László Lindner]], [[ICGA Journal#10_3|ICCA Journal, Vol. 10, No. 3]], pp. 138</ref> ]]
'''Conspiracy Numbers''' of the [[Root|root]] or [[Interior Node|interior nodes]] of a [[Search Tree|search tree]] for some value '''v''' are defined as the least number of conspirators, that are [[Leaf Node|leaves]] that must change their evaluation value to '''v''' in order to change the minimax value of the interior node or root <ref>Definition, Sample, and Pseudo code taken from [[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]</ref>. Conspiracy Numbers and their possible application for [[Minimax]] search within a [[Best-First|best-first search]] algorithm was first described by [[David McAllester]] <ref>[[David McAllester]] ('''1988'''). ''Conspiracy Numbers for Min-Max Search''. Artificial Intelligence, Vol. 35, No. 1, pp. 287-310. ISSN 0004-3702</ref>.
=Sample=
==Minimax Tree==
A sample minimax tree T with some arbitrary values of the leaves <ref>due to [[Jonathan Schaeffer]] ('''1989'''). ''Conspiracy Numbers.'' [[Advances in Computer Chess 5]]</ref>
</ref>:
<pre>
root ┌───────┐
max node │ 1 │
└───────┘
/ 3 \
┌───────┐ ┌───────┐
min nodes │ 1.1 │ │ 1.2 │
└───────┘ └───────┘
/ 2 \ / 3 \
┌───────┐ ┌───────┐ ┌───────┐ ┌───────┐
│ 1.1.1 │ │ 1.1.2 │ │ 1.2.1 │ │ 1.2.2 │
└───────┘ └───────┘ └───────┘ └───────┘
5 2 3 4
</pre>
==Conspiracy Numbers==
The conspiracy numbers for all possible value of the root of tree T
{| class="wikitable"
|-
! v
! cn(root, v)
! conspirators
|-
| style="text-align:center;" | <= 1
! 2
| style="text-align:center;" | (1.1.1 or 1.1.2) and (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 2
! 1
| style="text-align:center;" | (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 3
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 4
! 1
| style="text-align:center;" | (1.1.2 or 1.2.1)
|-
| style="text-align:center;" | 5
! 1
| style="text-align:center;" | 1.1.2
|-
| style="text-align:center;" | >= 6
! 2
| style="text-align:center;" | (1.1.1 and 1.1.2) or (1.2.1 and 1.2.2)
|}
The conspiracy numbers for all possible value of node 1.1 of tree T
{| class="wikitable"
|-
! v
! cn(1.1, v)
! conspirators
|-
| style="text-align:center;" | <= 1
! 1
| style="text-align:center;" | (1.1.1 or 1.1.2)
|-
| style="text-align:center;" | 2
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 3,4,5
! 1
| style="text-align:center;" | 1.1.2
|-
| style="text-align:center;" | >= 6
! 2
| style="text-align:center;" | (1.1.1 and 1.1.2)
|}
The conspiracy numbers for all possible value of node 1.2 of tree T
{| class="wikitable"
|-
! v
! cn(1.2, v)
! conspirators
|-
| style="text-align:center;" | <= 2
! 1
| style="text-align:center;" | (1.2.1 or 1.2.2)
|-
| style="text-align:center;" | 3
! 0
| style="text-align:center;" | none
|-
| style="text-align:center;" | 4
! 1
| style="text-align:center;" | 1.2.1
|-
| style="text-align:center;" | >= 5
! 2
| style="text-align:center;" | (1.2.1 and 1.2.2)
|}
=Recursive Definition=
Following [[Recursion|recursive]] definition in pseudo [[C]] is based on [[Maarten van der Meulen|Van der Meulen's]] code <ref>[[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]</ref>. '''V(J)''' represents the minimaxed value of node J. Opposed to McAllester's original definition which deals with pure game theoretic values, Van der Meulen's distinguished non terminal leaves with cn = 1 for values different of '''v''' from game theoretic terminal nodes to assign +oo, since it is impossible to change their value, independently been arrived at by [[Norbert Klingbeil]] and [[Jonathan Schaeffer]] <ref>[[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1988'''). ''Search Strategies for Conspiracy Numbers.'' Canadian Artificial Intelligence Conference, pp. 133-139</ref>:
<pre>
int cn(CNode J, int v) {
int c;
if ( V(J) == v ) {
c = 0;
} else if ( isTerminal(J) ) {
c = +oo; /* checkmate, stalemate, tablebase score, etc. */
} else if ( isLeaf(J) ) {
c = 1;
} else if (isMaxNode(J) && v < V(J) ) {
c = 0;
for (all childs J.j)
if (v < V(J.j) ) c += cn(J.j, v); /* sum */
} else if (isMinNode(J) && v > V(J) ) {
c = 0;
for (all childs J.j)
if (v > V(J.j) ) c += cn(J.j, v); /* sum */
} else {
c = +oo;
for (all childs J.j)
c = min( cn(J.j, v), c);
}
return c;
}
</pre>
=Search Algorithms=
[[David McAllester|McAllester's]] aim was related to some drawbacks of [[Alpha-Beta|alpha-beta]], at the worst, the decision at the root is based on a single evaluation of one leaf. If that leaf has assigned an erroneous value, the decision may be disastrous <ref>[[Ulf Lorenz]], [[Valentin Rottmann]] ('''1996'''). ''Parallel Controlled Conspiracy-Number Search.'' [[Advances in Computer Chess 8]]</ref>. The idea of [[Conspiracy Number Search]] (cn-search) and its variants is to continue until it is unlikely that the minimax value at the root will change.
* [[Alpha-Beta Conspiracy Search]]
* [[Conspiracy Number Search]]
* [[Controlled Conspiracy Number Search]]
* [[Parallel Controlled Conspiracy Number Search]]
* [[Proof-Number Search]]
=Chess Programs=
* [[Arachne]]
* [[P.ConNerS]]
* [[Ulysses]]
=Publications=
<ref>[http://ilk.uvt.nl/icga/journal/docs/References.pdf ICGA Reference Database](pdf)</ref>
==1985 ...==
* [[David McAllester]] ('''1985'''). ''A New Procedure for Growing Minimax Trees''. Technical Report, Artificial Intelligence Laboratory, MIT
* [[David McAllester]] ('''1988'''). ''Conspiracy Numbers for Min-Max Search''. Artificial Intelligence, Vol. 35, No. 1, pp. 287-310. ISSN 0004-3702
* [[Ingo Althöfer]] ('''1988'''). ''Root Evaluation Errors: How they Arise and Propagate''. [[ICGA Journal#11_23|ICCA Journal, Vol. 11, Nos. 2/3]]
* [[Maarten van der Meulen]] ('''1988'''). ''Parallel Conspiracy-Number Search''. M.Sc. thesis, Faculty of Mathematics and Computer Science, [https://en.wikipedia.org/wiki/Vrije_Universiteit Vrije Universteit, Amsterdam]
* [[Norbert Klingbeil]] ('''1988'''). ''Search Strategies for Conspiracy Numbers''. M.Sc. thesis
* [[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1988'''). ''Search Strategies for Conspiracy Numbers.'' Canadian Artificial Intelligence Conference, pp. 133-139
* [[Jonathan Schaeffer]] ('''1989'''). ''Conspiracy Numbers.'' [[Advances in Computer Chess 5]]. » [[Conspiracy Numbers#AI|also published]]
* [[Charles Elkan]] ('''1989'''). ''Conspiracy Numbers and Caching for Searching And/Or Trees and Theorem-Proving''. [[Conferences#IJCAI|IJCAI 1989]], [http://ijcai.org/Past%20Proceedings/IJCAI-89-VOL1/PDF/054.pdf pdf]
==1990 ...==
* [[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]
* [[Norbert Klingbeil]], [[Jonathan Schaeffer]] ('''1990'''). ''Empirical Results with Conspiracy Numbers.'' Computational Intelligence, Vol. 6, pp. 1-11, [http://webdocs.cs.ualberta.ca/%7Ejonathan/Papers/Papers/compi.ps ps]
* <span id="AI"></span>[[Jonathan Schaeffer]] ('''1990'''). ''Conspiracy Numbers''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_(journal) Artificial Intelligence], Vol. 43, No. 1, pp. 67-84
* [[Maarten van der Meulen]], [[Victor Allis]], [[Jaap van den Herik]] ('''1990'''). ''A Comment on `Conspiracy-Number Search'''. [[ICGA Journal#13_2|ICCA Journal, Vol. 13, No. 2]]
* [[Victor Allis]], [[Maarten van der Meulen]], [[Jaap van den Herik]] ('''1991'''). ''Conspiracy-Number Search.'' [[Advances in Computer Chess 6]]
* [[David McAllester]], [[Deniz Yuret]] ('''1993'''). ''[[Alpha-Beta Conspiracy Search]]''. [http://ttic.uchicago.edu/%7Edmcallester/abc.ps ps (draft)]
* [[Lisa Lister]], [[Jonathan Schaeffer]] ('''1994'''). ''An Analysis of the Conspiracy Numbers Algorithm''. [https://en.wikipedia.org/wiki/Computers_and_Mathematics_with_Applications Computers & Mathematics with Applications] Vol. 27, No. 1, [https://en.wikipedia.org/wiki/Elsevier Elsevier], [http://webdocs.cs.ualberta.ca/%7Ejonathan/publications/ai_publications/icn.pdf pdf]
* [[Deniz Yuret]] ('''1994'''). ''[https://scholar.google.com/citations?view_op=view_citation&hl=en&user=EJurXJ4AAAAJ&cstart=40&citation_for_view=EJurXJ4AAAAJ:TQgYirikUcIC The Principle of Pressure in Chess]''. TAINN 1994
==1995 ...==
* [[Ulf Lorenz]], [[Valentin Rottmann]], [[Rainer Feldmann]], [[Peter Mysliwietz]] ('''1995'''). ''Controlled Conspiracy-Number Search.'' [[ICGA Journal#18_3|ICCA Journal, Vol. 18, No. 3]]
* [[Ulf Lorenz]], [[Valentin Rottmann]] ('''1996'''). ''Parallel Controlled Conspiracy-Number Search.'' [[Advances in Computer Chess 8]]
* [[Ulf Lorenz]] ('''1999'''). ''Controlled Conspiracy-2 Search''. Technical Report, [[University of Paderborn]], [http://www2.cs.upb.de/cs/ag-monien/PUBLICATIONS/POSTSCRIPTS/Falgo.ps ps]
* [[Robin Upton]] ('''1999'''). ''[http://www.robinupton.com/research/phd/ Dynamic Stochastic Control - A New Approach to Game Tree Searching]''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Warwick University of Warwick]
==2000 ...==
* [[Ulf Lorenz]] ('''2000'''). ''Controlled Conspiracy-2 Search''. Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS)
* [[David McAllester]], [[Deniz Yuret]] ('''2002'''). ''[[Alpha-Beta Conspiracy Search]]''. [[ICGA Journal#25_1|ICGA Journal, Vol. 25, No. 1]]
==2010 ...==
* [[Mohd Nor Akmal Khalid]], [[Umi Kalsom Yusof]], [[Hiroyuki Iida]], [[Taichi Ishitobi]] ('''2015'''). ''[https://www.researchgate.net/publication/281152992_Critical_Position_Identification_in_Games_and_Its_Application_to_Speculative_Play Critical Position Identification in Games and Its Application to Speculative Play]''. [http://www.scitepress.org/DigitalLibrary/ProceedingsDetails.aspx?ID=+mGlly8Sp00=&t=1 ICAART 2015]
* [[Mohd Nor Akmal Khalid]], [[E. Mei Ang]], [[Umi Kalsom Yusof]], [[Hiroyuki Iida]], [[Taichi Ishitobi]] ('''2015'''). ''[http://link.springer.com/chapter/10.1007%2F978-3-319-27947-3_6 Identifying Critical Positions Based on Conspiracy Numbers]''. [http://link.springer.com/book/10.1007/978-3-319-27947-3 Agents and Artificial Intelligence], [http://dblp.uni-trier.de/db/conf/icaart/icaart2015s.html#KhalidAYII15 ICAART 2015 - Revised Selected Papers]
* [[Jakub Pawlewicz]], [[Ryan Hayward]] ('''2015'''). ''[https://www.aaai.org/ocs/index.php/SOCS/SOCS15/paper/view/11040 Sibling Conspiracy Number Search]''. [https://en.wikipedia.org/wiki/Symposium_on_Combinatorial_Search SoCS 2015]
=External Links=
==Conspiracy Numbers==
* [http://www.robinupton.com/research/phd/cp_intro.html Conspiracy Numbers, Conspiracy Probailities & PCN* Search] by [[Robin Upton]]
* [http://www.cs.duke.edu/brd/Teaching/Previous/AI/Lectures/conspiracy.txt Reading: McAllister paper on "Consipracy Theory"?] by [http://www.cs.duke.edu/brd/ Bruce Donald]
==Conspiracy==
* [https://en.wikipedia.org/wiki/Conspiracy Conspiracy (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Conspiracy_theory Conspiracy theory from Wikipedia]
* [https://en.wikipedia.org/wiki/List_of_conspiracy_theories List of conspiracy theories from Wikipedia]
* [https://en.wikipedia.org/wiki/Conspiracy_theory_%28disambiguation%29 Conspiracy theory (disambiguation) from Wikipedia]
* [[Videos#JeanneLee|Jeanne Lee]] - Sundance, [https://www.discogs.com/de/Jeanne-Lee-Conspiracy/release/687632 Conspiracy] (1975), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: feat.: [https://fr.wikipedia.org/wiki/Jack_Gregg Jack Gregg], [https://en.wikipedia.org/wiki/Mark_Whitecage Mark Whitecage], [https://en.wikipedia.org/wiki/Steve_McCall_(drummer) Steve McCall], [[Videos#GunterHampel|Gunter Hampel]], [https://en.wikipedia.org/wiki/Sam_Rivers Sam Rivers], [https://en.wikipedia.org/wiki/Marty_Cook Marty Cook]
: {{#evu:https://www.youtube.com/watch?v=CRqGVLEYbUc|alignment=left|valignment=top}}
* [[Videos#ChrisSquire|Squire]] & [https://en.wikipedia.org/wiki/Billy_Sherwood Sherwood], [https://en.wikipedia.org/wiki/Conspiracy_%28band%29 Conspiracy] - [https://en.wikipedia.org/wiki/Conspiracy_(band)#Conspiracy Conspiracy], [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=af-8Of_uBxw|alignment=left|valignment=top}}
=References=
<references />
'''[[Search|Up one Level]]'''
