P versus NP problem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "P versus NP problem" in English language version.

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academia.edu

Johnson, David S. (August 2012). "A Brief History of NP-Completeness, 1954–2012". In Grötschel, M. (ed.). Optimization Stories (PDF). Documenta Mathematica. pp. 359–376. ISBN 978-3-936609-58-5. ISSN 1431-0643.

acm.org

portal.acm.org

Cook, Stephen (1971). "The complexity of theorem proving procedures". Proceedings of the Third Annual ACM Symposium on Theory of Computing. pp. 151–158. doi:10.1145/800157.805047. ISBN 9781450374644. S2CID 7573663.

mags.acm.org

Rosenberger, Jack (May 2012). "P vs. NP poll results". Communications of the ACM. 55 (5): 10.

ams.org

mathscinet.ams.org

Babai, László (2018). "Group, graphs, algorithms: the graph isomorphism problem". Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. IV. Invited lectures. World Sci. Publ., Hackensack, NJ. pp. 3319–3336. MR 3966534.
Gondzio, Jacek; Terlaky, Tamás (1996). "3 A computational view of interior point methods". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Lecture Series in Mathematics and its Applications. Vol. 4. New York: Oxford University Press. pp. 103–144. MR 1438311. Postscript file at website of Gondzio and at McMaster University website of Terlaky.

archive-it.org

wayback.archive-it.org

Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM. 52 (9): 78–86. CiteSeerX 10.1.1.156.767. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original (PDF) on 24 February 2011. Retrieved 26 January 2010.

arxiv.org

See Horie, S.; Watanabe, O. (1997). "Hard instance generation for SAT". Algorithms and Computation. Lecture Notes in Computer Science. Vol. 1350. Springer. pp. 22–31. arXiv:cs/9809117. Bibcode:1998cs........9117H. doi:10.1007/3-540-63890-3_4. ISBN 978-3-540-63890-2. for a reduction of factoring to SAT. A 512-bit factoring problem (8400 MIPS-years when factored) translates to a SAT problem of 63,652 variables and 406,860 clauses.

claymath.org

Cook, Stephen (April 2000). "The P versus NP Problem" (PDF). Clay Mathematics Institute. Archived (PDF) from the original on 16 December 2013. Retrieved 18 October 2006.

computationalcomplexity.org

blog.computationalcomplexity.org

Gasarch, William (7 October 2013). "P vs NP is Elementary? No— P vs NP is ON Elementary". blog.computationalcomplexity.org. Retrieved 6 July 2018.

cornell.edu

ecommons.library.cornell.edu

Hartmanis, Juris. "Gödel, von Neumann, and the P = NP problem" (PDF). Bulletin of the European Association for Theoretical Computer Science. 38: 101–107.

doi.org

Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM. 52 (9): 78–86. CiteSeerX 10.1.1.156.767. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original (PDF) on 24 February 2011. Retrieved 26 January 2010.
Cook, Stephen (1971). "The complexity of theorem proving procedures". Proceedings of the Third Annual ACM Symposium on Theory of Computing. pp. 151–158. doi:10.1145/800157.805047. ISBN 9781450374644. S2CID 7573663.
William I. Gasarch (June 2002). "The P=?NP poll" (PDF). SIGACT News. 33 (2): 34–47. CiteSeerX 10.1.1.172.1005. doi:10.1145/564585.564599. S2CID 36828694. Archived (PDF) from the original on 15 June 2007.
Colbourn, Charles J. (1984). "The complexity of completing partial Latin squares". Discrete Applied Mathematics. 8 (1): 25–30. doi:10.1016/0166-218X(84)90075-1.
I. Holyer (1981). "The NP-completeness of some edge-partition problems". SIAM J. Comput. 10 (4): 713–717. doi:10.1137/0210054.
Aviezri Fraenkel and D. Lichtenstein (1981). "Computing a perfect strategy for n × n chess requires time exponential in n". Journal of Combinatorial Theory. Series A. 31 (2): 199–214. doi:10.1016/0097-3165(81)90016-9.
Valiant, Leslie G. (1979). "The complexity of enumeration and reliability problems". SIAM Journal on Computing. 8 (3): 410–421. doi:10.1137/0208032.
Ladner, R.E. (1975). "On the structure of polynomial time reducibility". Journal of the ACM. 22: 151–171 See Corollary 1.1. doi:10.1145/321864.321877. S2CID 14352974.
Arvind, Vikraman; Kurur, Piyush P. (2006). "Graph isomorphism is in SPP". Information and Computation. 204 (5): 835–852. doi:10.1016/j.ic.2006.02.002.
Schöning, Uwe (1988). "Graph isomorphism is in the low hierarchy". Journal of Computer and System Sciences. 37 (3): 312–323. doi:10.1016/0022-0000(88)90010-4.
Kawarabayashi, Ken-ichi; Kobayashi, Yusuke; Reed, Bruce (2012). "The disjoint paths problem in quadratic time". Journal of Combinatorial Theory. Series B. 102 (2): 424–435. doi:10.1016/j.jctb.2011.07.004.
Johnson, David S. (1987). "The NP-completeness column: An ongoing guide (edition 19)". Journal of Algorithms. 8 (2): 285–303. CiteSeerX 10.1.1.114.3864. doi:10.1016/0196-6774(87)90043-5.
See Horie, S.; Watanabe, O. (1997). "Hard instance generation for SAT". Algorithms and Computation. Lecture Notes in Computer Science. Vol. 1350. Springer. pp. 22–31. arXiv:cs/9809117. Bibcode:1998cs........9117H. doi:10.1007/3-540-63890-3_4. ISBN 978-3-540-63890-2. for a reduction of factoring to SAT. A 512-bit factoring problem (8400 MIPS-years when factored) translates to a SAT problem of 63,652 variables and 406,860 clauses.
See, for example, Massacci, F.; Marraro, L. (2000). "Logical cryptanalysis as a SAT problem". Journal of Automated Reasoning. 24 (1): 165–203. CiteSeerX 10.1.1.104.962. doi:10.1023/A:1006326723002. S2CID 3114247. in which an instance of DES is encoded as a SAT problem with 10336 variables and 61935 clauses. A 3DES problem instance would be about 3 times this size.
De, Debapratim; Kumarasubramanian, Abishek; Venkatesan, Ramarathnam (2007). "Inversion attacks on secure hash functions using SAT solvers". Theory and Applications of Satisfiability Testing – SAT 2007. International Conference on Theory and Applications of Satisfiability Testing. Springer. pp. 377–382. doi:10.1007/978-3-540-72788-0_36.
Berger, B.; Leighton, T. (1998). "Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete". J. Comput. Biol. 5 (1): 27–40. CiteSeerX 10.1.1.139.5547. doi:10.1089/cmb.1998.5.27. PMID 9541869.
L. R. Foulds (October 1983). "The Heuristic Problem-Solving Approach". Journal of the Operational Research Society. 34 (10): 927–934. doi:10.2307/2580891. JSTOR 2580891.
T. P. Baker; J. Gill; R. Solovay (1975). "Relativizations of the P =? NP Question". SIAM Journal on Computing. 4 (4): 431–442. doi:10.1137/0204037.
Razborov, Alexander A.; Steven Rudich (1997). "Natural proofs". Journal of Computer and System Sciences. 55 (1): 24–35. doi:10.1006/jcss.1997.1494.
S. Aaronson; A. Wigderson (2008). Algebrization: A New Barrier in Complexity Theory (PDF). Proceedings of ACM STOC'2008. pp. 731–740. doi:10.1145/1374376.1374481. Archived (PDF) from the original on 21 February 2008.
Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin (2004). "PRIMES is in P" (PDF). Annals of Mathematics. 160 (2): 781–793. doi:10.4007/annals.2004.160.781. JSTOR 3597229. Archived (PDF) from the original on 26 September 2006.

ed.ac.uk

maths.ed.ac.uk

Gondzio, Jacek; Terlaky, Tamás (1996). "3 A computational view of interior point methods". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Lecture Series in Mathematics and its Applications. Vol. 4. New York: Oxford University Press. pp. 103–144. MR 1438311. Postscript file at website of Gondzio and at McMaster University website of Terlaky.

fortnow.com

weblog.fortnow.com

Lance Fortnow. Computational Complexity Blog: Complexity Class of the Week: Factoring. 13 September 2002.

harvard.edu

ui.adsabs.harvard.edu

See Horie, S.; Watanabe, O. (1997). "Hard instance generation for SAT". Algorithms and Computation. Lecture Notes in Computer Science. Vol. 1350. Springer. pp. 22–31. arXiv:cs/9809117. Bibcode:1998cs........9117H. doi:10.1007/3-540-63890-3_4. ISBN 978-3-540-63890-2. for a reduction of factoring to SAT. A 512-bit factoring problem (8400 MIPS-years when factored) translates to a SAT problem of 63,652 variables and 406,860 clauses.

iitk.ac.in

cse.iitk.ac.in

Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin (2004). "PRIMES is in P" (PDF). Annals of Mathematics. 160 (2): 781–793. doi:10.4007/annals.2004.160.781. JSTOR 3597229. Archived (PDF) from the original on 26 September 2006.

informit.com

Knuth, Donald E. (20 May 2014). Twenty Questions for Donald Knuth. InformIT. Retrieved 20 July 2014.

jstor.org

L. R. Foulds (October 1983). "The Heuristic Problem-Solving Approach". Journal of the Operational Research Society. 34 (10): 927–934. doi:10.2307/2580891. JSTOR 2580891.
Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin (2004). "PRIMES is in P" (PDF). Annals of Mathematics. 160 (2): 781–793. doi:10.4007/annals.2004.160.781. JSTOR 3597229. Archived (PDF) from the original on 26 September 2006.

mathnet.ru

L. A. Levin (1973). Универсальные задачи перебора [Problems of Information Transmission]. Пробл. передачи информ (in Russian). 9 (3): 115–116.

mcmaster.ca

cas.mcmaster.ca

Gondzio, Jacek; Terlaky, Tamás (1996). "3 A computational view of interior point methods". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Lecture Series in Mathematics and its Applications. Vol. 4. New York: Oxford University Press. pp. 103–144. MR 1438311. Postscript file at website of Gondzio and at McMaster University website of Terlaky.

mit.edu

lcs.mit.edu

Fischer, Michael J.; Rabin, Michael O. (1974). "Super-Exponential Complexity of Presburger Arithmetic". Proceedings of the SIAM-AMS Symposium in Applied Mathematics. 7: 27–41. Archived from the original on 15 September 2006. Retrieved 15 October 2017.

news.mit.edu

Hardesty, Larry (29 October 2009). "Explained: P vs. NP".

nd.edu

science.nd.edu

Shadia, Ajam (13 September 2013). "What is the P vs. NP problem? Why is it important?".

nih.gov

pubmed.ncbi.nlm.nih.gov

Berger, B.; Leighton, T. (1998). "Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete". J. Comput. Biol. 5 (1): 27–40. CiteSeerX 10.1.1.139.5547. doi:10.1089/cmb.1998.5.27. PMID 9541869.

nsa.gov

NSA (2012). "Letters from John Nash" (PDF). Archived (PDF) from the original on 9 November 2018.

nytimes.com

John Markoff (8 October 2009). "Prizes Aside, the P-NP Puzzler Has Consequences". The New York Times.
Markoff, John (16 August 2010). "Step 1: Post Elusive Proof. Step 2: Watch Fireworks". The New York Times. Retrieved 20 September 2010.

ox.ac.uk

cs.ox.ac.uk

"MSc course: Foundations of Computer Science". www.cs.ox.ac.uk. Retrieved 25 May 2020.

princeton.edu

intractability.princeton.edu

"Tentative program for the workshop on "Complexity and Cryptography: Status of Impagliazzo's Worlds"". Archived from the original on 15 November 2013.

psu.edu

citeseerx.ist.psu.edu

Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM. 52 (9): 78–86. CiteSeerX 10.1.1.156.767. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original (PDF) on 24 February 2011. Retrieved 26 January 2010.
William I. Gasarch (June 2002). "The P=?NP poll" (PDF). SIGACT News. 33 (2): 34–47. CiteSeerX 10.1.1.172.1005. doi:10.1145/564585.564599. S2CID 36828694. Archived (PDF) from the original on 15 June 2007.
Johnson, David S. (1987). "The NP-completeness column: An ongoing guide (edition 19)". Journal of Algorithms. 8 (2): 285–303. CiteSeerX 10.1.1.114.3864. doi:10.1016/0196-6774(87)90043-5.
See, for example, Massacci, F.; Marraro, L. (2000). "Logical cryptanalysis as a SAT problem". Journal of Automated Reasoning. 24 (1): 165–203. CiteSeerX 10.1.1.104.962. doi:10.1023/A:1006326723002. S2CID 3114247. in which an instance of DES is encoded as a SAT problem with 10336 variables and 61935 clauses. A 3DES problem instance would be about 3 times this size.
Berger, B.; Leighton, T. (1998). "Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete". J. Comput. Biol. 5 (1): 27–40. CiteSeerX 10.1.1.139.5547. doi:10.1089/cmb.1998.5.27. PMID 9541869.

scottaaronson.com

Scott Aaronson. "PHYS771 Lecture 6: P, NP, and Friends". Retrieved 27 August 2007.
Scott Aaronson (4 September 2006). "Reasons to believe"., point 9.
S. Aaronson; A. Wigderson (2008). Algebrization: A New Barrier in Complexity Theory (PDF). Proceedings of ACM STOC'2008. pp. 731–740. doi:10.1145/1374376.1374481. Archived (PDF) from the original on 21 February 2008.
Aaronson, Scott. "Is P Versus NP Formally Independent?" (PDF). Archived (PDF) from the original on 16 January 2017..

semanticscholar.org

api.semanticscholar.org

Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM. 52 (9): 78–86. CiteSeerX 10.1.1.156.767. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original (PDF) on 24 February 2011. Retrieved 26 January 2010.
Cook, Stephen (1971). "The complexity of theorem proving procedures". Proceedings of the Third Annual ACM Symposium on Theory of Computing. pp. 151–158. doi:10.1145/800157.805047. ISBN 9781450374644. S2CID 7573663.
William I. Gasarch (June 2002). "The P=?NP poll" (PDF). SIGACT News. 33 (2): 34–47. CiteSeerX 10.1.1.172.1005. doi:10.1145/564585.564599. S2CID 36828694. Archived (PDF) from the original on 15 June 2007.
Ladner, R.E. (1975). "On the structure of polynomial time reducibility". Journal of the ACM. 22: 151–171 See Corollary 1.1. doi:10.1145/321864.321877. S2CID 14352974.
See, for example, Massacci, F.; Marraro, L. (2000). "Logical cryptanalysis as a SAT problem". Journal of Automated Reasoning. 24 (1): 165–203. CiteSeerX 10.1.1.104.962. doi:10.1023/A:1006326723002. S2CID 3114247. in which an instance of DES is encoded as a SAT problem with 10336 variables and 61935 clauses. A 3DES problem instance would be about 3 times this size.

stanford.edu

cs.stanford.edu

History of this letter and its translation from Sipser, Michael. "The History and Status of the P versus NP question" (PDF). Archived (PDF) from the original on 2 February 2014.

technion.ac.il

cs.technion.ac.il

Ben-David, Shai; Halevi, Shai (1992). On the independence of P versus NP. Technion (Technical report). Vol. 714. Archived from the original (GZIP) on 2 March 2012..

tue.nl

win.tue.nl

Gerhard J. Woeginger. "The P-versus-NP page". Retrieved 24 June 2018.

tv.com

Kirkpatrick, Noel (4 October 2013). "Elementary Solve for X Review: Sines of Murder". TV.com. Retrieved 6 July 2018.

uchicago.edu

cs.uchicago.edu

Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM. 52 (9): 78–86. CiteSeerX 10.1.1.156.767. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original (PDF) on 24 February 2011. Retrieved 26 January 2010.

uci.edu

ics.uci.edu

David Eppstein. "Computational Complexity of Games and Puzzles".

ucsd.edu

cseweb.ucsd.edu

R. Impagliazzo, "A personal view of average-case complexity", p. 134, 10th Annual Structure in Complexity Theory Conference (SCT'95), 1995.

umd.edu

cs.umd.edu

William I. Gasarch (June 2002). "The P=?NP poll" (PDF). SIGACT News. 33 (2): 34–47. CiteSeerX 10.1.1.172.1005. doi:10.1145/564585.564599. S2CID 36828694. Archived (PDF) from the original on 15 June 2007.
William I. Gasarch. "The Second P=?NP poll" (PDF). SIGACT News. 74. Archived (PDF) from the original on 24 January 2014.
"Guest Column: The Third P =? NP Poll1" (PDF). Archived (PDF) from the original on 31 March 2019. Retrieved 25 May 2020.

unizar.es

Elvira Mayordomo. "P versus NP" Archived 16 February 2012 at the Wayback Machine Monografías de la Real Academia de Ciencias de Zaragoza 26: 57–68 (2004).

web.archive.org

NSA (2012). "Letters from John Nash" (PDF). Archived (PDF) from the original on 9 November 2018.
William I. Gasarch (June 2002). "The P=?NP poll" (PDF). SIGACT News. 33 (2): 34–47. CiteSeerX 10.1.1.172.1005. doi:10.1145/564585.564599. S2CID 36828694. Archived (PDF) from the original on 15 June 2007.
William I. Gasarch. "The Second P=?NP poll" (PDF). SIGACT News. 74. Archived (PDF) from the original on 24 January 2014.
"Guest Column: The Third P =? NP Poll1" (PDF). Archived (PDF) from the original on 31 March 2019. Retrieved 25 May 2020.
Fischer, Michael J.; Rabin, Michael O. (1974). "Super-Exponential Complexity of Presburger Arithmetic". Proceedings of the SIAM-AMS Symposium in Applied Mathematics. 7: 27–41. Archived from the original on 15 September 2006. Retrieved 15 October 2017.
Cook, Stephen (April 2000). "The P versus NP Problem" (PDF). Clay Mathematics Institute. Archived (PDF) from the original on 16 December 2013. Retrieved 18 October 2006.
History of this letter and its translation from Sipser, Michael. "The History and Status of the P versus NP question" (PDF). Archived (PDF) from the original on 2 February 2014.
"Tentative program for the workshop on "Complexity and Cryptography: Status of Impagliazzo's Worlds"". Archived from the original on 15 November 2013.
S. Aaronson; A. Wigderson (2008). Algebrization: A New Barrier in Complexity Theory (PDF). Proceedings of ACM STOC'2008. pp. 731–740. doi:10.1145/1374376.1374481. Archived (PDF) from the original on 21 February 2008.
Aaronson, Scott. "Is P Versus NP Formally Independent?" (PDF). Archived (PDF) from the original on 16 January 2017..
Ben-David, Shai; Halevi, Shai (1992). On the independence of P versus NP. Technion (Technical report). Vol. 714. Archived from the original (GZIP) on 2 March 2012..
Elvira Mayordomo. "P versus NP" Archived 16 February 2012 at the Wayback Machine Monografías de la Real Academia de Ciencias de Zaragoza 26: 57–68 (2004).
Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin (2004). "PRIMES is in P" (PDF). Annals of Mathematics. 160 (2): 781–793. doi:10.4007/annals.2004.160.781. JSTOR 3597229. Archived (PDF) from the original on 26 September 2006.

wired.co.uk

Geere, Duncan (26 April 2012). "'Travelling Salesman' movie considers the repercussions if P equals NP". Wired UK. Retrieved 26 April 2012.

worldcat.org

Johnson, David S. (August 2012). "A Brief History of NP-Completeness, 1954–2012". In Grötschel, M. (ed.). Optimization Stories (PDF). Documenta Mathematica. pp. 359–376. ISBN 978-3-936609-58-5. ISSN 1431-0643.