Topic summary

P versus NP

P versus NP

Extracted from the Wikipedia article P versus NP problem.

References

  1. ^ 2026.
  2. ^ . Communications of the ACM. 52 (9): 78–86. doi:10.1145/1562164.1562186. S2CID 5969255. Archived from the original(PDF) on 24 February 2011 2010.
  3. ^
  4. ^ . IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E86-A (5): 1052–1060.
  5. ^ 158. doi:10.1145/800157.805047. ISBN . S2CID 7573663.
  6. ^ 116.
  7. ^ . See pages 7-8. Archived(PDF) from the original on 9 November 2018.
  8. ^ . pp. 445–450. doi:10.1142/9789812794499_0033. ISBN .
  9. ^
  10. ^ . SIGACT News. 33 (2): 34–47. doi:10.1145/564585.564599. S2CID 36828694. Archived(PDF) from the original on 15 June 2007.
  11. ^ . SIGACT News. 74. Archived(PDF) from the original on 24 January 2014.
  12. ^ . Archived(PDF) from the original on 31 March 2019 2020.
  13. ^ 2007.
  14. ^ 2020.
  15. ^ 30. doi:10.1016/0166-218X(84)90075-1.
  16. ^ 717. doi:10.1137/0210054.
  17. ^ 214. doi:10.1016/0097-3165(81)90016-9.
  18. ^
  19. ^ 41. Archived from the original on 15 September 2006 2017.
  20. ^ 421. doi:10.1137/0208032.
  21. ^ . S2CID 14352974.
  22. ^ 852. doi:10.1016/j.ic.2006.02.002.
  23. ^ 323. doi:10.1016/0022-0000(88)90010-4.
  24. ^ 3336. MR 3966534.
  25. ^
  26. ^
  27. ^ 435. doi:10.1016/j.jctb.2011.07.004.
  28. ^ 303. doi:10.1016/0196-6774(87)90043-5.
  29. ^ 144. MR 1438311. Postscript file at website of Gondzio and at McMaster University website of Terlaky.
  30. ^ . Clay Mathematics Institute. Archived(PDF) from the original on 16 December 2013 2006.
  31. ^
  32. ^ , point 9.
  33. ^ 2014.
  34. ^ , Theorem 3.9
  35. ^ 31. arXiv:cs/9809117. Bibcode:1998cs........9117H. doi:10.1007/3-540-63890-3_4. ISBN . 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.
  36. ^ 203. 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.
  37. ^ 382. doi:10.1007/978-3-540-72788-0_36.
  38. ^ 40. doi:10.1089/cmb.1998.5.27. PMID 9541869.
  39. ^ . Archived(PDF) from the original on 2 February 2014.
  40. ^ . Documenta Mathematica. pp. 359–376. ISBN . ISSN 1431-0643.
  41. ^ 934. doi:10.2307/2580891. JSTOR 2580891.
  42. ^
  43. ^ ". Archived from the original on 15 November 2013.
  44. ^ 442. doi:10.1137/0204037.
  45. ^ 35. doi:10.1006/jcss.1997.1494.
  46. ^ . Proceedings of ACM STOC'2008. pp. 731–740. doi:10.1145/1374376.1374481. Archived(PDF) from the original on 21 February 2008.
  47. ^ . Archived(PDF) from the original on 16 January 2017..
  48. ^ on 2 March 2012..
  49. ^ 73.
  50. ^ 3): 86–104. doi:10.1016/S0019-9958(86)80029-8.
  51. ^ 146. doi:10.1145/800070.802186.
  52. ^ . 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.
  53. ^
  54. ^ 2018.
  55. ^ 2010.
  56. ^ 'Travelling Salesman' movie considers the repercussions if P equals NP". Wired UK 2026.
  57. ^ 2026. The on-screen lecture by Janek — Russian mathematician demonstrating that P = NP would collapse cryptography — is a real result presented in cleaned-up form.
  58. ^
  59. ^
  60. ^ 2018.
  61. ^ 2018.
  62. ^
  63. ^ . Math Horizons. 11 (4): 12–15. doi:10.1080/10724117.2004.12021767.
  64. ^
  65. ^