Abstract
Using the complexity measure developed in [7,3,4] and the extensions obtained by using inductive register machines of various orders in [1,2], we determine an upper bound on the inductive complexity of second order of the P versus NP problem. From this point of view, the P versus NP problem is more complex than the Riemann hypothesis.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Burgin, M.: Super-recursive Algorithms. Springer, Heidelberg (2005)
Burgin, M., Calude, C.S., Calude, E.: Inductive Complexity Measures for Mathematical Problems. CDMTCS Research Report 416, 11 (2011)
Calude, C.S., Calude, E.: Evaluating the complexity of mathematical problems. Part 1. Complex Systems 18(3), 267–285 (2009)
Calude, C.S., Calude, E.: Evaluating the complexity of mathematical problems. Part 2. Complex Systems 18(4), 387–401 (2010)
Calude, C.S., Calude, E.: The complexity of the Four Colour Theorem. LMS J. Comput. Math. 13, 414–425 (2010)
Calude, C.S., Calude, E.: The Complexity of Mathematical Problems: An Overview of Results and Open Problems. CDMTCS Research Report 410, 12 (2011)
Calude, C.S., Calude, E., Dinneen, M.J.: A new measure of the difficulty of problems. Journal for Multiple-Valued Logic and Soft Computing 12, 285–307 (2006)
Calude, C.S., Calude, E., Queen, M.S.: The complexity of Euler’s integer partition theorem. Theoretical Computer Science (2012), doi:10.1016./j.tcs.2012.03.02
Calude, C.S., Calude, E., Svozil, K.: The complexity of proving chaoticity and the Church-Turing Thesis. Chaos 20, 037103, 1–5 (2010)
Calude, C.S.: Information and Randomness: An Algorithmic Perspective, 2nd edn. Springer, Berlin (2002) (revised and extended)
Calude, E.: The complexity of Riemann’s Hypothesis. Journal for Multiple-Valued Logic and Soft Computing 18(3-4), 257–265 (2012)
Cook, S.: The complexity of theorem proving procedures. In: STOC 1971, Proceedings of the Third Annual ACM Symposium on Theory of Computing, pp. 151–158. ACM, New York (1971)
Cook, S.: The P versus NP Problem, 12 pages (manuscript), http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf (visited on June 16, 2012)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001) [1990]
Dinneen, M.J.: A Program-Size Complexity Measure for Mathematical Problems and Conjectures. In: Dinneen, M.J., Khoussainov, B., Nies, A. (eds.) Computation, Physics and Beyond. LNCS, vol. 7160, pp. 81–93. Springer, Heidelberg (2012)
Fortnow, L.: The status of the P vs NP problem. CACM 52(9), 78–86 (2009)
Horowitz, E., Sahni, S.: Computing partitions with applications to the knapsack problem. JACM 21, 277–292 (1974)
Jackson, A.: Interview with Martin Davis. Notices AMS 55(5), 560–571 (2008)
Levin, L.: Universal search problems. Problemy Peredachi Informatsii 9, 265–266 (1973) (in Russian), English translation in [22]
Moore, C., Mertens, S.: The Nature of Computation. Oxford University Press, Oxford (2011)
Mulmuley, K.D.: The GCT program toward the P vs NP problem. CACM 55(6), 98–107 (2012)
Trakhtenbrot, B.A.: A survey of Russian approaches to Perebor (brute-force search) algorithms. Annals of the History of Computing 6, 384–400 (1984)
http://www.claymath.org/millennium/P_vs_NP/ (visited on June 16, 2012)
http://www.claymath.org/millennium/Riemann_Hypothesis/ (visited on June 16, 2012)
Wöginger, G.J.: The P-versus-NP webpage, http://www.win.tue.nl/~gwoegi/P-versus-NP.htm (visited on June 16, 2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calude, C.S., Calude, E., Queen, M.S. (2012). Inductive Complexity of P versus NP Problem. In: Durand-Lose, J., Jonoska, N. (eds) Unconventional Computation and Natural Computation. UCNC 2012. Lecture Notes in Computer Science, vol 7445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-32894-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32893-0
Online ISBN: 978-3-642-32894-7
eBook Packages: Computer ScienceComputer Science (R0)