Advertisement

Some Theorems Concerning the Core Function

  • Angelo Raffaele Meo
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5065)

Abstract

In a preceding paper an NP-complete problem has been discussed pertaining to a function, called “core function”, which plays an important role in the well known Boolean satisfiability problem (see the first item in the references list). In this paper, some theorems concerning the minimal Boolean implementation of the core function are proved.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Meo, A.R.: On the minimization of core function Acc. Sc. Torino – Memorie Sc. Fis. 29, 155–178, 7 ff. (2005)Google Scholar
  2. 2.
    Sipser, M.: Introduction to the theory of computation, PWS Publ.Comp. (1997)Google Scholar
  3. 3.
    Smale, S.: Mathematical problems for the next century. Mathematical Intelligencer 20(2), 7–15 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and intractability. W.H.Freeman and Co., New York (1979)zbMATHGoogle Scholar
  5. 5.
    Asser, G.: Das Reprasentantenproblem im Pradikatenkalkul der ersten Stufe mit Identitat, Zietschr.f.Mathematisches Logik u. Grundlagen der Math. 1, 252–263 (1955)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Cook, S.A.: The complexity of theorem proving procedures. In: Proc. 3rd Annual ACM Symp. on Theory of Computing, pp. 151–158. ACM Press, New York (1971)CrossRefGoogle Scholar
  7. 7.
    Cook, S.A.: Computational complexity of higher type functions. In: Sarake, I. (ed.) Proceeding of the International Congress of Mathematicians, Kyoto, Japan, pp. 55–60. Springer, Heidelberg (1991)Google Scholar
  8. 8.
    Godel, K.: A letter to J.von Neumann, in Sipser’s article listed above. In: Clote, P., Krajicek, J. (eds.) Arithmetic, Proof Theory and Computational Complexity, Oxford University Press, Oxford (1993)Google Scholar
  9. 9.
    Karp, R.M.: Reducibility Among Combinatorial Problems, Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)Google Scholar
  10. 10.
    Levin, L.: Universal Search Problems. Problemy Peredachi Informatsii (= Problems of Information Transmission) 9(3), 265–266 (in Russian) (1973); A partial English transalation, In: Trakhtenbrot, B.A.: A Survey of Russian Approches to Perebor (Brute-force Search) Algorithms. Annals of the History of Computing 6(4), 384–400 (1984)Google Scholar
  11. 11.
    Scholz, H.: Problem #1: Ein ungelostes Problem in der symbolisches Logik. Symbolic Logic 17, 160 (1952)Google Scholar
  12. 12.
    Sipser, M.: The history and status of the P versus NP question. In: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pp. 603–618. ACM Press, New York (1992)Google Scholar
  13. 13.
    Baker, T., Gill, J., Solovay, R.: Relativizations of the P =? NP question. IAM J. of Computing 4, 431–442 (1975)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Boppana, R., Sipser, M.: Complexity of finite functions. In: van Leeuwen, J. (ed.) Handbook of heoretical Computer Science, pp. 758–804 (1990)Google Scholar
  15. 15.
    Krajicek, J.: Bounded arithmetic, propositional logic, and omplexity theory, Encyclopedia of Mathematics and Its Applications, vol. 60. Cambridge University Press, Cambridge (1995)Google Scholar
  16. 16.
    Pudlak, P.: The lengths of proofs. In: Buss, S.R. (ed.) Handbook of Proof Theory, North-Holland, Amsterdam (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Angelo Raffaele Meo
    • 1
  1. 1.Politecnico di Torino 

Personalised recommendations