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Arithmetical complexity of some problems in computer science

  • P. Hájek
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 53)

Abstract

We show that the set of all (indices of) Turing machines running in time n2 is a complete π 1 0 set and that the set of all (indices of Turing machines computing characteristic functions of) recursive sets A such that PA ≠ NPA is a complete π 2 0 set. As corollaries we obtain results saying that some assertions concerning running time of Turing machines and some instances of the relativized P = NP problem are independent of set theory (or of another theory containing arithmetic).

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • P. Hájek
    • 1
  1. 1.Mathematical Institute, CSAVPrague

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