Arithmetical complexity of some problems in computer science

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


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

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

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