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Acta Informatica

, Volume 7, Issue 1, pp 95–107 | Cite as

The network complexity and the Turing machine complexity of finite functions

  • C. P. Schnorr
Article

Summary

Let L(f) be the network complexity of a Boolean function L(f). For any n-ary Boolean function L(f) let \(TC(f) = min\{ T_p^{\bar A} (n){\text{ (}}\parallel p\parallel + 1gS_p^{\bar A} {\text{(}}n{\text{):}}res_p^{\bar A} {\text{(}}n{\text{) = }}f\} \). Hereby p ranges over all relative Turing programs and Ā ranges over all oracles such that given the oracle Ā, the restriction of p to inputs of length n is a program for L(f). ∥p∥ is the number of instructions of p. T p Ā (n) is the time bound and S p Ā of the program p relative to the oracle Ā on inputs of length n. Our main results are (1) L(f) ≦ O(TC(L(f))), (2) TC(f) ≦ O(L(f)22+ɛ) for every ɛ ⋙ O.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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.

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References

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • C. P. Schnorr
    • 1
  1. 1.Fachbereich MathematikUniversität FrankfurtFrankfurt/M.Germany

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