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


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.


Information System Operating System Data Structure Communication Network Information Theory 
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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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