The network complexity and the Turing machine complexity of finite functions

  title={The network complexity and the Turing machine complexity of finite functions},
  author={Claus-Peter Schnorr},
  journal={Acta Informatica},
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… CONTINUE READING
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