# The network complexity and the Turing machine complexity of finite functions

@article{Schnorr1976TheNC,
title={The network complexity and the Turing machine complexity of finite functions},
author={Claus-Peter Schnorr},
journal={Acta Informatica},
year={1976},
volume={7},
pages={95-107}
}
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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#### References

##### Publications referenced by this paper.
Showing 1-6 of 6 references

## Lower bounds for the product of time and space requirements of Turing machine computations

• C. P. Schuorr
• Proc. Symposium on the Mathematical Foundations…
• 1973
1 Excerpt

## Complexity of formula realisation of functions of logical algebra

• O. B. Lupanov
• Prob. Cybernetics 3
• 1962
1 Excerpt

## An improved overlap argument for on - line multiplication . In : Complexity of Computation

• M. S. Paterson, M. J. Fischer, A. R. Meyer
• SIAM AMS Proceedings