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On the power of straight- line computations in finite fields

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3 Author(s)

It is shown that a lower hound of n^{3} or more on the straight-line complexity of a function f over GF (2^{n}) is also a lower bound on the network complexity of f and, hence, on the product of run time and program size of Turing machines. It is further shown that most functions over a finite field are hard to compute and that for most hard functions there exists no approximation via an easy algorithm.

Published in:

IEEE Transactions on Information Theory  (Volume:28 ,  Issue: 6 )