Binary Representations of Finite Fields and Their Application to Complexity Theory
Finite Fields and Their Applications
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It is shown that a lower hound ofn^{3}or more on the straight-line complexity of a functionfover GF(2^{n})is also a lower bound on the network complexity offand, 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.