Trade-off between the Boolean and Arithmetic Depths of Modulo p Functions
For a polynomial f(X) ∈ ℤ[X] we consider Boolean functions producing the second leftmost bit of the smallest non-negative residues of f(x) modulo p from the bit representation of x and obtain a lower bound on their sensitivity (see Chapter 6 for the definition of this notion). Then a similar but a weaker bound is obtained for the sensitivity of Boolean functions producing the second leftmost bit of rational functions modulo p.
KeywordsRational Function Boolean Function Unique Root Arithmetic Circuit Boolean Circuit
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