A More Accurate Approximation of the Sign Function
نویسندگان
چکیده
For the simpler functions (such as and,or), a degree-Θ( √ n) polynomial suffices. For more complicated functions (such as majority), a degree-n polynomial is necessary. Note that in this formalism, any function can be approximated to arbitrary accuracy with a degree-n polynomial. It suffices (i) to form the sum of the 2 polynomials each of which evaluates to 1 on a distinct assignment to the variables and to 0 on all others; and (ii) to weigh these polynomials by the output of the actual function.
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