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It is shown that the problem of evaluating an Nth degree polynomial is reducible to the problem of dividing the polynomial. A method for dividing an Nth degree polynomial by an N/2 degree polynomial in O(N log 2N) steps is given. Using this it is shown that the evaluation of an Nth degree polynomial at N points can be done in O(N log 3N). The related problem of computing of computing the resides of...
Let Φ be any abstract measure of computational complexity, and let L denote the specific measure of memory resource (tape) on one tape Turing machines. Denote by Rt( )Φ the class of all total functions whose Φ-complexity is bounded by the function t( ) almost everywhere. Call such classes Φ-complexity classes. We are interested in relationships among these classes, under proper set inclusion (⊂)....
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