LOWER BOUNDS FOR THE COMPLEXITY OF FUNCTIONS IN A REALISTIC RAM MODEL

Abstract

This paper develops a new technique that finds lower bounds for the complexity of programs that compute or approximate functions in a realistic RAM model. The nonuniform realistic RAM model is a model that uses the arithmetic operations {+, -, x}, the standard bit operations Shift, Rotate, AND, OR, XOR, NOT (bitwise), comparisons and indirect addressing. We prove general results that give almost tight bounds for the complexity of computing and approximating functions in this model. The functions considered here are integer division, modulo, square root, gcd and logarithms. We also show that if we add the integer division to the realistic RAM model then no nontrivial lower bound can be proven. Our results can be also generalized to probabilistic, nondeterministic and parallel RAM models.