This book forms the much needed strong interface between algorithmic complexity and computer experiments using a careful blending of traditional ideas in algorithms with untraditional research in computer experiments (esp. fitting stochastic models to non-random data). While establishing the aforesaid interface, the important role of statistical bounds and their empirical estimates obtained over a finite range (called empirical O) is discovered as a bonus. While these bounds are very valuable for the average case, our research suggests in addition that there is no need to be ...