A new kind of temporal inequalities are discussed, which apply to algorithmic processes, involving a finite memory processing unit. They are an alternative to the Leggett–Grag ones, as well as to the modified ones by Brukner et al. If one considers comparison of quantum and classical processes involving systems of finite memory (of the same capacity in both cases), the inequalities give a clear message why we can expect quantum speed-up. In a classical process one always has clearly defined values of possible measurements, or in terms of the information processing language, if we have a sequential computations of some function depending on data arriving at each step on an algorithm, the function always has a clearly defined value. In the quantum case only the final value, after the end of the algorithm, is defined. All intermediate values, in agreement with Bohr’s complementarity, cannot be ascribed a definite value.