The difference between optimality and universality

We discuss the difference between optimality and universality. The sequence of measures of a universal test is well studied. To analyze the sequence of measures of an optimal Martin-Löf test, we introduce uniform Solovay reducibility. Solovay reducibility is a measure of relative randomness between two reals. In contrast uniform Solovay reducibility is a measure of relative randomness between two sequences of reals. Finally we prove that a sequence is uniform Solovay complete iff it is the sequence of measures of an optimal Martin-Löf test.