Computation Power of Randomization and Nondeterminism

The fundamental questions of computation theory are related to the relative power of determinism, nondeterminism, and randomization. The famous P vs. NP problem is not the only one of main interest. The class of practically solvable algorithmic problems is not specified by deterministic polynomial time (P) anymore, but by bounded-error polynomial time algorithms. Hence, the comparison of the efficiency of randomized and deterministic computations is not only a fundamental question of theoretical depth, but also a very practical question, the answer to which is often crucial to the success of particular applications. Currently, one is not able to solve problems about the relations between deterministic, randomized, and nondeterministic polynomial time classes, and our methods are not powerful enough to give us a realistic chance to attack these problems seriously. But what can be done is to try to estimate the relations between determinism, nondeterminism, and different modes of randomization in distinct restricted frameworks in order to gain experience with different computation modes and a deeper understanding of the nature of randomization and nondeterminism. Our main research aims can be stated as follows: