Nondeterministic witnesses and nonuniform advice

Several results related to nonuniform complexity classes and their comparison with uniform ones are surveyed. The relevance of the main tools in these arguments, namely, self-reducibility structures is explained by showing that the methods for proving relationships between nonuniform and uniform classes, including the so-called round-robin tournament method, can be presented as general properties of self-reducible sets. New results can be obtained from these general properties. One of the mentioned proof techniques is shown to be closely related to the notion of helping