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Characterizations of Logarithmic Advice Complexity Classes

The complexity classes P=log and Full-P=log, corresponding to the two standard forms of logarithmic advice for polynomial time, are studied. The novel proof technique of \doubly exponential skip" is introduced, and characterizations for these classes are found in terms of several other concepts, among them easy-to-describe boolean circuits and reduction classes of tally sets with high regularity. Similar results hold for many other complexity classes. In this extended abstract most of the proofs are deferred to the appendix, where they are provided for the interested reader but are intended to be read discretionarily.