The roles of advice to one-tape linear-time turing machines and finite automata

Abstract

We discuss the power and limitations of various "advice," when it is given particularly to weak computational models of one-tape two-way linear-time Turing machines and one-way finite (state) automata. Of various advice types, we consider deterministically-chosen advice, which is selected depending only on input size, and randomly-chosen advice, which is chosen according to certain probability distributions. We show that machines can be significantly enhanced in computational power when advice is provided; on the contrary, there are clear limitations on such a power. © 2009 Springer-Verlag Berlin Heidelberg.