The head hierarchy for oblivious finite automata with polynomial advice collapses

Abstract

We show that the hierarchy of classes of languages accepted by finite multi-head automata with oblivious head movements that receive polynomial advice strings collapses to the fifth level. A characterization of nondeterministic logarithmic space with polynomial advice is simplified. In the presence of polynomial advice, the question whether deterministic and nondeterministic logarithmic space are equivalent can be reduced to the question whether simple nondeterministic automata can be simulated deterministically. Polynomial time can be characterized by a one-head device.

For automata without advice we prove that multi-head counter automata, stack automata, and on-erasing stack automata do not lose power by the restriction to oblivious head movements.