Advice hierarchies among finite automata

We examine the effects of supplying increasing amounts of trusted advice to a finite automaton. Previous work has shown that allowing such automata with a single advice tape to make a single pass over their input renders them unable to recognize the palindromes language, whereas both two-way machines reading advice from a single tape and one-way machines with multiple advice tapes can recognize all languages with exponentially bounded amounts of advice. We study several architectural variants and demonstrate the existence of language hierarchies based on increased advice length, runtime (measured in terms of the number of allowed left-to-right passes on the input), and number of advice tapes. We also prove some lower bounds for recognizing certain concrete languages.