On the power of alternation in finite automata

Abstract

We shall deal with the following three questions concerning the power of alternation in finite automata theory:

• 1. What is the simplest kind of device for which alternation adds computational power ?

• 2. What are the simplest devices (according to the language family accepted by them) such that the alternating version of these devices is as powerful as Turing machines ?

• 3. Can the number of alternations in the computations of alternating devices be bounded by a function of input word length without the loss of the computational power ?

We give a partial answer to the Questions 1 and 2, i.e. we find the simplest known devices having the required properties according to alternation (multihead simple finite automata and one-way multicounter machines with blind counters respectively). Besides this considering one-way multicounter machines whose counter contents is bounded by the input word length we find a new characterisation of P (the class of languages accepted by deterministic Turing machines in polynomial time). For one-way alternating multihead finite automata we show that the number of alternations in computations cannot be bounded by n^1/3 for input words of length n.

The research was supported by SPZV I-5-7/7 grant.