On the power of alternation in automata theory

Abstract

We shall deal with the following three questions concerning the power of alternation in 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 branchings (universal configurations) in the computations of alternating devices be bounded by a function of the input word length without loss of computational power? We give a partial answer to Questions 1 and 2, i.e., we find the simplest known devices (multihead simple finite automata and one-way blind multicounter machines, respectively) having the required properties according to alternation. Besides this, considering one-way multicounter machines whose counter contents are bounded by the input word length, we find a new characterization of P. For one-way alternating (simple) multihead finite automata we show that the number of universal configurations in computations cannot be bounded by o( n log 2 n ) 1 2 ( o( n log 2 n ) ), where n is the input word length.