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 ?
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