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https://hdl.handle.net/2142/71229
Description
Title
Alternation and Omega-Type Turing Acceptors
Author(s)
Lindsay, Peter Alexander
Issue Date
1984
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
An (omega)-language is a set of infinite ((omega)-type) strings of symbols. We study the classes of (omega)-languages accepted by Turing Acceptors when infinite computations are allowed. There are various possible "natural" acceptance conditions to consider, including those already common in the literature of (omega)-automata. There are also the deterministic (D), nondeterministic (N) and alternating (A) models to consider. Alternating machines were introduced by Chandra, Kozen and Stockmeyer (J. Assoc. Comp. Mach. 28 (1981), 114-133) as a natural extension of nondeterministic machines. (In symbols: D (LESSTHEQ) N (LESSTHEQ) A.)
It is seen that under certain acceptance conditions alternating (omega)-TA's are no more powerful than their nondeterministic counterparts, while under other conditions they are far more powerful. In fact, each of the following cases occurs: D < N < A; D = N < A; D < N = A. We characterize the classes in terms of the arithmetical and analytical hierarchies of (omega)-languages (c.f. Rogers, Theory of Recursive Functions and Effective Computability, chapter 14) and give examples of (omega)-languages which are in some sense the most complicated in each class.
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