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Title:  Alternating Automata and the Temporal Logic of Ordinals 
Author(s):  Rohde, Gareth Scott 
Doctoral Committee Chair(s):  Schupp, Paul E. 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Computer Science 
Abstract:  In their 1995 paper, Muller and Schupp define the concept of an alternating automaton, a sort of completion of the notion of a nondeterministic automaton, and show how the notion may be used to prove a number of major results in the theory of automata on infinite inputs in a unified way. In this thesis, we extend the notion of an alternating automaton to accommodate linear inputs of arbitrary ordinal length and then use these automata to prove a number of results about linear propositional temporal logic, a form of modal logic. First, we show that there is a natural interpretation of automaton inputs as structures for the logic and that under this interpretation, alternating automata and temporal logic are equally powerful. We then use this fact to investigate the satisfiability problem for temporal logic. In particular, not only do we look at the question of whether a given formula has a model, but we look at this question when the lengths of models is restricted to a specific ordinal. We show that the temporal logic of an arbitrary (but fixed) ordinal is decidable in exponential time, generalizing the known result that the temporal logic of $\omega$ is decidable in exponential time. We also look at which classes of ordinals are definable by temporal logic formulas (more precisely, which classes of ordinals result from projecting the class of models of a formula onto their respective lengths), and give a characterization of such classes. 
Issue Date:  1997 
Type:  Text 
Language:  English 
Description:  267 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1997. 
URI:  http://hdl.handle.net/2142/86954 
Other Identifier(s):  (MiAaPQ)AAI9812757 
Date Available in IDEALS:  20150928 
Date Deposited:  1997 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois