This thesis continues the studies of A. Waksman (1969) in the repeated generation of finite strings in a one dimensional array of finite automata. Waksman handles this problem by the use of a "modulo arithmetic" algorithm. This is shown to be very restrictive with regard to the number of characters permitted in the output string. In fact, it is shown that unless the length of the string which is to be repeated is of the form p(formula omitted) where p is prime, only one output character is permitted. This of course makes the process quite meaningless. For this reason, a new algorithm is developed. This is referred to as the wheel algorithm, since there is an obvious analogy between it and a wheel, with the output string on its circumference rolling along the array and leaving the imprint of the characters in the string behind it in the same way that a wheel leaves tire tracks. The number of states required for such an algorithm is large and so the binary wheel algorithm is introduced. By using this algorithm, in which an output state is represented as a string of bits in several cells, the number of states required, in addition to the n output states, can be reduced to about 4 log₂ n. Both the wheel and binary wheel algorithms are then extended to the two dimensional and finally the d-dimensional cases. / Science, Faculty of / Computer Science, Department of / Graduate

"Number is one of man's schemes for adapting himself to his environment. Development of the concept of number in man is intricately bound up with growth in him of language. Man is a social being and almost from birth, language activity becomes a part of his reactions to stimuli. He is therefore apt to use a partial language response even when the stimulus does not come from a strictly social setting"-- / Typescript / "June, 1920" / M.A. Florida State College for Women / Includes bibliographical references (leaves 89-91)

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The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total domination number. First, this thesis provides a complete survey of established bounds on the domination subdivision number and the total domination subdivision number. Then in Chapter 4, new results regarding bounds on the total domination subdivision number are given. Finally, a characterization of the total domination subdivision number of caterpillars is presented in Chapter 5.

This thesis deals with the properties of the coefficients of Hypergeometric Series. Specifically, we are interested in which primes appear in the denominators to a bounded power. The first main result gives a method of categorizing the primes up to equivalence class which appear finitely many times in the denominators of generalized hypergeometric series nFm over the rational numbers. Necessary and sufficient conditions for when the density is zero are provided as well as a categorization of the n and m for which the problem is interesting. The second main result is a similar condition for the appearance of primes in the denominators of the hypergeometric series 2F1 over number fields, specifically quadratic extensions Q(D). A novel conjecture to the study of p-adic numbers is also provided, which discusses the digits of irrational algebraic numbers' p-adic expansions. / Thesis / Master of Science (MSc)

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