Date of Award


Document Type


Degree Name

Master of Arts (MA)



First Advisor

Dr. Vyacheslav Rykov


This thesis began with a question about how the human brain works and then two type of Boolean Networks , 1-D Cellular Automata and Associate Memory Model are chosen to explore this question. In the first part of this thesis the computability of 1-D Cellular Automata is studied by inventing a simple model, 3 colored balls model and several logical gates are implemented in its space. Although this model is so simple, by implementing three important logical gates, "NOT", "AND" and "OR", 3 colored balls model is proved to be computational universal. Since a common property " annihilation" is seen in each gate for having computability, the property is also used to prove the computational universality of Elemental Cellular Automata. ln the other part of thesis the probability of errors in the recurrent associate memory model is studied. To study dynamics of the recurrent model, I use the same MDS code as an input and an output and found the probability distribution of the number of extra ones that may appear through associate map. By the probability distribution we found that the number of error is going to decrease when the larger MOS code is used and also by comparing to binomial distribution both results are close and when we choose the larger MDS code the difference of both is getting closer.


A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree (Master of Art) University of Nebraska at Omaha. Copyright 2004 Masahiko Kimura

Files over 3MB may be slow to open. For best results, right-click and select "save as..."