Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.

Thesis (M.A.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 80-82). Also available via the Internet.

Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.

Modern cellular networks including LTE (Long Term Evolution) and the evolving LTE- Advanced provide high-speed and high-capacity data services for mobile users. As we become more reliant on wireless connectivity, the security of voice and data transmissions on the network becomes increasingly important. While the LTE network standards provide strict security guidelines, these requirements may not be completely followed when LTE networks are deployed in practice. This project provides a method for improving the security of LTE networks by 1) characterizing a gap between security requirements defined in the standards and practical implementations, 2) designing a language to express the encoding formats of one of LTE’s network-layer protocols, 3) developing a compiler to translate a protocol description in our language into an implementation, and 4) providing recommendations on lessons learned during development of the language and compiler to support development of future protocols that employ formal representations. In this way, our work demonstrates how a formal language can be utilized to represent a cellular network protocol and serves as an example for further research on how adding formalism to network standards can help ensure that the security goals defined in the standards can be upheld in an implementation.

Thesis (Ph. D.)--University of Michigan.

Thesis (Ph. D.)--University of Michigan.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, December 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references (leaves 152-200). Also available in electronic version.

Thesis (Ph. D.)--University of Queensland, 2004. / Includes bibliographical references.