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The notion of communication complexity was introduced by Yao in his seminal paper [Yao79]. In [BFS86], Babai Frankl and Simon developed a rich structure of communication complexity classes to understand the relationships between various models of communication complexity. This made it apparent that communication complexity was a self-contained mini-world within complexity theory. In this thesis, we study the place of regular languages within this mini-world. In particular, we are interested in the non-deterministic communication complexity of regular languages. / We show that a regular language has either O(1) or O(log n) non-deterministic complexity. We obtain several linear lower bound results which cover a wide range of regular languages having linear non-deterministic complexity. These lower bound results also imply a result in semigroup theory: we obtain sufficient conditions for not being in the positive variety Pol(Com). / To obtain our results, we use algebraic techniques. In the study of regular languages, the algebraic point of view pioneered by Eilenberg ([Eil74]) has led to many interesting results. Viewing a semigroup as a computational device that recognizes languages has proven to be prolific from both semigroup theory and formal languages perspectives. In this thesis, we provide further instances of such mutualism.

Please read the abstract in the section 00front of this document / Dissertation (MSc (Computer Science))--University of Pretoria, 2003. / Computer Science / unrestricted

This thesis presents a Finite State Machine (FSM) Synthesizer developed at Portland State University. The synthesizer starts from a high level behavioral description, in which no states are specified, and generates the lower level FSM descriptions for simulation and physical layout generation.

A complete program to ease the task of large scale Finite State Machine (FSM) minimization presented in this thesis: TDFM (Two Dimensional FSM Minimizer), is a part of the DIADES system. DIADES is an Automatic Design Synthesis System whose development in the Department of Electrical Engineering at Portland State University is supported in part by a research grant from SHARP Microelectronics Technology.

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