Abstract
The aim of this thesis is to obtain better understanding of the nature of computer systems, that is, to develop a mathematical theory of computer systems. By computer systems we mean information-processing systems consisting of computers. We cannot overemphasize their important roles in the modern world. Unfortunately, however, computer systems are very much error-prone at the same time. This thesis ultimately aims at proper understanding of computer systems which will help us getting them right; we do so through extending the theory of coalgebras. The use of coalgebras as a mathematical model of state-based systems has been increasingly recognized in the last couple of decades. We follow this view since, we believe, the theory of coalgebras has a right balance of (potential) applicability and mathematical simplicity. The very core of the existing theory of coalgebras that we start with can be summarized as follows. - A system is modeled mathematically as a coalgebra; - a behavior-preserving map between systems as a morphism of coalgebras; and - the behavior of a system is given by the principle of coinduction. These points have been established by many authors in a large body of existing work. In each chapter of this thesis, however, we try to shed new light on them.
