With the rapid growth of integration scale of VLSI chips and the present need for reliable computers in space exploration, fault diagnosis and fault toleran- ce have become more important than before, and hence reveal a lot of interest- ing topics which attract many researchers to make a great number of contribu- tions to this field. In recent years, many new and significant results have been achieved. A quick scan over the proceedings of the conferences on fault- tolerant computing and design automation as well as on testing will convince the reader of that. But unfortunately these achievements have not been entire- ly reflected in the textbooks, so that there seems to be a gap for the new researcher who already has the basic knowledge and wants to begin research in this area. As a remedy for this deficiency, this book is intended for begin- ners, especially graduate students, as a textbook which will lead them to the frontier of some branches of the fault-tolerant computing field. The first chapter introduces the four-valued logic B4 and its applica- tions. In 1966 Roth first proposed this four-valued logic as a technique to generate tests for logical circuits, but this work did not concern the mathe- matical basis of B4 itself.