Concluding Remarks

Abstract

This book aims at the concise presentation of fascinating results chosen from three fields, which together constitute the theory of computation: automata and language theory, computability theory, and complexity theory. The author will be grateful if this book helps readers find it pleasurable to explore those fields. The theory of computation incorporates not only aspects of science, but also intimate connections with engineering practices that might be useful to businesses. Among such typical examples are public key cryptography, which obviates risks in sending a key to someone far away, the concept of relational databases, which enables expression of enormous amounts of data in tabular form, thereby facilitating updating and searching for data, and an algorithm to compute linear programming efficiently, which solves many practical optimization problems. The database industry, for example, has grown to a tens-of-billion-dollar scale. I hope that the theory of computation, which has such an extensive effect on business, will develop along a relevant and healthy direction in the future.