Investigations in the Theory of Descriptive Complexity (Classic Reprint)

William L. Gewirtz

ISBN 10: 1332145310 / ISBN 13: 9781332145317

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book explores the fascinating concept of 'descriptive complexity' in computer science. The author presents various formulations of the notion of descriptive complexity, seeking to define and measure the randomness of infinite binary strings. The book considers how the complexity of a program might change when given more information about the object it operates on, such as its length. A key question is whether there exist truly random sequences or if all sequences can be described using some finite program. This question is explored through a 'subrecursive formulation' which places restrictions on the functions which can be computed. The author ultimately concludes that truly random sequences do exist and that they cannot be described using any finite program. This book will appeal to computer scientists, mathematicians, and anyone interested in the foundations of computing and information theory. Its insights into the nature of randomness and complexity provide valuable contributions to our understanding of these fundamental concepts. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781332145317_0

Bibliographic Details

• Title: Investigations in the Theory of Descriptive Complexity (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1332145310
• ISBN 13: 9781332145317
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
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About this title

Synopsis

Dive into descriptive complexity and discover how randomness, optimal programs, and subrecursive ideas shape this branch of theory. This work presents foundational concepts and key results in a rigorous, approachable way.

The book surveys several formulations of descriptive complexity, explains how different definitions relate, and shows what these differences mean for infinite and finite strings. It uses clear, structured chapters to compare absolute and conditional complexity, introduce subrecursive approaches, and discuss the behavior of universal computers and optimal programs. Readers will see how ideas about randomness, immunity, and complexity interact across formulations.

• Learn how descriptive complexity is defined for binary strings and how randomness is characterized in this framework.


• Explore the concept of optimal programs and why their behavior differs across formulations.


• See how the theory extends to subrecursive formalisms and what that implies for limits of computation.


• Understand key proofs and the logical structure behind results about immune sets and universal computers.

Ideal for readers of theoretical computer science and mathematical logic seeking a rigorous treatment of descriptive complexity and its foundational questions.