Investigations in the Theory of Descriptive Complexity (Classic Reprint) - Softcover

Gewirtz, William L.

Softcover

ISBN 10: 1332145310 ISBN 13: 9781332145317

Verlag: Forgotten Books, 2019

Inhaltsangabe

Excerpt from Investigations in the Theory of Descriptive Complexity

In terms of each of the three above approaches a random or patternless string 5 is defined as one whose shortest program is of length essentially equal to it self. Intuitively, if a string contains some pattern then that pattern can be exploited by the computer in outputting the string. However, if a string 5 is genuinely patternless the shortest program for outputting it might consist of inputting s and instructing the computer to output its input.

Chapter 1. Will present most of the fundamental notations, definitions and results developed for the most part by others which are relevant to our work.

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Excerpt from Investigations in the Theory of Descriptive Complexity

Introduction; 1. Fundamental Notations, Definitions and Results of Descriptive Complexity; 1.1 Notational Conventions; 1.2 Fundamental Definitions and Results of the Kolmogorov Formulations; 1.3 Chaitin's Formulation of Descriptive Complexity; 1.4 Elementary Theorems Relating the Kolmogorov and Chaitin Formulations; 1.5 Recursive and Recursively Enumerable Sequences; 2. Infinite Random Sequences; 2.1 Basic Definitions and Results of the Kolmogorov Formulation; 2.2 Chaitin's Proposed Definitions; 2.3 A Definition Based on Chaitin's Formulation; 2.4 Recursive and Recursively Enumerable Subsequences; 3. An Analysis Of K(s/s); 3.1 The Set of Optimal Programs; 3.2 K(s/s) 5. Subrecursive Formulations Of Descriptive Complexity; 5.1 Introduction and Fundamental Definitions; 5.3 A Hierarchy of Random Sequences; 5.4 The Maximum Grzegorczyk Level of All Programs of Length Less than n; 5.5 The Longest String of Complexity Less than n; Notes; Bibliography

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2019
• Sprache: Englisch
• ISBN 10: 1332145310
• ISBN 13: 9781332145317
• Einband: Tapa blanda
• Anzahl der Seiten: 70
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar