Sinopsis
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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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.
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Reseña del editor
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.
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.
Reseña del editor
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.
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Investigations in the Theory of Descriptive Complexity (Classic Reprint)
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Paperback. Condición: New. 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. print-on-demand item. Nº de ref. del artículo: 9781332145317_0
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Investigations in the Theory of Descriptive Complexity (Classic Reprint)
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