Randomness Through Computation
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Randomness Through Computation
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Author : Hector Zenil
language : en
Publisher: World Scientific
Release Date : 2011
Randomness Through Computation written by Hector Zenil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computers categories.
This review volume consists of an indispensable set of chapters written by leading scholars, scientists and researchers in the field of Randomness, including related subfields specially but not limited to the strong developed connections to the Computability and Recursion Theory. Highly respected, indeed renowned in their areas of specialization, many of these contributors are the founders of their fields. The scope of Randomness Through Computation is novel. Each contributor shares his personal views and anecdotes on the various reasons and motivations which led him to the study of the subject. They share their visions from their vantage and distinctive viewpoints. In summary, this is an opportunity to learn about the topic and its various angles from the leading thinkers.
Computational Analysis Of Randomness In Structural Mechanics
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Author : Christian Bucher
language : en
Publisher: CRC Press
Release Date : 2009-03-30
Computational Analysis Of Randomness In Structural Mechanics written by Christian Bucher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-30 with Mathematics categories.
Proper treatment of structural behavior under severe loading - such as the performance of a high-rise building during an earthquake - relies heavily on the use of probability-based analysis and decision-making tools. Proper application of these tools is significantly enhanced by a thorough understanding of the underlying theoretical and computation
Randomness And Completeness In Computational Complexity
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Author : Dieter van Melkebeek
language : en
Publisher: Springer
Release Date : 2003-06-29
Randomness And Completeness In Computational Complexity written by Dieter van Melkebeek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-29 with Computers categories.
This book contains a revised version of the dissertation the author wrote at the Department of Computer Science of the University of Chicago. The thesis was submitted to the Faculty of Physical Sciences in conformity with the requirements for the PhD degree in June 1999. It was honored with the 1999 ACM Doctoral Dissertation Award in May 2000. Summary Computational complexity is the study of the inherent di culty of compu- tional problems and the power of the tools we may use to solve them. It aims to describe how many resources we need to compute the solution as a function of the problem size. Typical resources include time on sequential and parallel architectures and memory space. As we want to abstract away from details of input representation and speci cs of the computer model, we end up with classes of problems that we can solve within certain robust resource bounds such as polynomial time, parallel logarithmic time, and logarithmic space. Research in complexity theory boils down to determining the relationships between these classes { inclusions and separations. In this dissertation, we focus on the role of randomness and look at various properties of hard problems in order to obtain separations. We also investigate the power of nondeterminism and alternation, as well as space versus time issues. Randomness provides a resource that seems to help in various situations.
Randomness And Undecidability In Physics
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Author : Karl Svozil
language : en
Publisher: World Scientific
Release Date : 1993-10-05
Randomness And Undecidability In Physics written by Karl Svozil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-05 with Science categories.
Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an “inner description”, a “virtual physics” of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as “randomness” in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the “distant future”. In other words: no “speedup” or “computational shortcut” is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.
Probability And Random Number A First Guide To Randomness
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Author : Sugita Hiroshi
language : en
Publisher: World Scientific
Release Date : 2017-10-06
Probability And Random Number A First Guide To Randomness written by Sugita Hiroshi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-06 with Mathematics categories.
This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age. Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists. Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus. Contents: Mathematics of Coin TossingMathematical ModelRandom NumberLimit TheoremMonte Carlo MethodInfinite coin TossesRandom Number: Recursive FunctionKolmogorov Complexity and Random NumberLimit Theorem: Bernoulli's TheoremLaw of Large NumbersDe Moivre–Laplace's TheoremCentral Limit TheoremMathematical StatisticsMonte Carlo Method: Monte Carlo Method as GamblingPseudorandom GeneratorMonte Carlo IntegrationFrom the Viewpoint of Mathematical StatisticsAppendices: Symbols and TermsBinary Numeral SystemLimit of Sequence and FunctionLimits of Exponential Function and LogarithmC Language Program Readership: First year university students to professionals. Keywords: Probability;Probability Theory;Randomness;Random Number;Pseudorandom Number;Monte Carlo Method;Monte Carlo IntegrationReview: Key Features: This is the first book that presents both probability theory and algorithmic randomness for from 1st year university students to experts. It is technically easy but worth reading for experts as wellThis book presents basic limit theorems with proofs that are not seen in usual probability textbooks; for readers should learn that a good solution is not always uniqueThis book rigorously treats the Monte Carlo method. In particular, it presents the random Weyl sampling, which produces pseudorandom numbers for the Monte Carlo integration that act complete substitutes for random numbers
Randomness And Computation
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Author :
language : en
Publisher:
Release Date : 1989
Randomness And Computation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computational complexity categories.
Algorithmic Randomness
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Author : Johanna N. Y. Franklin
language : en
Publisher: Cambridge University Press
Release Date : 2020-05-07
Algorithmic Randomness written by Johanna N. Y. Franklin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-07 with Computers categories.
Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.
Algorithmic Randomness And Complexity
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Author : Rodney G. Downey
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Algorithmic Randomness And Complexity written by Rodney G. Downey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Computers categories.
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Information Randomness Incompleteness
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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1987
Information Randomness Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computers categories.
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on ?Algorithmic Information Theory? by the author. There the strongest possible version of Gdel's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics.
Computability And Randomness
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Author : André Nies
language : en
Publisher: OUP Oxford
Release Date : 2012-03-29
Computability And Randomness written by André Nies and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-29 with Mathematics categories.
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.