Algorithmic Probability

Algorithmic Probability

Author: Marcel F. Neuts

Publisher: CRC Press

Published: 1995-07-01

Total Pages: 488

ISBN-13: 9780412996917

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This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.


Book Synopsis Algorithmic Probability by : Marcel F. Neuts

Download or read book Algorithmic Probability written by Marcel F. Neuts and published by CRC Press. This book was released on 1995-07-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.

Algorithmic Probability and Combinatorics

Algorithmic Probability and Combinatorics

Author: Manuel Lladser

Publisher: American Mathematical Soc.

Published: 2010-07-30

Total Pages: 251

ISBN-13: 082184783X

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This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.


Book Synopsis Algorithmic Probability and Combinatorics by : Manuel Lladser

Download or read book Algorithmic Probability and Combinatorics written by Manuel Lladser and published by American Mathematical Soc.. This book was released on 2010-07-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.

Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

Author: David L. Dowe

Publisher: Springer

Published: 2013-10-22

Total Pages: 457

ISBN-13: 3642449581

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Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff (1926-2009), honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines (UTMs) could be used for universal Bayesian prediction and artificial intelligence (machine learning). This work continues to increasingly influence and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of (general) intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy.


Book Synopsis Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence by : David L. Dowe

Download or read book Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence written by David L. Dowe and published by Springer. This book was released on 2013-10-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff (1926-2009), honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines (UTMs) could be used for universal Bayesian prediction and artificial intelligence (machine learning). This work continues to increasingly influence and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of (general) intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy.

Algorithmic Probability

Algorithmic Probability

Author: Fouad Sabry

Publisher: One Billion Knowledgeable

Published: 2023-06-28

Total Pages: 129

ISBN-13:

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What Is Algorithmic Probability In the field of algorithmic information theory, algorithmic probability is a mathematical method that assigns a prior probability to a given observation. This method is sometimes referred to as Solomonoff probability. In the 1960s, Ray Solomonoff was the one who came up with the idea. It has applications in the theory of inductive reasoning as well as the analysis of algorithms. Solomonoff combines Bayes' rule and the technique in order to derive probabilities of prediction for an algorithm's future outputs. He does this within the context of his broad theory of inductive inference. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Algorithmic Probability Chapter 2: Kolmogorov Complexity Chapter 3: Gregory Chaitin Chapter 4: Ray Solomonoff Chapter 5: Solomonoff's Theory of Inductive Inference Chapter 6: Algorithmic Information Theory Chapter 7: Algorithmically Random Sequence Chapter 8: Minimum Description Length Chapter 9: Computational Learning Theory Chapter 10: Inductive Probability (II) Answering the public top questions about algorithmic probability. (III) Real world examples for the usage of algorithmic probability in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of algorithmic probability' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of algorithmic probability.


Book Synopsis Algorithmic Probability by : Fouad Sabry

Download or read book Algorithmic Probability written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2023-06-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Algorithmic Probability In the field of algorithmic information theory, algorithmic probability is a mathematical method that assigns a prior probability to a given observation. This method is sometimes referred to as Solomonoff probability. In the 1960s, Ray Solomonoff was the one who came up with the idea. It has applications in the theory of inductive reasoning as well as the analysis of algorithms. Solomonoff combines Bayes' rule and the technique in order to derive probabilities of prediction for an algorithm's future outputs. He does this within the context of his broad theory of inductive inference. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Algorithmic Probability Chapter 2: Kolmogorov Complexity Chapter 3: Gregory Chaitin Chapter 4: Ray Solomonoff Chapter 5: Solomonoff's Theory of Inductive Inference Chapter 6: Algorithmic Information Theory Chapter 7: Algorithmically Random Sequence Chapter 8: Minimum Description Length Chapter 9: Computational Learning Theory Chapter 10: Inductive Probability (II) Answering the public top questions about algorithmic probability. (III) Real world examples for the usage of algorithmic probability in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of algorithmic probability' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of algorithmic probability.

Universal Artificial Intelligence

Universal Artificial Intelligence

Author: Marcus Hutter

Publisher: Springer Science & Business Media

Published: 2005-12-29

Total Pages: 294

ISBN-13: 3540268774

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Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.


Book Synopsis Universal Artificial Intelligence by : Marcus Hutter

Download or read book Universal Artificial Intelligence written by Marcus Hutter and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.

Algorithmic Information Dynamics

Algorithmic Information Dynamics

Author: Hector Zenil

Publisher: Cambridge University Press

Published: 2023-05-25

Total Pages: 346

ISBN-13: 1108659268

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Biological systems are extensively studied as interactions forming complex networks. Reconstructing causal knowledge from, and principles of, these networks from noisy and incomplete data is a challenge in the field of systems biology. Based on an online course hosted by the Santa Fe Institute Complexity Explorer, this book introduces the field of Algorithmic Information Dynamics, a model-driven approach to the study and manipulation of dynamical systems . It draws tools from network and systems biology as well as information theory, complexity science and dynamical systems to study natural and artificial phenomena in software space. It consists of a theoretical and methodological framework to guide an exploration and generate computable candidate models able to explain complex phenomena in particular adaptable adaptive systems, making the book valuable for graduate students and researchers in a wide number of fields in science from physics to cell biology to cognitive sciences.


Book Synopsis Algorithmic Information Dynamics by : Hector Zenil

Download or read book Algorithmic Information Dynamics written by Hector Zenil and published by Cambridge University Press. This book was released on 2023-05-25 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological systems are extensively studied as interactions forming complex networks. Reconstructing causal knowledge from, and principles of, these networks from noisy and incomplete data is a challenge in the field of systems biology. Based on an online course hosted by the Santa Fe Institute Complexity Explorer, this book introduces the field of Algorithmic Information Dynamics, a model-driven approach to the study and manipulation of dynamical systems . It draws tools from network and systems biology as well as information theory, complexity science and dynamical systems to study natural and artificial phenomena in software space. It consists of a theoretical and methodological framework to guide an exploration and generate computable candidate models able to explain complex phenomena in particular adaptable adaptive systems, making the book valuable for graduate students and researchers in a wide number of fields in science from physics to cell biology to cognitive sciences.

Universal Artificial Intelligence

Universal Artificial Intelligence

Author: Marcus Hutter

Publisher: Springer Science & Business Media

Published: 2004-10-12

Total Pages: 294

ISBN-13: 3540221395

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Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.


Book Synopsis Universal Artificial Intelligence by : Marcus Hutter

Download or read book Universal Artificial Intelligence written by Marcus Hutter and published by Springer Science & Business Media. This book was released on 2004-10-12 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.

Methods and Applications of Algorithmic Complexity

Methods and Applications of Algorithmic Complexity

Author: Hector Zenil

Publisher: Springer Nature

Published: 2022-05-16

Total Pages: 270

ISBN-13: 3662649853

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This book explores a different pragmatic approach to algorithmic complexity rooted or motivated by the theoretical foundations of algorithmic probability and explores the relaxation of necessary and sufficient conditions in the pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance and applicability. Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently coexist for the first time, ranging from the dominant ones based upon popular statistical lossless compression algorithms (such as LZW) to newer approaches that advance, complement, and also pose their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented, and despite their many challenges, some of these methods are better grounded in or motivated by the principles of algorithmic information. The authors propose that the field can make greater contributions to science, causation, scientific discovery, networks, and cognition, to mention a few among many fields, instead of remaining either as a technical curiosity of mathematical interest only or as a statistical tool when collapsed into an application of popular lossless compression algorithms. This book goes, thus, beyond popular statistical lossless compression and introduces a different methodological approach to dealing with algorithmic complexity. For example, graph theory and network science are classic subjects in mathematics widely investigated in the twentieth century, transforming research in many fields of science from economy to medicine. However, it has become increasingly clear that the challenge of analyzing these networks cannot be addressed by tools relying solely on statistical methods. Therefore, model-driven approaches are needed. Recent advances in network science suggest that algorithmic information theory could play an increasingly important role in breaking those limits imposed by traditional statistical analysis (entropy or statistical compression) in modeling evolving complex networks or interacting networks. Further progress on this front calls for new techniques for an improved mechanistic understanding of complex systems, thereby calling out for increased interaction between systems science, network theory, and algorithmic information theory, to which this book contributes.


Book Synopsis Methods and Applications of Algorithmic Complexity by : Hector Zenil

Download or read book Methods and Applications of Algorithmic Complexity written by Hector Zenil and published by Springer Nature. This book was released on 2022-05-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores a different pragmatic approach to algorithmic complexity rooted or motivated by the theoretical foundations of algorithmic probability and explores the relaxation of necessary and sufficient conditions in the pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance and applicability. Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently coexist for the first time, ranging from the dominant ones based upon popular statistical lossless compression algorithms (such as LZW) to newer approaches that advance, complement, and also pose their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented, and despite their many challenges, some of these methods are better grounded in or motivated by the principles of algorithmic information. The authors propose that the field can make greater contributions to science, causation, scientific discovery, networks, and cognition, to mention a few among many fields, instead of remaining either as a technical curiosity of mathematical interest only or as a statistical tool when collapsed into an application of popular lossless compression algorithms. This book goes, thus, beyond popular statistical lossless compression and introduces a different methodological approach to dealing with algorithmic complexity. For example, graph theory and network science are classic subjects in mathematics widely investigated in the twentieth century, transforming research in many fields of science from economy to medicine. However, it has become increasingly clear that the challenge of analyzing these networks cannot be addressed by tools relying solely on statistical methods. Therefore, model-driven approaches are needed. Recent advances in network science suggest that algorithmic information theory could play an increasingly important role in breaking those limits imposed by traditional statistical analysis (entropy or statistical compression) in modeling evolving complex networks or interacting networks. Further progress on this front calls for new techniques for an improved mechanistic understanding of complex systems, thereby calling out for increased interaction between systems science, network theory, and algorithmic information theory, to which this book contributes.

From Parallel to Emergent Computing

From Parallel to Emergent Computing

Author: Andrew Adamatzky

Publisher: CRC Press

Published: 2019-03-13

Total Pages: 608

ISBN-13: 1351681923

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Modern computing relies on future and emergent technologies which have been conceived via interaction between computer science, engineering, chemistry, physics and biology. This highly interdisciplinary book presents advances in the fields of parallel, distributed and emergent information processing and computation. The book represents major breakthroughs in parallel quantum protocols, elastic cloud servers, structural properties of interconnection networks, internet of things, morphogenetic collective systems, swarm intelligence and cellular automata, unconventionality in parallel computation, algorithmic information dynamics, localized DNA computation, graph-based cryptography, slime mold inspired nano-electronics and cytoskeleton computers. Features Truly interdisciplinary, spanning computer science, electronics, mathematics and biology Covers widely popular topics of future and emergent computing technologies, cloud computing, parallel computing, DNA computation, security and network analysis, cryptography, and theoretical computer science Provides unique chapters written by top experts in theoretical and applied computer science, information processing and engineering From Parallel to Emergent Computing provides a visionary statement on how computing will advance in the next 25 years and what new fields of science will be involved in computing engineering. This book is a valuable resource for computer scientists working today, and in years to come.


Book Synopsis From Parallel to Emergent Computing by : Andrew Adamatzky

Download or read book From Parallel to Emergent Computing written by Andrew Adamatzky and published by CRC Press. This book was released on 2019-03-13 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern computing relies on future and emergent technologies which have been conceived via interaction between computer science, engineering, chemistry, physics and biology. This highly interdisciplinary book presents advances in the fields of parallel, distributed and emergent information processing and computation. The book represents major breakthroughs in parallel quantum protocols, elastic cloud servers, structural properties of interconnection networks, internet of things, morphogenetic collective systems, swarm intelligence and cellular automata, unconventionality in parallel computation, algorithmic information dynamics, localized DNA computation, graph-based cryptography, slime mold inspired nano-electronics and cytoskeleton computers. Features Truly interdisciplinary, spanning computer science, electronics, mathematics and biology Covers widely popular topics of future and emergent computing technologies, cloud computing, parallel computing, DNA computation, security and network analysis, cryptography, and theoretical computer science Provides unique chapters written by top experts in theoretical and applied computer science, information processing and engineering From Parallel to Emergent Computing provides a visionary statement on how computing will advance in the next 25 years and what new fields of science will be involved in computing engineering. This book is a valuable resource for computer scientists working today, and in years to come.

Probabilistic Methods for Algorithmic Discrete Mathematics

Probabilistic Methods for Algorithmic Discrete Mathematics

Author: Michel Habib

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 342

ISBN-13: 3662127881

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Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.


Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib

Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.