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Thursday, April 30, 2020 | History

2 edition of Some results in computational complexity. found in the catalog.

Some results in computational complexity.

Ali Juma

Some results in computational complexity.

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  • 33 Currently reading

Published .
Written in English


About the Edition

In this thesis, we present some results in computational complexity. We consider two approaches for showing that #P has polynomial-size circuits. These approaches use ideas from the interactive proof for #3-SAT. We show that these approaches fail. We discuss whether there are instance checkers for languages complete for the class of approximate counting problems. We provide evidence that such instance checkers do not exist. We discuss the extent to which proofs of hierarchy theorems are constructive. We examine the problems that arise when trying to make the proof of Fortnow and Santhanam"s nonuniform BPP hierarchy theorem more constructive.

The Physical Object
Pagination64 leaves.
Number of Pages64
ID Numbers
Open LibraryOL19214691M
ISBN 100494021683

"This book analyzes quantitative aspects of some of the most important results in computational complexity. It will benefit most the reader who already knows the basic tenets of complexity and wants to find out more about it than what is covered in standard courses."- .


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Some results in computational complexity. by Ali Juma Download PDF EPUB FB2

Computational Complexity: A Modern Approach Draft of a book: Dated January Comments welcome. Sanjeev Arora and Boaz Barak Princeton University [email protected] Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more finished than others.

References and. This whole work discusses the important thing topics in complexity precept, along with elementary topics along with present breakthroughs not beforehand obtainable in book sort.

Theory of Computational Complexity presents a radical presentation of the fundamentals of complexity idea, along with NP-completeness idea, the polynomial-time.

Thus, complexity theory contains more questions, and relationships between questions, than actual answers. Nevertheless, we will learn about some fascinating insights, connections, and even few answers, that emerged from complexity theory research. Among the questions we will tackle (for various types of computational problems) are.

The book is well presented, fit for self studies, and covered most contents of computability and complexity. The book is slightly old, some of the latest result are not included, e.g., a P-algorithm of solving "prime problem" was found in This book is not good for advanced researchers in theoretical computer science, it is way to shallow/5(14).

"This book analyzes quantitative aspects of some of the most important results in computational complexity. It will benefit most the reader who already knows the basic tenets of complexity and wants to find out more about it than what is covered in standard courses."--Gerhard LischkeAuthor: Marius Zimand.

The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.

Emphasis is on relevant quantitative attributes of important results in complexity. Haslum P., Jonsson P. () Some Results on the Complexity of Planning with Incomplete Information.

In: Biundo S., Fox M. (eds) Recent Advances in AI Planning. ECP Cited by: A New Kind of Science is a best-selling book by Stephen Wolfram, published Some results in computational complexity.

book his company Wolfram Research under the imprint Wolfram Media in It contains an empirical and systematic study of computational systems such as cellular m calls these systems simple programs and argues that the scientific philosophy and methods appropriate Author: Stephen Wolfram.

Partly as a consequence of such results, research efforts have shifted to the problem of finding approximations of μ which are easy to compute and that are as close as possible to the exact value of μ; see Fu () and Toker and de Jager () for some discussion on computational complexity problems related to the approximate computation of Cited by: About this book Computational complexity theory has developed rapidly in the past three decades.

The list of surprising and fundamental results proved since alone could fill a book: these include new probabilistic definitions of. In this book I tried to present some of the knowledge and understanding I acquired in my four decades in the eld.

The main source of this knowledge was the Theory of Computation community, which has been. Computational models are designed to take advantage of cheap, Some results in computational complexity. book computation. Philosophy of science: The models and results in this book raise a number of questions relevant to the philosophy of science, including the nature of scientific laws, theory choice, realism and instrumentalism, holism and reductionism, and Bayesian epistemology.

Measure One Results In Computational Complexity Theory. This paper is dedicated to Ronald V. Book on the occasion of his 60th birthday. Some. Complexity theory is the study of the intrinsic complexity of computational tasks. The book is aimed at exposing the students to the basic results and research directions in the field.

The focus was on concepts, complex technical proofs were avoided. you have read that book or have equivalent knowledge of Python. I try to emphasize fundamental ideas that apply to programming in many languages, but along the way you will learn some useful features that are specific to Python.

Computational modeling: A model is a simplified description of a system used for simu-complexity scienceFile Size: 1MB. on the computational complexity of 13 measures wrt. three decision problems, namely deciding whether a given value is an upper, resp.

lower bound, or is the e xact value, as well. Publisher Summary. This chapter discusses the complexity of obtaining starting points for solving operator equations by Newton's method. Most results in analytic computational complexity assume that good initial approximations are available and deal with the iteration phase only.

Computational complexity theory focuses on classifying computational problems according to their inherent difficulty, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.

A problem is regarded as inherently difficult if its. In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it.

Particular focus is given to time and memory requirements. As the amount of resources required to run an algorithm generally varies with the size of the input, the complexity is typically expressed as a function n → f(n), where n is the. Avi Wigderson Mathematics and Computation Draft: Ma Acknowledgments In this book I tried to present some of the knowledge and understanding I acquired in my four decades in the eld.

The main source of this knowledge was the Theory of Computation commu-nity, which has been my academic and social home throughout this period. Get this from a library. Computational complexity: a quantitative perspective. [Marius Zimand] -- There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real.

Computational Complexity: A Conceptual Perspective [drafts of a book by Oded Goldreich] See copyright notice. Below is the book's tentative preface and Organization. The following versions are available on-line.

A preliminary draft (dated January ): in format and in six parts corresponding to chapters, B, C Theory of Computational Complexity, Second Edition is an excellent textbook for courses on computational theory and complexity at the graduate-level.

The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct. The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.

Emphasis is on relevant quantitative attributes of important results in complexity. Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch. Personally Bill came out with his new book Problems with a Point; InBoixo et al.

proposed to replace the class of quantum circuits for which some hardness results were known (commuting circuits and boson sampling) by. Computational complexity is an area of increasing importance and deep mathematical results, many of which have substantial practical relevance.

The field will continue to be important due to the continuing development of the technology and due also to the increasing links with other disciplines.4/5(2). This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory.

Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as. Simple. You work out the time complexity of different machine learning algorithms; you can also work out the memory complexity.

For some algorithms you can look at the worst-case or average-case complexities, and so on. For some algorithms, you ca. Find books like Computational Complexity from the world’s largest community of readers. Goodreads members who liked Computational Complexity also liked.

Questions tagged [computational-complexity] Ask Question For unstable homotopy groups there are some results showing that there cannot be homotopy-theory computational-complexity stable-homotopy computational-topology.

asked Sep 18 '18 at Simon Henry. computational-complexity computational-number-theory fourier-transform. This study turned out to be related to complexity theory, where the most tight connection is between some type of randomness extractors and some type of pseudorandom generators.

So far we have focused on the time complexity of computational tasks, while relying on the natural association of efficiency with time. Relativization and algebrization show that proof methods in complexity theory which are “invariant” under certain high-level modifications to the computational model (access to arbitrary oracles, or low-degree extensions thereof) are not “fine-grained enough” to distinguish (even) pairs of classes that seem to be obviously different, such as \(\mathsf{NEXP}\) and Cited by: 4.

Some theorists seem able to hold in their minds, in one instant, the results of every FOCS, STOC, and Complexity paper ever published. Not every proof, of course - but those can be looked up if one knows the results and to whom they’re due.

I am not one of those theorists. The sprawling web of known relations among complexityFile Size: 1MB. This is a good introductory book of computational theory for students in computer science, good juniors, seniors and first year graduates. The book is well presented, fit for self studies, and covered most contents of computability and complexity.

The book is slightly old, some of the latest result are. Some of the most fundamental results in computational complexity are time hierarchies - that we can solve more decision problems on some model of computation when given a bit more of some resource.

Such hierarchies have been established for any reasonable model of computation that is syntactic, i.e., for which there exists a computable.

As I said a few lines above: Compare the recent books by Arora and Safra: "Computational Complexity: A Modern Approach" (draft available online) and by Goldreich: "Computational Complexity: A conceptual perspective" (drafts of some chapters available online).

It IS indeed a subject on its own, and is as such different from Kolmogorov complexity. security. Almost all results in computational complexity and cryptography, while usually stated asymptotically, can be interpreted in concrete terms.

However, they are often not optimized for concrete security (where even constant factors hidden in O-notation are important).

Even with asymptotic security, it is sometimes preferable to demandFile Size: KB. This link might help you find Vaibhav's book as it is currently out of print: Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences) () by Nielsen, Michael A.

A fun book is Scott Aarons. These were "On the Complexity of Real Functions" by Mark Braverman and "On the Complexity of Two-Player Win-Lose Games" by Tim Abbott, Daniel Kane, and Paul Valiant.

As all readers of this weblog know, the next CCC (Computational Complexity Conference) will be held in Prague from JulyThe submission deadline is December 4. The book is recommended to anyone working in the areas of computational complexity, combinatorial optimization, and engineering." (Manish Gupta, Computing Reviews, May, ) “This book treats bio-inspired computing methods as stochastic algorithms and presents rigorous results on their runtime behavior.

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity .I strongly recommend the book Computational Complexity: A Modern Approach by Arora and Barak.

When I took computational complexity at my Master level, the main textbook is Computational Complexity by Papadimitriou. But, maybe due to my background in Software Engineering, I found the writing in Papadimitriou challenging at times.

"This book analyzes quantitative aspects of some of the most important results in computational complexity. It will benefit most the reader who already knows the basic tenets of complexity and wants to find out more about it than what is covered in standard courses."--Gerhard Lischke show moreAuthor: Marius Zimand.