Geometry and Complexity Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry and Complexity Theory write by J. M. Landsberg. This book was released on 2017-09-28. Geometry and Complexity Theory available in PDF, EPUB and Kindle. This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.
Geometry and Complexity Theory
Geometry and Complexity Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry and Complexity Theory write by J. M. Landsberg. This book was released on 2017-09-28. Geometry and Complexity Theory available in PDF, EPUB and Kindle. Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Algebraic Complexity Theory
Algebraic Complexity Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Complexity Theory write by Peter Bürgisser. This book was released on 2013-03-14. Algebraic Complexity Theory available in PDF, EPUB and Kindle. The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Complexity and Real Computation
Complexity and Real Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Complexity and Real Computation write by Lenore Blum. This book was released on 2012-12-06. Complexity and Real Computation available in PDF, EPUB and Kindle. The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Computational Complexity
Computational Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Complexity write by Sanjeev Arora. This book was released on 2009-04-20. Computational Complexity available in PDF, EPUB and Kindle. New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
