Feasible Mathematics
Download Feasible Mathematics full books in PDF, epub, and Kindle. Read online free Feasible Mathematics ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : S.R. Buss |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2013-03-07 |
| Genre | : Computers |
| ISBN | : 1461234662 |
A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.
| Author | : Peter Clote |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 456 |
| Release | : 2013-03-13 |
| Genre | : Computers |
| ISBN | : 1461225663 |
Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa tion device, such as a 'lUring machine or boolean circuit. Feasible math ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.
| Author | : Paul W. Beame |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 335 |
| Release | : 1998 |
| Genre | : Computers |
| ISBN | : 0821805770 |
The 16 papers reflect some of the breakthroughs over the past dozen years in understanding whether or not logical inferences can be made in certain situations and what resources are necessary to make such inferences, questions that play a large role in computer science and artificial intelligence. They discuss such aspects as lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, and the relationship between proof complexity and Boolean circuit complexity. No index. Member prices are $47 for institutions and $35 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 799 |
| Release | : 1998-11-30 |
| Genre | : Computers |
| ISBN | : 0080533701 |
Recursive Algebra, Analysis and Combinatorics
| Author | : Stephen G. Simpson |
| Publisher | : Cambridge University Press |
| Total Pages | : 413 |
| Release | : 2017-03-30 |
| Genre | : Mathematics |
| ISBN | : 1108637221 |
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the foundations of mathematics, motivated by two foundational questions: 'what are appropriate axioms for mathematics?' and 'what are the logical strengths of particular axioms and particular theorems?' This volume, the twenty-first publication in the Lecture Notes in Logic series, contains twenty-four original research papers from respected authors that present exciting new developments in reverse mathematics and subsystems of second order arithmetic since 1998.
| Author | : Stephen G. Ross |
| Publisher | : CRC Press |
| Total Pages | : 416 |
| Release | : 2005-09-01 |
| Genre | : Mathematics |
| ISBN | : 1439864284 |
Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting rece
| Author | : Daniel Leivant |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 534 |
| Release | : 1995-08-02 |
| Genre | : Computers |
| ISBN | : 9783540601784 |
This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 619 |
| Release | : 1998-11-30 |
| Genre | : Computers |
| ISBN | : 9780080533698 |
| Author | : Ronald L. Graham |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 412 |
| Release | : 1999-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780821885819 |
Discrete mathematics stands among the leading disciplines of mathematics and theoretical computer science. This is due primarily to its increasing role in university curriculae and its growing importance in applications ranging from optimization to molecular biology. An inaugural conference was held cooperatively by DIMATIA and DIMACS to focus on the versatility, width, and depth of current progress in the subject area. This volume offers a well-balanced blend of research and survey papers reflecting the exciting, attractive topics in contemporary discrete mathematics. Discussed in the book are topics such as graph theory, partially ordered sets, geometrical Ramsey theory, computational complexity issues and applications.
| Author | : Jacques Dubucs |
| Publisher | : Springer |
| Total Pages | : 223 |
| Release | : 2014-08-27 |
| Genre | : Philosophy |
| ISBN | : 9401792178 |
Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic.
