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Author: S.R. Buss
Publisher: Springer Science & Business Media
ISBN: 1461234662
Category : Computers
Languages : en
Pages : 352
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Book Description
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: S.R. Buss
Publisher: Springer Science & Business Media
ISBN: 1461234662
Category : Computers
Languages : en
Pages : 352
Get Book Here
Book Description
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
ISBN: 1461225663
Category : Computers
Languages : en
Pages : 456
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Book Description
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: European Association for Computer Science Logic. Conference
Publisher: Springer Science & Business Media
ISBN: 3540425543
Category : Computers
Languages : en
Pages : 631
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Book Description
This book constitutes the refereed proceedings of the 15th International Workshop on Computer Science Logic, CSL 2001, held as the 10th Annual Conerence of the EACSL in Paris, France in September 2001. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected from 91 submissions. The papers are organized in topical sections on linear logic, descriptive complexity, semantics, higher-order programs, model logics, verification, automata, lambda calculus, induction, equational calculus, and constructive theory of types.
Author: Patricio Felmer
Publisher: Springer
ISBN: 3319280236
Category : Education
Languages : en
Pages : 400
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Book Description
This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.
Author: Branislav Rovan
Publisher: Springer
ISBN: 3540451382
Category : Computers
Languages : en
Pages : 706
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Book Description
This book constitutes the refereed proceedings of the 28th International Symposium on Mathematical Foundations of Computer Science, MFCS 2003, held in Bratislava, Slovakia in August 2003. The 55 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 137 submissions. All current aspects in theoretical computer science are addressed, ranging from discrete mathematics, combinatorial optimization, graph theory, networking, algorithms, and complexity to programming theory, formal methods, and mathematical logic.
Author: E.R. Griffor
Publisher: Elsevier
ISBN: 0080533043
Category : Mathematics
Languages : en
Pages : 741
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Book Description
The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
Author: Daniel Leivant
Publisher: Springer Science & Business Media
ISBN: 9783540601784
Category : Computers
Languages : en
Pages : 534
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Book Description
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: Igor Shparlinski
Publisher: Birkhäuser
ISBN: 3034886640
Category : Mathematics
Languages : en
Pages : 181
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Book Description
The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields and residue rings. It also contains a number of open problems and proposals for further research. We obtain several lower bounds, exponential in terms of logp, on the de grees and orders of • polynomials; • algebraic functions; • Boolean functions; • linear recurring sequences; coinciding with values of the discrete logarithm modulo a prime p at suf ficiently many points (the number of points can be as small as pI/He). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the right most bit of the discrete logarithm and defines whether the argument is a quadratic residue. We also obtain non-trivial upper bounds on the de gree, sensitivity and Fourier coefficients of Boolean functions on bits of x deciding whether x is a quadratic residue. These results are used to obtain lower bounds on the parallel arithmetic and Boolean complexity of computing the discrete logarithm. For example, we prove that any unbounded fan-in Boolean circuit. of sublogarithmic depth computing the discrete logarithm modulo p must be of superpolynomial size.
Author: Laurent Fribourg
Publisher: Springer
ISBN: 3540448020
Category : Computers
Languages : en
Pages : 631
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Book Description
This book constitutes the refereed proceedings of the 15th International Workshop on Computer Science Logic, CSL 2001, held as the 10th Annual Conerence of the EACSL in Paris, France in September 2001. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected from 91 submissions. The papers are organized in topical sections on linear logic, descriptive complexity, semantics, higher-order programs, model logics, verification, automata, lambda calculus, induction, equational calculus, and constructive theory of types.
Author: Gheorghe Paun
Publisher: World Scientific
ISBN: 9814492051
Category : Computers
Languages : en
Pages : 881
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Book Description
The scientific developments at the end of the past millennium were dominated by the huge increase and diversity of disciplines with the common label “computer science”. The theoretical foundations of such disciplines have become known as theoretical computer science. This book highlights some key issues of theoretical computer science as they seem to us now, at the beginning of the new millennium.The text is based on columns and tutorials published in the Bulletin of the European Association for Theoretical Computer Science in the period 1995-2000. The columnists themselves selected the material they wanted for the book, and the editors had a chance to update their work. Indeed, much of the material presented here appears in a form quite different from the original. Since the presentation of most of the articles is reader-friendly and does not presuppose much knowledge of the area, the book constitutes suitable supplementary reading material for various courses in computer science.
