Open AccessBook
Complexity and Real Computation
TLDR
This chapter discusses decision problems and Complexity over a Ring and the Fundamental Theorem of Algebra: Complexity Aspects.Abstract:
1 Introduction.- 2 Definitions and First Properties of Computation.- 3 Computation over a Ring.- 4 Decision Problems and Complexity over a Ring.- 5 The Class NP and NP-Complete Problems.- 6 Integer Machines.- 7 Algebraic Settings for the Problem "P ? NP?".- 8 Newton's Method.- 9 Fundamental Theorem of Algebra: Complexity Aspects.- 10 Bezout's Theorem.- 11 Condition Numbers and the Loss of Precision of Linear Equations.- 12 The Condition Number for Nonlinear Problems.- 13 The Condition Number in ?(H(d).- 14 Complexity and the Condition Number.- 15 Linear Programming.- 16 Deterministic Lower Bounds.- 17 Probabilistic Machines.- 18 Parallel Computations.- 19 Some Separations of Complexity Classes.- 20 Weak Machines.- 21 Additive Machines.- 22 Nonuniform Complexity Classes.- 23 Descriptive Complexity.- References.read more
Citations
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MonographDOI
Planning Algorithms: Introductory Material
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
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Stability of Time-Delay Systems
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
Journal ArticleDOI
On the mathematical foundations of learning
TL;DR: A main theme of this report is the relationship of approximation to learning and the primary role of sampling (inductive inference) and relations of the theory of learning to the mainstream of mathematics are emphasized.
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Computable Analysis : An Introduction
TL;DR: This book provides a solid fundament for studying various aspects of computability and complexity in analysis and is written in a style suitable for graduate-level and senior students in computer science and mathematics.
Journal ArticleDOI
Mathematical problems for the next century
TL;DR: Arnabels invitation is inspired in part by Hilbert's list of 1900 (see e.g. [Browder, 1976]) and I have used that list to help design this essay.
References
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Proceedings ArticleDOI
On the parallel computation for the knapsack problem
TL;DR: It is shown that an exponential number of processors have to be used if the knapsack problem with n input real numbers on a parallel computer is to be solved in time t ≤ @@@@n/2.
Book ChapterDOI
A Survey of the Logic of Effective Definitions
TL;DR: LED, the Logic of Effective Definitions, is an extension of first order predicate calculus used for making assertions about programs modeled as effective definitional schemes (following Friedman).
Book
The Combinatory Programme
Erwin Engeler,K. Aberer,B. Amrhein,O. Gloor,M. von Mohrenschildt,D. Otth,G. Schwärzler,T. Weibel +7 more
TL;DR: In this paper, a combinatory algebra is constructed, using a programmatic mixture of the classical axiomatic and set-theoretic approaches, which can serve as a platform from which to develop the algorithmic aspects of many areas in computer science, mathematics and their applications.
Proceedings ArticleDOI
Effective computation over the real numbers
TL;DR: By closing the computation scheme under the GLB-operation, the ETM is obtained, a system closed under limiting operations in general, but one for which the question of effectively choosing elements from effectively defined sets is presently unanswered.