On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
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This article is published in Bulletin of the American Mathematical Society.The article was published on 1989-07-01 and is currently open access. It has received 1131 citations till now. The article focuses on the topics: μ-recursive function & Real computation.read more
Citations
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Journal ArticleDOI
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
Book
Understanding Machine Learning: From Theory To Algorithms
TL;DR: The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way in an advanced undergraduate or beginning graduate course.
Book
Complexity and Real Computation
TL;DR: This chapter discusses decision problems and Complexity over a Ring and the Fundamental Theorem of Algebra: Complexity Aspects.
Journal ArticleDOI
A unified framework for hybrid control: model and optimal control theory
TL;DR: This work introduces a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuous-variable state spaces and subject to continuous controls and discrete transitions, and develops a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework.
Book
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.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
Theory of Recursive Functions and Effective Computability.
Solomon Feferman,Hartley Rogers +1 more
TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.
Book
Computation: Finite and Infinite Machines
TL;DR: In this article, the authors present an abstract theory that categorically and systematically describes what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment, and the abstract theory tells us in no uncertain terms that the machines' potential range is enormous and that its theoretical limitations are of the subtlest and most elusive sort.
Book
A decision method for elementary algebra and geometry
TL;DR: A decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K; by a decision problem for K, we mean the problem of finding a decision algorithm for K.