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
More filters
Journal ArticleDOI
Warm-starting quantum optimization
TL;DR: Results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth, and it is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.
Journal ArticleDOI
Fixed Points, Nash Equilibria, and the Existential Theory of the Reals
TL;DR: It is shown that the complexity of decision variants of fixed-point problems, including Nash equilibria, are complete for this class, complementing work by Etessami and Yannakakis.
BookDOI
P, NP and mathematics a computational complexity perspective
TL;DR: This paper shall try to explain why the P vs. NP problem, and others in computational complexity, are not only mathematical problems but also problems about mathematics, faced by the working mathematician.
Foundations of dynamic geometry
TL;DR: In this article, the authors have studied the mathematischen, informationstechnischen and didaktischen Grundlagen der Dynamischen Geometrie.
Journal ArticleDOI
The Complexity Era in Economics
TL;DR: The authors argues that the neoclassical era in economics has ended and is being replaced by a new era, which they call the complexity era, defined by the acceptance that the economy is complex.
References
More filters
Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
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.