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
The computationalist reformulation of the mind-body problem.
TL;DR: The main point is that the derivation is constructive, and it provides the technical means to derive physics from arithmetic, and this will make the computationalist hypothesis empirically testable, and thus scientific in the Popperian analysis of science.
Journal Article
A complex analogue of Toda's Theorem.
TL;DR: The techniques developed in Basu and Zell are extended to the complex projective case and a complex analogue of Toda’s theorem is obtained, illustrating the central role of the Poincaré polynomial in algorithmic algebraic geometry, as well as in computational complexity theory over the complex and real numbers.
Proceedings Article
Sample Complexity of Policy Search with Known Dynamics
Peter L. Bartlett,Ambuj Tewari +1 more
TL;DR: It is shown that under bounds on the amount of computation involved in computing policies, transition dynamics and rewards, uniform convergence of empirical estimates to true value functions occurs.
Book ChapterDOI
Computability and dynamical systems
TL;DR: Results are explored that establish a link between dynamical systems and computability theory (not numerical analysis) and suggest some lines of research for further work on this fascinating topic.
Book ChapterDOI
On the Complexity of Combinatorial and Metafinite Generating Functions of Graph Properties in the Computational Model of Blum, Shub and Smale
TL;DR: A unified frame work for the study of the complexity of counting functions and multivariate polynomials such as the permanent and the hamiltonian in the computational model of Blum, Shub and Smale is presented.
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.