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A complexity theory of constructible functions and sheaves (Q2340508)

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Language	Label	Description	Also known as
English	A complexity theory of constructible functions and sheaves	scientific article

Statements

scholarly article

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A complexity theory of constructible functions and sheaves (English)

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Foundations of Computational Mathematics

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publication date

20 April 2015

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full work available at URL

https://arxiv.org/abs/1309.5905

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zbMATH Keywords

constructible functions

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constructible sheaves

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polynomial hierarchy

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complexity classes

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adjoint functors

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MaRDI profile type

MaRDI publication profile

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Torification and factorization of birational maps

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Feasibility testing for systems of real quadratic equations

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Euler integration over definable functions

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On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets

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Computing the first few Betti numbers of semi-algebraic sets in single exponential time

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Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities

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Computing the top Betti numbers of semialgebraic sets defined by quadratic inequalities in polynomial time

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A complex analogue of Toda's theorem

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Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities

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Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

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On the number of cells defined by a family of polynomials on a variety

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Computing the Euler-Poincaré characteristics of sign conditions

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Algorithms in real algebraic geometry

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Computing the first Betti number of a semi-algebraic set

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On the number of homotopy types of fibres of a definable map

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Polynomial hierarchy, Betti numbers, and a real analogue of Toda's theorem

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Effective Hironaka resolution and its complexity

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The universal Euler characteristic for varieties of characteristic zero

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COMPLEXITY AND REAL COMPUTATION: A MANIFESTO

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On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines

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Completeness and reduction in algebraic complexity theory

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Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets

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An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP}\neq\mathbf{VNP}$

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Integration of positive constructible functions against Euler characteristic and dimension

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Constructible function and motivic integration. I.

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Equations différentielles à points singuliers réguliers

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Théorie de Hodge. II. (Hodge theory. II)

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Théorie de Hodge. III

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Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier

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Singularities and topology of hypersurfaces

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Sheaves in topology

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Approximation of definable sets by compact families, and upper bounds on homotopy and homology

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Complexity of deciding Tarski algebra

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Bounds on numers of vectors of multiplicities for polynomials which are easy to compute

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Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings

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Cohomology of sheaves

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Sheaves in geometry and logic: a first introduction to topos theory

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On the Betti Numbers of Real Varieties

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Lower bounds for arithmetic networks. II: Sum of Betti numbers

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A fast parallel algorithm to compute the rank of a matrix over an arbitrary field

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Geometric Complexity Theory I: An Approach to the<i>P</i>vs.<i>NP</i>and Related Problems

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Motivic aspects of Hodge theory

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Singularités des systèmes différentiels de Gauss-Manin. Avec des contributions de Lo Kam Chan, Philippe Maisonobe et Jean-Etienne Rombaldi

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On the computational complexity and geometry of the first-order theory of the reals. III: Quantifier elimination

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Operations on constructible functions

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The polynomial-time hierarchy

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PP is as Hard as the Polynomial-Time Hierarchy

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The complexity of computing the permanent

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Decision tree complexity and Betti numbers

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Identifiers

zbMATH Open document ID

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10.1007/s10208-014-9222-z

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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