Results 1 to 10 of about 3,204,797 (388)

Open sets in computability theory and reverse mathematics [PDF]

Journal of Logic and Computation, 2020
AbstractTo enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this paper, what the influence of this extra data and structure is on the logical and computational properties ...
Sam Sanders, Dag Normann
openaire   +5 more sources

Applicable Mathematics in a Minimal Computational Theory of Sets [PDF]

Logical Methods in Computer Science, 2018
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored. In this work we first improve that framework by enriching it with means for coherently extending by definitions ...
Arnon Avron, Liron Cohen
  +7 more sources

Computational Complexity Theory and the Philosophy of Mathematics† [PDF]

Philosophia Mathematica, 2019
AbstractComputational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally.
Walter Dean
openalex   +3 more sources

A Basis for a Mathematical Theory of Computation [PDF]

, 1959
Publisher Summary This chapter discusses the mathematical theory of computation. Computation essentially explores how machines can be made to carry out intellectual processes. Any intellectual process that can be carried out mechanically can be performed by a general purpose digital computer.
John McCarthy
openalex   +5 more sources

A mathematical theory of the computational resolution limit in one dimension [PDF]

Applied and Computational Harmonic Analysis, 2021
Abstract Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem involves reconstructing the source number, positions, and amplitudes. This problem is related to many important applications in imaging and signal processing.
Ping Liu, Hai Zhang
openalex   +5 more sources

Interactions of computational complexity theory and mathematics

, 2023
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational complexity theory and different fields of mathematics.
Avi Wigderson
openalex   +3 more sources

Meta-Mathematics of Computational Complexity Theory [PDF]

Sigact News
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity bounds within theories of bounded arithmetic.
Igor C. Oliveira
arxiv   +2 more sources

The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation [PDF]

, 2020
International ...
Simone Martini
openalex   +8 more sources

A basis for a mathematical theory of computation, preliminary report [PDF]

Papers presented at the May 9-11, 1961, western joint IRE-AIEE-ACM computer conference on - IRE-AIEE-ACM '61 (Western), 1961
Programs that learn to modify their own behaviors require a way of representing algorithms so that interesting properties and interesting transformations of algorithms are simply represented. Theories of computability have been based on Turing machines, recursive functions of integers and computer programs.
John McCarthy
openalex   +3 more sources

Some Completeness Results in the Mathematical Theory of Computation [PDF]

Journal of the ACM, 1968
A formal theory is described which incorporates the “assignment” function a ( i , k , ξ ) and the “contents” function c ( i , ξ ).
Donald M. Kaplan
openalex   +3 more sources