Results 11 to 20 of about 491,707 (327)
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
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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
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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
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A mathematical theory of randomized computation, I [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1988 In previous work [ibid. 64, No.4, 115-118 (1988; Zbl 0657.68061)] a randomized program was considered as a linear operator mapping an input probability measure to the output subprobability measure. In the present article the identity between the order topology on a randomized domain and the Scott topology is shown.
Shinichi Yamada
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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
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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
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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
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The Standard Model for Programming Languages: The Birth of a Mathematical Theory of Computation [PDF]
, 2020 Despite the insight of some of the pioneers (Turing, von Neumann, Curry, Böhm), programming the early computers was a matter of fiddling with small architecture-dependent details. Only in the sixties some form of "mathematical program development" will be in the agenda of some of the most influential players of that time.
Simone Martini
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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
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Pincherle's theorem in reverse mathematics and computability theory [PDF]
Annals of Pure and Applied Logic, 2020 We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first 'local-to-global' principles.
Normann, Dag, Sanders, Sam
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