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Remarks on randomization of quasi-random numbers
Monte Carlo Methods and Applications, 2018Abstract In this paper we discuss estimation of the quasi-Monte Carlo methods error in the case of calculation of high-order integrals. Quasi-random Halton sequences are considered as a special case. Randomization of these sequences by the random shift method turns out to lead to well-known random quadrature formulas with one free node ...
Sergej M. Ermakov, Svetlana N. Leora
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Converting random bits into random numbers
The Journal of Supercomputing, 2014Converting random bits into random numbers is necessary for cryptographic protocols such as key agreements, public key encryptions, digital signatures and so on. In this paper, we propose the simple partial discard method and the complex partial discard method that convert random bits into random numbers.
Bonwook Koo, Dongyoung Roh, Daesung Kwon
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Communications of the ACM, 1990
In the mind of the average computer user, the problem of generating uniform variates by computer has been solved long ago. After all, every computer :system offers one or more function(s) to do so. Many software products, like compilers, spreadsheets, statistical or numerical packages, etc. also offer their own.
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In the mind of the average computer user, the problem of generating uniform variates by computer has been solved long ago. After all, every computer :system offers one or more function(s) to do so. Many software products, like compilers, spreadsheets, statistical or numerical packages, etc. also offer their own.
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Random Number Generation [PDF]
, 2011 The fields of probability and statistics are built over the abstract concepts of probability space and random variable. This has given rise to elegant and powerful mathematical theory, but exact implementation of these concepts on conventional computers seems impossible.
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Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery on - ACM '59, 1959
One requirement common to all Monte Carlo computer simulations is an abundant and automatic supply of random numbers. For most purposes it generally suffices to draw this supply from the uniform distribution in the unit interval. The mathematical tricks used to convert these samplings to samplings from other distributions are well-known.
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One requirement common to all Monte Carlo computer simulations is an abundant and automatic supply of random numbers. For most purposes it generally suffices to draw this supply from the uniform distribution in the unit interval. The mathematical tricks used to convert these samplings to samplings from other distributions are well-known.
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2001
In his celebrated 1936 paper Turing defined a machine to be circular iff it performs an infinite computation outputting only finitely many symbols. We define α as the probability that an arbitrary machine be circular and we prove that α is a random number that goes beyond Ω, the probability that a universal self delimiting machine halts.
Verónica Becher +2 more
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In his celebrated 1936 paper Turing defined a machine to be circular iff it performs an infinite computation outputting only finitely many symbols. We define α as the probability that an arbitrary machine be circular and we prove that α is a random number that goes beyond Ω, the probability that a universal self delimiting machine halts.
Verónica Becher +2 more
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Computers and Biomedical Research, 1968
Abstract A commonly used uniform random-number generator is examined in light of a genetic-simulation problem. Although this generator is often useful, it proves defective in this case. The author suggests that any proposed generator be checked for the properties needed by the simulation problem at hand.
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Abstract A commonly used uniform random-number generator is examined in light of a genetic-simulation problem. Although this generator is often useful, it proves defective in this case. The author suggests that any proposed generator be checked for the properties needed by the simulation problem at hand.
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Local Randomness in Polynomial Random Number and Random Function Generators
SIAM Journal on Computing, 1993Summary: A distribution on \(n\)-bit strings is called \((\varepsilon,e)\)-locally random, if for every choice of \(e \leq n\) positions the induced distribution on \(e\)-bit strings is in the \(L_ 1\)-norm at most \(\varepsilon\) away from the uniform distribution on \(e\)-bit strings. Local randomness in polynomial random number generators (RNG) that
Harald Niederreiter, Claus-Peter Schnorr
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Sci. Ann. Cuza Univ., 1994
Summary: Random strings have been studied in many papers. A natural number represented in a basis of numeration can be considered as a string consisting of its digits. Our present aim is to develop a framework and the necessarily tools for deciding if a natural number is random or not.
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Summary: Random strings have been studied in many papers. A natural number represented in a basis of numeration can be considered as a string consisting of its digits. Our present aim is to develop a framework and the necessarily tools for deciding if a natural number is random or not.
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Random number generators are chaotic
ACM SIGPLAN Notices, 1989We observe that pseudo-random number generators, familiar to all programmers, are examples of deterministic chaotic dynamical systems. We discuss the implications of this finding and compare computer generation of pseudo-random numbers to the theoretical ideal of a (noncomputable) random sequence.
Charles Herring, Julian I. Palmore
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