On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
The Runs Up-and-Down Performance of Tausworthe Pseudo-Random Number Generators
Journal of the ACM (JACM)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Shift Register Sequences
The orders of equidistribution of subsequences of some asymptotically random sequences
Communications of the ACM
Initializing generalized feedback shift register pseudorandom number generators
Journal of the ACM (JACM)
Walsh-spectral test for GFSR pseudorandom numbers
Communications of the ACM
Efficient and portable combined Tausworthe random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The multiple prime random number generator
ACM Transactions on Mathematical Software (TOMS)
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Generalized Feedback Shift Register Pseudorandom Number Algorithm
Journal of the ACM (JACM)
Partitioning the Period of a Class of m-Sequences and Application to Pseudorandom Number Generation
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
The k-distribution of generalized feedback shift register pseudorandom numbers
Communications of the ACM
Tables of 64-bit Mersenne twisters
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A new class of linear feedback shift register generators
Proceedings of the 32nd conference on Winter simulation
Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
Combined generators with components from different families
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Fast hardware random number generator for the Tausworthe sequence
ANSS '83 Proceedings of the 16th annual symposium on Simulation
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
Fast random number generators based on linear recurrences modulo 2: overview and comparison
WSC '05 Proceedings of the 37th conference on Winter simulation
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Phase-Shift Analysis of Linear Feedback Shift Register Structures Generating Pseudorandom Sequences
IEEE Transactions on Computers
Maximally equidistributed pseudorandom number generators via linear output transformations
Mathematics and Computers in Simulation
Cryptography using modular software elements
AFIPS '76 Proceedings of the June 7-10, 1976, national computer conference and exposition
Resolution-stationary random number generators
Mathematics and Computers in Simulation
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The theoretical limitations on the orders of equidistribution attainable by Tausworthe sequences are derived from first principles and are stated in the form of a criterion to be achieved. A second criterion, extending these limitations to multidimensional uniformity, is also defined. A sequence possessing both properties is said to be asymptotically random as no other sequence of the same period could be more random in these respects.An algorithm is presented which, for any Tausworthe sequence based on a primitive trinomial over GF(2), establishes how closely or otherwise the conditions necessary for the criteria are achieved. Given that the necessary conditions are achieved, the conditions sufficient for the first criterion are derived from Galois theory and always apply. For the second criterion, however, the period must be prime.An asymptotically random 23-bit number sequence of astronomic period, 2607 - 1, is presented. An initialization program is required to provide 607 starting values, after which the sequence can be generated with a three-term recurrence of the Fibonacci type. In addition to possessing the theoretically demonstrable randomness properties associated with Tausworthe sequences, the sequence possesses equidistribution and multidimensional uniformity properties vastly in excess of anything that has yet been shown for conventional congruentially generated sequences. It is shown that, for samples of a size it is practicable to generate, there can exist no purely empirical test of the sequence as it stands capable of distinguishing between it and an ∞-distributed sequence. Bounds for local nonrandomness in respect of runs above (below) the mean and runs of equal numbers are established theoretically.The claimed randomness properties do not necessarily extend to subsequences, though it is not yet known which particular subsequences are at fault. Accordingly, the sequence is at present suggested only for simulations with no fixed dimensionality requirements.