Applications of the collision test to produce results consistent with the spectral test
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The collision test is one of many tests that can be used to check a sequence of numbers for randomness. The current work extends the use of the collision test to produce information about the number of bits of accuracy similar to the powerful spectral test [1]. The spectral test is limited to use with only a few types of generators, but the collision test can be applied to any sequence of numbers. The analysis suggested would be ideal for non-linear congruential types of generators; indeed, one need not know the origin of the number sequence, only the sequence would be needed to perform the analysis.
[1] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .
[2] Shu Tezuka,et al. Walsh-spectral test for GFSR pseudorandom numbers , 1987, CACM.