A Randomness Test Based on T-Complexity

We propose a randomness test based on the T-complexity of a sequence, which can be calculated using a parsing algorithm called Tdecomposition. Recently, the Lempel-Ziv (LZ) randomness test based on LZ-complexity using the LZ78 incremental parsing was officially excluded from the NIST test suite in NIST SP 800-22. This is caused from the problem that the distribution of P-values for random sequences of length 106 is strictly discrete for the LZ-complexity. Our proposed test can overcome this problem because T-complexity has almost ideal continuous distribution of P-values for random sequences of length 106. We also devise a new sequential T-decomposition algorithm using forward parsing, while the original T-decomposition is an off-line algorithm using backward parsing. Our proposed test can become a supplement to NIST SP 800-22 because it can detect several undesirable pseudo-random numbers that the NIST test suite almost fails to detect. key words: T-code, T-complexity, Lempel-Ziv complexity, NIST SP 800-22, NIST statistical test suite, multiplicative congruential generator