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Relations between evaluations of NIST tests and Lyapunov exponents of sequences generated by the logistic map over integers

We have been studying the characteristics of the sequence generated by the logistic map over integers. In this paper, we examine the relationship of the NIST statistical tests to the Lyapunov exponents of the sequence. Then, we confirm good correlations between a sign of the exponents and both p-value and proportion of the NIST statistical tests. Therefore, we prove that the exponents indicates randomness of sequences generated by the logistic map over integers.