A NEW VERSION OF FIRST RETURN TIME TEST OF PSEUDORANDOMNESS

We present a new version of the first return time test for pseudorandomness. Let R n be the first return time of initial n-block with overlapping. An algorithm to calculate the probability distribution of the first return time R n for each starting block is presented and used to test pseudorandom number generators. The standard Z-test for log R n is applied to test the pseudorandom number generators.