R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences

In this article a family of statistical randomness tests for binary strings are introduced, based on Golomb’s pseudorandomness postulate R-2 on the number of runs. The basic idea is to construct recursive formulae with computationally tenable probability distribution functions. The technique is illustrated on testing strings of 2^7 , 2^8 , 2^10 and 2^12 bits. Furthermore, the expected value of the number of runs with a specific length is obtained. Finally the tests are applied to several collections of strings arising from different pseudorandom number generators.