An easy criterion for randomness

We propose a single valued criterion for randomness of a binary sequence (Formula presented) defined by (Formula presented) where (Formula presented) is the set of nonempty finite sequences over (Formula presented). We prove (Formula presented) that holds with probability 1 if X₁X₂…X_n is an i.i.d. process with P(X_i = 0) = P(X_i = 1) = 1/2. Moreover, if a sample path x₁x₂…satisfies this almost all condition, then it is a normal number in the sense of E. Borel, but this converse is not true. We also propose a method to generate infinite sequences (Formula presented)… satisfying this almost all condition, which are found out to be reasonable pseudorandom numbers from the point view of the block frequencies.