— The so-called first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs on Bernoulli sequences.

Strong correlations between output distribution means of a variety of random binary processes and prestated intentions of some 100 individual human operators have been established over a 12-year experimental program. More than 1000 experimental series, employing four different categories of random devices and several distinctive protocols, show comparable magnitudes of anomalous mean shifts fro...

We study the random Fibonacci sequences defined by F 1 = F 2 = e F 1 = e F 2 = 1 and for n ≥ 1, F n+2 = F n+1 ± Fn (linear case) and e F n+2 = | e F n+1 ± e Fn| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1 − p (0 < p ≤ 1). Our main result is that the exponential growth of Fn for 0 < p ≤ 1, and of e Fn for 1/3 ≤ p ≤ 1 is almost surel...

If S and T are infinite sequences over a finite alphabet, then the lower and upper mutual dimensions mdim(S : T ) and Mdim(S : T ) are the upper and lower densities of the algorithmic information that is shared by S and T . In this paper we investigate the relationships between mutual dimension and coupled randomness, which is the algorithmic randomness of two sequences R1 and R2 with respect t...

Tootill et al. proposed the concept of an asymptotically random Tausworthe sequence, and gave an example of such sequence found by chance. However, no systematic way of nding such sequences has been proposed by now. In this paper we will give an algorithm for designing GFSR sequences which satisfy the asymptotic randomness approximately. Our algorithm is based on repeated applications of the al...

Realization of modern telecommunication systems is inconceivable without use of different binary sequences. In this paper, an overview of random binary sequences used in different telecommunication systems is given. Basic principles of pseudorandom, chaotic, and true random sequence generation are presented, as well as their application in telecommunications in respect to advantages and drawbac...

Kolmogorov has defined tile conditional complexity of an object y when the object x is already given to us as the minimal length of a binary program which by means of x computes y on a certain asymptotically optimal machine. On the basis of this definition he has proposed to consider those elements of a given large finite population to be random whose complexity is maximal. Almost all elements ...

Biometrics are traditionally employed in user authentication and authorization mechanisms. The vast majority of research effort focuses on applications of biometrics in authentication, aiming to replace passwords as the access control mechanism for cryptographic keys in one way or another. However, the inherent variability in biometrics presents a readily available source of randomness, which, ...