Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there
have been significant advancements on the topic of complexity measures for randomness …

Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro
sequence, have some desirable features of pseudorandomness such as a large linear …

The Nth linear complexity of a sequence is a measure of predictability. Any unpredictable
sequence must have large Nth linear complexity. However, in this paper we show that for q …

Expansion complexity and maximum order complexity are both finer measures of
pseudorandomness than the linear complexity which is the most prominent quality measure …

The 2-adic complexity has been well-analyzed in the periodic case. However, we are not
aware of any theoretical results in the aperiodic case. In particular, the N th 2-adic …

We prove a relation between two measures of pseudorandomness, the arithmetic
autocorrelation, and the correlation measure of order k. Roughly speaking, we show that any …

Automatic sequences can be defined by DFAs with output (DFAO) in two natural ways. We
propose to consider the minimal size of a corresponding DFAO as the complexity measure …

In 2012, Diem introduced a new figure of merit for cryptographic sequences called
expansion complexity. In this paper, we slightly modify this notion to obtain the so-called …

Let 1<; g 1<;⋯<; g φ (p-1)<; p-1 be the ordered primitive roots modulo p. We study the
pseudorandomness of the binary sequence (sn) defined by sn≡ g n+ 1+ g n+ 2 mod 2, n= 0 …

The expansion complexity is a new figure of merit for cryptographic sequences. In this paper,
we present an explicit formula of the (irreducible) expansion complexity of ultimately periodic …