Related papers: Opacity complexity of automatic sequences. The gen…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
Opacity is an information flow property characterizing whether a system reveals its secret to an intruder. Verification of opacity for discrete-event systems modeled by automata is in general a hard problem. We discuss the question whether…
We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.
This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative…
In this paper we develop a method to transfer density results for primitive automatic sequences to logarithmic-density results for general automatic sequences. As an application we show that the logarithmic densities of any automatic…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
We consider options that pay the complexity deficiency of a sequence of up and down ticks of a stock upon exercise. We study the price of European and American versions of this option numerically for automatic complexity, and theoretically…
Expansion complexity and maximum order complexity are both finer measures of pseudorandomness than the linear complexity which is the most prominent quality measure for cryptographic sequences. The expected value of the $N$th maximum order…
Let $t_n = (-1)^{s_2(n)}$, where $s_2(n)$ is the sum of binary digits function. The sequence $(t_n)_{n\in \mathbb N}$ is the well-known Prouhet-Thue-Morse sequence. In this note we initiate the study of the sequence $(h_n)_{n\in \mathbb…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
The Krohn-Rhodes complexity theory for pure (without linearity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear…