Related papers: Maximum-order complexity and $2$-adic complexity

In 2002, Kamae and Zamboni introduced maximal pattern complexity and determined that any aperiodic sequence must have maximal pattern complexity at least $2k$. In 2006, Kamae and Rao examined the maximal pattern complexity of sequences over…

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 linear complexity of a sequence has been used as an important measure of keystream strength, hence designing a sequence which possesses high linear complexity and $k$-error linear complexity is a hot topic in cryptography and…

We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.

Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…

In this paper we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection.…

The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an…

This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…

In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…

The linear complexity and k-error linear complexity of a sequence have been used as important measures of keystream strength, hence designing a sequence with high linear complexity and $k$-error linear complexity is a popular research topic…

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

The $N$th linear complexity of a sequence is a measure of predictability. Any unpredictable sequence must have large $N$th linear complexity. However, in this paper we show that for $q$-automatic sequences over $\mathbb{F}_q$ the converse…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

In cryptography, we hope a sequence over $\mathbb{Z}_m$ with period $N$ having larger $m$-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In…

We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…

The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…