Related papers: On the linear complexity for multidimensional sequ…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
As a research field of stream ciphers, the pursuit of a balance of security and practicality is the focus. The conditions for security usually have to satisfy at least high period and high linear complexity. Because the feedforward…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
We consider the homeomorphic classification of finite-dimensional continua as well as several related equivalence relations. We show that, when $n \geq 2$, the classification problem of $n$-dimensional continua is strictly more complex than…
We first give a method to get multidimensional Leja sequences by considering intertwining sequences from one-dimensional ones. An application is the existence of explicit Leja sequences for the closed unit polydisc. Next, we deal with some…
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last…
The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity…
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…
Sequences with {\em perfect linear complexity profile} were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently {\em apwenian sequences}, first with values $\pm 1$, then with values…
We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.
We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.
In this short paper, a formula for the sequence defined by the nonhomogeneous linear difference equation with variable coefficients is presented. A connection with the homogeneous case is shown.
The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper…
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…