Related papers: Complexity of Linear Subsequences of $k$-Automatic…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
We study the problem of synchronization of automata with random inputs. We present a series of automata such that the expected number of steps until synchronization is exponential in the number of states. At the same time, we show that the…
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current…
Finitely many two-way automata work independently and synchronously on a unary input. Some of their states are broadcasting, i.e., dispatched to all other automata. At each step of the computation, each automaton changes state and moves…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
In this article we define the semigroup associated to a substitution. We use it to construct a minimal automaton which generates a substitution sequence u in reverse reading. We show, in the case where the substitution has a coincidence,…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
The linear complexity and the $k$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By studying the linear complexity of binary…
Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
In a recent paper, Jason P. Bell and Jeffrey Shallit introduced the notion of {\em Lie complexity} and proved that the Lie complexity function of an automatic sequence is automatic. In this note, we give more facts concerning Lie complexity…
We revisit staircases for words and prove several exact as well as asymptotic results for longest left-most staircase subsequences and subwords and staircase separation number, the latter being defined as the number of consecutive maximal…
We investigate questions related to the presence of primitive words and Lyndon words in automatic and linearly recurrent sequences. We show that the Lyndon factorization of a k-automatic sequence is itself k-automatic. We also show that the…
We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to…
In this paper we use the framework of automatic sequences to study combinatorial sequences modulo prime powers. Given a sequence whose generating function is the diagonal of a rational power series, we provide a method, based on work of…
The generic limit set of a dynamical system is the smallest set that attracts most of the space in a topological sense: it is the smallest closed set with a comeager basin of attraction. Introduced by Milnor, it has been studied in the…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
An interleaving sequence is obtained by combining or intertwining elements from two or more sequences. On the other hand, cellular automata are known to be generators for keystream sequences. In this paper we present two families of…