Related papers: Automatic sequences based on Parry or Bertrand num…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…
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…
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods from ergodic theory, we are able to partially resolve this…
We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of…
We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An orientation preserving homeomorphism of the…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…
We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest…
Currie and Saari initiated the study of least periods of infinite words, and they showed that every integer n >= 1 is a least period of the Thue-Morse sequence. We generalize this result to show that the characteristic sequence of least…
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
This article is concerned with automated complexity analysis of term rewrite systems. Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest. Among…
We study correlation estimates of automatic sequences (that is, sequences computable by finite automata) with polynomial phases. As a consequence, we provide a new class of good weights for classical and polynomial ergodic theorems, not…
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
We show that any automatic multiplicative sequence either coincides with a Dirichlet character or is identically zero when restricted to integers not divisible by small primes. This answers a question of Bell, Bruin and Coons. A similar…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…