Related papers: A Class of Automatic Sequences

We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…

The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic…

Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This…

We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

The autocorrelation values of two classes of binary sequences are shown to be good in [6]. We study the 2-adic complexity of these sequences. Our results show that the 2-adic complexity of such sequences is large enough to resist the attack…

We provide an ergodic theory framework to study statistical properties of smooth sequences over the odd alphabet {1, 3}. The arithmetic nature of this alphabet yields a partition of the subshift of smooth sequences based on their local…

Context-free grammars are not able to model cross-serial dependencies in natural languages. To overcome this issue, Seki et al. introduced a generalization called $m$-multiple context-free grammars ($m$-MCFGs), which deal with $m$-tuples of…

We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…

In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by D\'iaz-Caro and Yakary{\i}lmaz \cite{DCY16A} referred as affine automata. First, we present…

We show that any automatic sequence can be separated into a structured part and a Gowers uniform part in a way that is considerably more efficient than guaranteed by the Arithmetic Regularity Lemma. For sequences produced by strongly…

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 introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…

A regular language $L$ is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-free-path finite automaton; this is…

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of…

These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…

We present a comparison of word-based and character-based sequence-to-sequence models for data-to-text natural language generation, which generate natural language descriptions for structured inputs. On the datasets of two recent generation…

Form a random k-SAT formula on n variables by selecting uniformly and independently m=rn clauses out of all 2^k (n choose k) possible k-clauses. The Satisfiability Threshold Conjecture asserts that for each k there exists a constant r_k…

Let k be a positive integer. A sequence s over an n-element alphabet A is called a k-radius sequence if every two symbols from A occur in s at distance of at most k. Let f_k(n) denote the length of a shortest k-radius sequence over A. We…