Related papers: On asymptotically automatic sequences
The purpose of this paper is to study subsequences of synchronizing $k$-automatic sequences $a(n)$ along Piatetski-Shapiro sequences $\lfloor n^c \rfloor$ with non-integer $c>1$. In particular, we show that $a(\lfloor n^c \rfloor)$…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
We provide an asymptotic estimate for certain sums over k-free integers with small prime factors. These sums depend upon a complex parameter \alpha and involve a smooth cut-off f. They are a variation of several classical number-theoretical…
This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the…
Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination,…
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just take into account whether two symbols are identical. We show…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over a finite field Fq. Research on bounds for A(q) is closely connected with the…
A tournament on a graph is an orientation of its edges. The score sequence lists the in-degrees in non-decreasing order. Works by Winston and Kleitman (1983) and Kim and Pittel (2000) showed that the number $S_n$ of score sequences on the…
In order to achieve deep natural language understanding, syntactic constituent parsing is a vital step, highly demanded by many artificial intelligence systems to process both text and speech. One of the most recent proposals is the use of…
We study the generic limit sets of one-dimensional cellular automata, which intuitively capture their asymptotic dynamics while discarding transient phenomena. As our main results, we characterize the automata whose generic limit set is a…
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous…
We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected…
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…
Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap,…
Sequence-to-sequence learning with neural networks has become the de facto standard for sequence prediction tasks. This approach typically models the local distribution over the next word with a powerful neural network that can condition on…
A word~$w$ has a border $u$ if $u$ is a non-empty proper prefix and suffix of $u$. A word~$w$ is said to be \emph{closed} if $w$ is of length at most $1$ or if $w$ has a border that occurs exactly twice in $w$. A word~$w$ is said to be…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…