Related papers: Generalization of automatic sequences for numerati…

A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…

Let $L=(L_d)_{d \in \mathbb N}$ be any ordered probability sequence, i.e., satisfying $0 < L_{d+1} \le L_d$ for each $d \in \mathbb N$ and $\sum_{d \in \mathbb N} L_d =1$. We construct sequences $A = (a_i)_{i \in \mathbb N}$ on the…

We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

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 propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…

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…

Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…

The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…

Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the…

We investigate a learning algorithm in the context of nominal automata, an extension of classical automata to alphabets featuring names. This class of automata captures nominal regular languages; analogously to the classical language…

Sequence-to-sequence transduction is the core problem in language processing applications as diverse as semantic parsing, machine translation, and instruction following. The neural network models that provide the dominant solution to these…

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 study automatic question generation for sentences from text passages in reading comprehension. We introduce an attention-based sequence learning model for the task and investigate the effect of encoding sentence- vs. paragraph-level…

The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A…

In this paper, general logic-systems are investigated. It is shown that there are infinitely many finite consequence operators defined on a fixed language L that cannot be generated from a finite logic-system. It is shown that a set map is…

We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…