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We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition…
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…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.
Although many machine learning methods, especially from the field of deep learning, have been instrumental in addressing challenges within robotic applications, we cannot take full advantage of such methods before these can provide…
One of the central aspects of contextualised language models is that they should be able to distinguish the meaning of lexically ambiguous words by their contexts. In this paper we investigate the extent to which the contextualised…
Much of the knowledge encoded in transformer language models (LMs) may be expressed in terms of relations: relations between words and their synonyms, entities and their attributes, etc. We show that, for a subset of relations, this…
Cross-lingual alignment in pretrained language models enables knowledge transfer across languages. Similar alignment has been reported in Whisper-style speech encoders, based on spoken translation retrieval using representational…
We say that a language $L$ is \emph{constantly growing} if there is a constant $c$ such that for every word $u\in L$ there is a word $v\in L$ with $\vert u\vert<\vert v\vert\leq c+\vert u\vert$. We say that a language $L$ is…
We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…
Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i.e., $L=\{f(n)\mid n\in \mathbb N\}\subset\mathbb N$. We show that the base-$q$ representation of $L$ is a context-free language if…
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $\mathfrak{C}$(including context-free), every completely regular semigroup that is a union of…
Sequential LSTM has been extended to model tree structures, giving competitive results for a number of tasks. Existing methods model constituent trees by bottom-up combinations of constituent nodes, making direct use of input word…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate various comet-like types of languages and compare such language…
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a…
Transformer-based Large Language Models (LLMs) have demonstrated powerful in-context learning capabilities. However, their predictions can be disrupted by factually correct context, a phenomenon known as context hijacking, revealing a…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…
Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while…