Related papers: A substitution lemma for multiple context-free lan…
In our era of widespread false information, human fact-checkers often face the challenge of duplicating efforts when verifying claims that may have already been addressed in other countries or languages. As false information transcends…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
Probing the multilingual knowledge of linguistic structure in LLMs, often characterized as sequence labeling, faces challenges with maintaining output templates in current text-to-text prompting strategies. To solve this, we introduce a…
Instead of a monolithic programming language trying to cover all features of interest, some programming systems are designed by combining together simpler languages that cooperate to cover the same feature space. This can improve usability…
We show that the set of binary words containing overlaps is not unambiguously context-free and that the set of ternary words containing overlaps is not context-free. We also show that the set of binary words that are not subwords of the…
Let $w$ be a word in the free group of rank $n \in \mathbb{N}$ and let $\mathcal{V}(w)$ be the variety of groups defined by the law $w=1$. Define $\mathcal{V}(w^*)$ to be the class of all groups $G$ in which for any infinite subsets $X_1,…
Language models (LMs) can hallucinate when performing complex mathematical reasoning. Physics provides a rich domain for assessing their mathematical capabilities, where physical context requires that any symbolic manipulation satisfies…
Context-free S grammars are introduced, for arbitrary (storage) type S, as a uniform framework for recursion-based grammars, automata, and transducers, viewed as programs. To each occurrence of a nonterminal of a context-free S grammar an…
Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…
Let $G$ be a finitely generated group, and let $\Sigma$ be a finite subset that generates $G$ as a monoid. The \emph{word problem of $G$ with respect to $\Sigma$} consists of all words in the free monoid $\Sigma^{\ast}$ that are equal to…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for…
The problem of \emph{regular separability} asks, given two languages $K$ and $L$, whether there exists a regular language $S$ with $K\subseteq S$ and $S\cap L=\emptyset$. This problem has recently been studied for various classes of…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Word Sense Induction (WSI) is the task of discovering senses of an ambiguous word by grouping usages of this word into clusters corresponding to these senses. Many approaches were proposed to solve WSI in English and a few other languages,…
We consider two-variable first-order logic $\text{FO}^2$ and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel…
We propose a straightforward vocabulary adaptation scheme to extend the language capacity of multilingual machine translation models, paving the way towards efficient continual learning for multilingual machine translation. Our approach is…
Previous work indicates that large language models exhibit a significant "English bias", i.e. they often perform better when tasks are presented in English. Interestingly, we have observed that using certain other languages in reasoning…
Deciding the amalgamation property for a given class of finite structures is an important subroutine in classifying countable finitely homogeneous structures. We study the computational complexity of the amalgamation decision problem for…