Related papers: Optimal Test Sets for Context-Free Languages

Recent advancements in open vocabulary models, like CLIP, have notably advanced zero-shot classification and segmentation by utilizing natural language for class-specific embeddings. However, most research has focused on improving model…

In this paper, we study the density of subsets of nonabelian free groups using relative densities of languages. We start by proving some basic properties about the density of a language $L_1$ relative to another language $L_2$ containing…

For a given subset $A\subseteq \mathbb F_q^*$, we study the problem of finding a large packing set $B$ of $A$, that is, a set $B \subseteq \mathbb F_q^*$ such that $|AB|=|A||B|$. We prove the existence of such a $B$ of size $|B|\ge…

An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and…

We study the question of local testability of low (constant) degree functions from a product domain $S_1 \times \dots \times {S}_n$ to a field $\mathbb{F}$, where ${S_i} \subseteq \mathbb{F}$ can be arbitrary constant sized sets. We show…

This paper solves an open problem concerning the generative power of nonerasing context-free rewriting systems using a simple mechanism for checking for context dependencies, in the literature known as semi-conditional grammars of degree…

We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference…

At the staggering pace with which the capabilities of large language models (LLMs) are increasing, creating future-proof evaluation sets to assess their understanding becomes more and more challenging. In this paper, we propose a novel…

We study the role of linguistic context in predicting quantifiers (`few', `all'). We collect crowdsourced data from human participants and test various models in a local (single-sentence) and a global context (multi-sentence) condition.…

A set of edges $T$ in a graph $G$ is triangle-independent if $T$ contains at most one edge from each triangle in $G$. Let $\alpha_1(G)$ denote the maximum size of the triangle-independent set in $G$, and let $\tau_B(G)$ denote minimum size…

Large language models are trained on vast amounts of internet data, prompting concerns and speculation that they have memorized public benchmarks. Going from speculation to proof of contamination is challenging, as the pretraining data used…

Measuring similarities between strings is central for many established and fast growing research areas including information retrieval, biology, and natural language processing. The traditional approach for string similarity measurements is…

A language $L$ is said to be ${\cal C}$-measurable, where ${\cal C}$ is a class of languages, if there is an infinite sequence of languages in ${\cal C}$ that ``converges'' to $L$. We investigate the properties of ${\cal C}$-measurability…

We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega…

We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include…

This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…

For a graph $G$ let $L(G)$ and $l(G)$ denote the size of the largest and smallest maximum matching of a graph obtained from $G$ by removing a maximum matching of $G$. We show that $L(G)\leq 2l(G),$ and $L(G)\leq (3/2)l(G)$ provided that $G$…

We present a uniform approach for solving language inclusion problems. Our approach relies on a least fixpoint characterization and a quasiorder to compare words of the "smaller" language, reducing the inclusion check to a finite number of…

We show that the equality language of two non-periodic binary morphisms is generated by at most two words. If its rank is two, then the generators start (and end) with different letters. This in particular implies that any binary language…

How much data is required to learn the structure of a language via next-token prediction? We study this question for synthetic datasets generated via a Probabilistic Context-Free Grammar (PCFG) -- a tree-like generative model that captures…