Related papers: Optimal Test Sets for Context-Free Languages
An independent set of a graph $G$ is a vertex subset $I$ such that there is no edge joining any two vertices in $I$. Imagine that a token is placed on each vertex of an independent set of $G$. The $\mathsf{TS}$- ($\mathsf{TS}_k$-)…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
In this paper we offer a complete methodology for sufficient dimension reduction called the test function (TF). TF provides a new family of methods for the estimation of the central subspace (CS) based on the introduction of a nonlinear…
Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches…
Language models built using semi-supervised machine learning on large corpora of natural language have very quickly enveloped the fields of natural language generation and understanding. In this paper we apply a zero-shot approach…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
We describe a compression-aware method to compute all-vs-all maximal exact matches (MEM) among strings of a repetitive collection $\mathcal{T}$. The key concept in our work is the construction of a fully-balanced grammar $\mathcal{G}$ from…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Traditional language processing tools constrain language designers to specific kinds of grammars. In contrast, model-based language specification decouples language design from language processing. As a consequence, model-based language…
Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…
We consider context-free languages equipped with the lexicographic ordering. We show that when the lexicographic ordering of a context-free language is scattered, then its Hausdorff rank is less than $\omega^\omega$. As a corollary of this…
A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to…
Probabilistic context-free grammars (PCFGs) with neural parameterization have been shown to be effective in unsupervised phrase-structure grammar induction. However, due to the cubic computational complexity of PCFG representation and…
Recent foundational language models have shown state-of-the-art performance in many NLP tasks in zero- and few-shot settings. An advantage of these models over more standard approaches based on fine-tuning is the ability to understand…
A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning…
Machine learning approaches applied to NLP are often evaluated by summarizing their performance in a single number, for example accuracy. Since most test sets are constructed as an i.i.d. sample from the overall data, this approach overly…
Classifying formal languages according to the expressiveness of grammars able to generate them is a fundamental problem in computational linguistics and, therefore, in the theory of computation. Furthermore, such kind of analysis can give…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, existing scaling methods have key limitations: parallel…