Related papers: Optimal Test Sets for Context-Free Languages
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size…
FreeST is an experimental concurrent programming language. Based on a core linear functional programming language, it features primitives to fork new threads, and for channel creation and communication. A powerful type system of…
This paper presents a multilingual study of word meaning representations in context. We assess the ability of both static and contextualized models to adequately represent different lexical-semantic relations, such as homonymy and synonymy.…
Superlatives are used to single out elements with a maximal/minimal property. Semantically, superlatives perform a set comparison: something (or some things) has the min/max property out of a set. As such, superlatives provide an ideal…
We study the problem of deciding whether a given language is directed. A language $L$ is \emph{directed} if every pair of words in $L$ have a common (scattered) superword in $L$. Deciding directedness is a fundamental problem in connection…
A longstanding debate in semiotics centers on the relationship between linguistic signs and their corresponding semantics: is there an arbitrary relationship between a word form and its meaning, or does some systematic phenomenon pervade?…
Lexical states provide a powerful mechanism to scan regular expressions in a context sensitive manner. At the same time, lexical states also make it hard to reason about the correctness of the grammar. We first categorize the related…
We define a suffixient set for a text $T [1..n]$ to be a set $S$ of positions between 1 and $n$ such that, for any edge descending from a node $u$ to a node $v$ in the suffix tree of $T$, there is an element $s \in S$ such that $u$'s path…
A group $G$ has cube-free order if no prime to the third power divides $|G|$. We describe an algorithm that given two cube-free groups $G$ and $H$ of known order, decides whether $G\cong H$, and, if so, constructs an isomorphism $G\to H$.…
A machine translation system is said to be *complete* if all expressions that are correct according to the source-language grammar can be translated into the target language. This paper addresses the completeness issue for compositional…
Comparing two (large) language models (LMs) side-by-side and pinpointing their prediction similarities and differences on the same set of inputs are crucial in many real-world scenarios, e.g., one can test if a licensed model was…
Large language models (LLMs) operate in two fundamental learning modes - fine-tuning (FT) and in-context learning (ICL) - raising key questions about which mode yields greater language proficiency and whether they differ in their inductive…
This paper is a continuation of the study of topological properties of omega context free languages (omega-CFL). We proved before that the class of omega-CFL exhausts the hierarchy of Borel sets of finite rank, and that there exist some…
We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…
Let G be a context-free grammar with a total alphabet V, and let F be a final language over an alphabet W such that W is a subset of V. A final sentential form is any sentential form of G that, after omitting symbols from V - W, it belongs…
Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to…
Given a linear equation $\mathcal{L}$, a set $A \subseteq [n]$ is $\mathcal{L}$-free if $A$ does not contain any `non-trivial' solutions to $\mathcal{L}$. In this paper we consider the following three general questions: (i) What is the size…
Understanding context is key to understanding human language, an ability which Large Language Models (LLMs) have been increasingly seen to demonstrate to an impressive extent. However, though the evaluation of LLMs encompasses various…
Let a text $T[1..n]$ be the only string generated by a context-free grammar with $g$ (terminal and nonterminal) symbols, and of size $G$ (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a…