Related papers: $O_2$ is a multiple context-free grammar: an imple…
It is shown that every tree of size $n$ over a fixed set of $\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\big(\frac{n}{\log_\sigma n}\big) = O\big(\frac{n \log \sigma}{\log n}\big)$ many…
Large Language Models (LLMs) have shown remarkable abilities recently, including passing advanced professional exams and demanding benchmark tests. This performance has led many to suggest that they are close to achieving humanlike or…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…
This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky…
Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related…
In a recent paper (M. Barash, A. Okhotin, "Defining contexts in context-free grammars", LATA 2012), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the…
Context-free language (CFL) reachability is a standard approach in static analyses, where the analysis question is phrased as a language reachability problem on a graph $G$ wrt a CFL L. While CFLs lack the expressiveness needed for high…
Right-linear (or left-linear) grammars are a well-known class of context-free grammars computing just the regular languages. They may naturally be written as expressions with (least) fixed points but with products restricted to letters as…
We show that if a context-free grammar generates a language whose lexicographic ordering is well-ordered of type less than $\omega^2$, then its order type is effectively computable.
The impressive ability of large language models to generate natural text across various tasks has led to critical challenges in authorship authentication. Although numerous detection methods have been developed to differentiate between…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of…
A prefix grammar is a context-free grammar whose nonterminals generate prefix-free languages. A prefix grammar $G$ is an ordinal grammar if the language $L(G)$ is well-ordered with respect to the lexicographic ordering. It is known that…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the…
High-quality text generation capability of recent Large Language Models (LLMs) causes concerns about their misuse (e.g., in massive generation/spread of disinformation). Machine-generated text (MGT) detection is important to cope with such…
Let $A_N$ denote nondeterministic automatic complexity and \[ L_{k,c}=\{x\in [k]^* : A_N(x)> |x|/c\}. \] In particular, $L_{k,2}$ is the language of all $k$-ary words for which $A_N$ is maximal, while $L_{k,3}$ gives a rough dividing line…
Back in the 80s, the class of mildly context-sensitive formalisms was introduced so as to capture the syntax of natural languages. While the languages generated by such formalisms are constrained by the constant-growth property, the most…
It is known that if a B\"uchi context-free language (BCFL) consists of scattered words, then there is an integer $n$, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by $n$. Every BCFL is…