Related papers: Geometric Characterization of Context-Free Interse…
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…
We say that a language $L$ is \emph{constantly growing} if there is a constant $c$ such that for every word $u\in L$ there is a word $v\in L$ with $\vert u\vert<\vert v\vert\leq c+\vert u\vert$. We say that a language $L$ is…
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
This paper concerns the structure of meanings within natural language. Earlier, a framework named DisCoCirc was sketched that (1) is compositional and distributional (a.k.a. vectorial); (2) applies to general text; (3) captures linguistic…
We study the computational complexity of finite intersections and finite unions of deterministic context-free (dcf) languages. Earlier, Wotschke [J. Comput. System Sci. 16 (1978) 456--461] demonstrated that intersections of $(d+1)$ dcf…
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…
A derivation step in a Graph Interpolation Grammar has the effect of scanning an input token. This feature, which aims at emulating the incrementality of the natural parser, restricts the formal power of GIGs. This contrasts with the fact…
We prove complexity dichotomies for \#CSP problems (not necessarily symmetric) with Boolean domain and complex range on several typical minor-closed graph classes. These dichotomies give a complete characterization of the complexity of…
We study classes of countable graphs where every member does not contain a given finite graph as an induced subgraph -- denoted by $\mathsf{Free}(\mathcal{G})$ for a given finite graph $\mathcal{G}$. Our main results establish a structural…
In quantum field theories defined on a spacetime with boundaries, the entanglement entropy exhibits subleading, boundary-induced corrections to the ubiquitous area law. At critical points described by conformal field theories (CFTs), and…
By simply incorporating demonstrations into the context, in-context learning (ICL) enables large language models (LLMs) to yield awesome performance on many tasks. In this study, we focus on passage-level long-context ICL for generation…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
Context-free languages (CFLs) are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma is a property that is valid for all context-free languages, and is used to show the…
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…
Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a…
In the Intersection Non-Emptiness problem, we are given a list of finite automata $A_1,A_2,\dots,A_m$ over a common alphabet $\Sigma$ as input, and the goal is to determine whether some string $w\in \Sigma^*$ lies in the intersection of the…
In the realm of machine learning theory, to prevent unnatural coding schemes between teacher and learner, No-Clash Teaching Dimension was introduced as provably optimal complexity measure for collusion-free teaching. However, whether…
The rational index of a context-free language $L$ is a function $f(n)$, such that for each regular language $R$ recognized by an automaton with $n$ states, the intersection of $L$ and $R$ is either empty or contains a word shorter than…
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to…