Related papers: Dynamic Membership for Regular Tree Languages
In this paper we present a robust parsing algorithm based on the link grammar formalism for parsing natural languages. Our algorithm is a natural extension of the original dynamic programming recognition algorithm which recursively counts…
Characterizing the computational power of neural network architectures in terms of formal language theory remains a crucial line of research, as it describes lower and upper bounds on the reasoning capabilities of modern AI. However, when…
We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language…
In this paper, we consider tree decompositions, branch decompositions, and clique decompositions. We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…
The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem…
In this paper we introduce and study fuzzy deterministic top-down (DT) tree automata over a lattice L. The L-fuzzy tree languages recognized by these automata are said to be DT-recognizable, and they form a proper subfamily $DRec_L$ of the…
Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured…
We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…
In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT)…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
The swift advancement in the scales and capabilities of Large Language Models (LLMs) positions them as promising tools for a variety of downstream tasks. In addition to the pursuit of better performance and the avoidance of violent feedback…
In this paper we consider the problem of deciding membership in Dyck languages, a fundamental family of context-free languages, comprised of well-balanced strings of parentheses. In this problem we are given a string of length $n$ in the…
The dynamic partial sorting problem asks for an algorithm that maintains lists of numbers under the link, cut and change value operations, and queries the sorted sequence of the $k$ least numbers in one of the lists. We first solve the…
Continual instruction tuning enables large language models (LLMs) to learn incrementally while retaining past knowledge, whereas existing methods primarily focus on how to retain old knowledge rather than on selecting which new knowledge to…