Related papers: Parsing Linear Context-Free Rewriting Systems with…
In this paper, we consider the following inverse maintenance problem: given $A \in \mathbb{R}^{n\times d}$ and a number of rounds $r$, we receive a $n\times n$ diagonal matrix $D^{(k)}$ at round $k$ and we wish to maintain an efficient…
For matrices with displacement structure, basic operations like multiplication, inversion, and linear system solving can all be expressed in terms of the following task: evaluate the product $\mathsf{A}\mathsf{B}$, where $\mathsf{A}$ is a…
We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string.…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
We present an algorithm for extracting a subclass of the context free grammars (CFGs) from a trained recurrent neural network (RNN). We develop a new framework, pattern rule sets (PRSs), which describe sequences of deterministic finite…
The currently fastest algorithm for regular expression pattern matching and membership improves the classical O(nm) time algorithm by a factor of about log^{3/2}n. Instead of focussing on general patterns we analyse homogeneous patterns of…
The applications of LLM Agents are becoming increasingly complex and diverse, leading to a high demand for structured outputs that can be parsed into code, structured function calls, and embodied agent commands. These developments bring…
Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an $O(m \sqrt{n})$-time algorithm for the problem, where $n$ and $m$…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most $\ell.$ The goal is to learn a cover 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…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
Low-resource languages pose a challenge for machine translation with large language models (LLMs), which require large amounts of training data. One potential way to circumvent this data dependence is to rely on LLMs' ability to use…
A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
We give algorithms to accelerate the computation of deterministic finite automata (DFA) by calculating the state of a DFA n positions ahead utilizing a reverse scan of the next n characters. Often this requires scanning fewer than n…
A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are parallel to an existing row/column or have at most one 1-entry. Equivalently, series-parallel matrices…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
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