Related papers: On Match Lengths, Zero Entropy and Large Deviation…

Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…

The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…

Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this…

Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…

Highly-repetitive collections of strings are increasingly being amassed by genome sequencing and genetic variation experiments, as well as by storing all versions of human-generated files, like webpages and source code. Existing indexes for…

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is…

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a…

Large Language Models (LLMs) have demonstrated remarkable proficiency in language comprehension and generation; however, their widespread adoption is constrained by substantial bandwidth and computational demands. While pruning and low-rank…

Text compression for large language model (LLM) systems is usually framed as token deletion, retrieval, summarization, or exact reconstruction. We study a more aggressive but explicitly lossy setting: compress text into compact codes that…

We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1..M] and a text t[1..N] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time…

A guessing wiretapper's performance on a Shannon cipher system is analyzed for a source with memory. Close relationships between guessing functions and length functions are first established. Subsequently, asymptotically optimal encryption…

We propose a new approach for calculating the Lempel-Ziv factorization of a string, based on run length encoding (RLE). We present a conceptually simple off-line algorithm based on a variant of suffix arrays, as well as an on-line algorithm…

Code generation under long contexts is becoming increasingly critical as Large Language Models (LLMs) are required to reason over extensive information in the codebase. While recent advances enable code LLMs to process long inputs, high API…

Large Language Models (LLMs) often experience performance degradation during long-running interactions due to increasing context length, memory saturation, and computational overhead. This paper presents an adaptive context compression…

Due to the fundamental connection between next-symbol prediction and compression, modern predictive models, such as large language models (LLMs), can be combined with entropy coding to achieve compression rates that surpass those of…

Many information retrieval algorithms rely on the notion of a good distance that allows to efficiently compare objects of different nature. Recently, a new promising metric called Word Mover's Distance was proposed to measure the divergence…

At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…

Grammar compression is, next to Lempel-Ziv (LZ77) and run-length Burrows-Wheeler transform (RLBWT), one of the most flexible approaches to representing and processing highly compressible strings. The main idea is to represent a text as a…

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…