Related papers: Bit-Optimal Lempel-Ziv compression
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless…
We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently…
The sensitivity of a string compression algorithm $C$ asks how much the output size $C(T)$ for an input string $T$ can increase when a single character edit operation is performed on $T$. This notion enables one to measure the robustness of…
The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…
Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
In this paper, the context dependence multilevel pattern matching(in short CDMPM) grammar transform is proposed; based on this grammar transform, the universal lossless data compression algorithm, CDMPM code is then developed. Moreover we…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
Data compression is a powerful tool for managing massive but repetitive datasets, especially schemes such as grammar-based compression that support computation over the data without decompressing it. In the best case such a scheme takes a…
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix…
We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
A new approach to data compression is developed and applied to multimedia content. This method separates messages into components suitable for both lossless coding and 'lossy' or statistical coding techniques, compressing complex objects by…
In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
For both the Lempel Ziv 77- and 78-factorization we propose algorithms generating the respective factorization using $(1+\epsilon) n \lg n + O(n)$ bits (for any positive constant $\epsilon \le 1$) working space (including the space for the…
Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at…