Related papers: US Code growth 1991-2025
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
In recent years, thanks to breakthroughs in neural network techniques especially attentive deep learning models, natural language processing has made many impressive achievements. However, automated legal word processing is still a…
It has been known since the 60's that any complete discrete $n$-state automaton admits a reset word of length not exceeding $\alpha n^3+o(n^3)$ for some absolute constant $\alpha$. J.-E. Pin and P. Frankl proved this statement with…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
Any finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is reached, the word $w$ is called rich. The number of rich words of length $n$ over an alphabet of cardinality $q$ is denoted…
The speeches stated by influential politicians can have a decisive impact on the future of a country. In particular, the economic content of such speeches affects the economy of countries and their financial markets. For this reason, we…
Enhancing word usage is a desired feature for writing assistance. To further advance research in this area, this paper introduces "Smart Word Suggestions" (SWS) task and benchmark. Unlike other works, SWS emphasizes end-to-end evaluation…
We speak of a \textit{computational law} when that law is intended to be enforced by software through an automated decision-making process. As digital technologies evolve to offer more solutions for public administrations, we see an…
We prove that for every $n \in \mathbb{N}$ and $\delta>0$ there exists a word $w_n \in F_2$ of length $n^{2/3} \log(n)^{3+\delta}$ which is a law for every finite group of order at most $n$. This improves upon the main result of [A. Thom,…
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…
The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…
Analyzing 13,455 journals listed in the Journal Citation Report (Thomson Reuters) from 1997 through 2013, we report that the mean cited half-life of the scholarly literature is 6.5 years and growing at a rate of 0.13 years per annum.…
The purpose of this work is to share an English-Yor\`ub\'a evaluation dataset for open-book reading comprehension and text generation to assess the performance of models both in a high- and a low- resource language. The dataset contains 358…
List-decoding and list-recovery are important generalizations of unique decoding that received considerable attention over the years. However, the optimal trade-off among list-decoding (resp. list-recovery) radius, list size, and the code…
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…
In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…
For any synchronizing $n$-state deterministic automaton, \v{C}ern\'{y} conjectures the existence of a synchronizing word of length at most $(n-1)^2$. We prove that there exists a synchronizing word of length at most $2n^2 - 7n + 7$ for…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
Large language models are highly capable of answering difficult questions by retrieving, recombining, and attending to information in long contexts. For agentic tasks, an additional capability is required: the preservation of an exact state…
Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…