Related papers: US Code growth 1991-2025
We present the new empirical parameter $f_c$, the most probable usage frequency of a word in a language, computed via the distribution of documents over frequency $x$ of the word. This parameter allows for filtering the core lexicon of a…
Twins in a finite word are formed by a pair of identical subwords placed at disjoint sets of positions. We investigate the maximum length of twins in a random word over a $k$-letter alphabet. The obtained lower bounds for small values of…
Since the early days of computers and programs, the process and outcomes of software development has been a minefield plagued with problems and failures, as much as the complexity and complication of software and its development has…
There is no doubt that there has been a drastic increase in abusive and sexually explicit content in music, particularly in Billboard Music Charts. However, there is a lack of studies that validate the trend for effective policy…
The number of frequencies of factors of length $n+1$ in a recurrent aperiodic infinite word does not exceed $3\Delta \C(n)$, where $\Delta \C (n)$ is the first difference of factor complexity, as shown by Boshernitzan. Pelantov\'a together…
Code-related benchmarks play a critical role in evaluating large language models (LLMs), yet their quality fundamentally shapes how the community interprets model capabilities. In the past few years, awareness of benchmark quality has…
Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…
Automatic extraction of definitions from legal texts is critical for enhancing the comprehension and clarity of complex legal corpora such as the United States Code (U.S.C.). We present an advanced NLP system leveraging transformer-based…
We enumerate all ternary length-l square-free words, which are words avoiding squares of words up to length l, for l<=24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds…
A non-empty word $w$ is a border of the word $u$ if $\vert w\vert<\vert u\vert$ and $w$ is both a prefix and a suffix of $u$. A word $u$ with the border $w$ is closed if $u$ has exactly two occurrences of $w$. A word $u$ is privileged if…
The past few centuries have witnessed a dramatic growth in scientific and technological knowledge. However, the nature of that growth - whether exponential or otherwise - remains controversial, perhaps partly due to the lack of quantitative…
We perform a critical examination of the scientific methodology behind contemporary large language model (LLM) research. For this we assess over 2,000 research works released between 2020 and 2024 based on criteria typical of what is…
Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…
Wordle, a word guessing game rose to global popularity in the January of 2022. The goal of the game is to guess a five-letter English word within six tries. Each try provides the player with hints by means of colour changing tiles which…
We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language $L\subseteq \{0,1\}^n$ is bounded…
Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs. This…
We look at the puzzle \textit{In the Details} which appeared in the 2013 MIT Mystery Hunt and which gained fame as the \textit{fractal word search}. This seemingly impossible puzzle, whose solution could not fit the memory of a modern…
As program comprehension is a vast research area, it is necessary to get an overview of its rising and falling trends. We performed an n-gram frequency analysis on titles, abstracts and keywords of 1885 articles about program comprehension…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…