Related papers: There Are Fewer Facts Than Words: Communication Wi…
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two…
Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…
We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite word contains an imaged factor of length at…
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems and has been widely reported in a variety of natural language processing applications. However, the emergence of natural language…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…
The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in…
Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity…
The frequencies at which individual words occur across languages follow power law distributions, a pattern of findings known as Zipf's law. A vast literature argues over whether this serves to optimize the efficiency of human communication,…
The word-frequency distribution provides the fundamental building blocks that generate discourse in language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at…
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…
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…
Motivated by recent connections to factorised databases, we analyse the efficiency of representations by context free grammars (CFGs). Concretely, we prove a recent conjecture by Kimelfeld, Martens, and Niewerth (ICDT 2025), that for finite…
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
By determining which were the most common English words and phrases since the beginning of the 16th century, we obtain a unique large-scale view of the evolution of written text. We find that the most common words and phrases in any given…
This article introduces three invariance principles under which P is different from NP. In the second part a theorem of convergence is proven. This theorem states that for any language L there exists an infinite sequence of languages from…