Related papers: Complexity and fractal dimensions for infinite seq…
The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word $w$ in a given sequence $x$ can be used for classifying $w$ as avoided or overabundant. The definitions used for the expectation…
Entropy is one of physical bases for fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using fractal dimension, we can describe urban growth and form and characterize spatial complexity. A…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance p match. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of…
For a stationary stochastic process $\{X_n\}$ with values in some set $A$, a finite word $w \in A^K$ is called a memory word if the conditional probability of $X_0$ given the past is constant on the cylinder set defined by $X_{-K}^{-1}=w$.…
A regular continuant is the denominator $K$ of a terminating regular continued fraction, interpreted as a function of the partial quotients. We regard $K$ as a function defined on the set of all finite words on the alphabet $1<2<3<\dots$…
Given word on $n$ letters, we study groups which satisfiy "iterated identity" $w$, meaning that for all $x_1, \dots, x_n$ there exists $m$ such that $m$-the iteration of $w$ of Engel type, applied to $x_1, \dots, x_n$, is equal to the…
A word $u$ is a subsequence of another word $w$ if $u$ can be obtained from $w$ by deleting some of its letters. The word $w$ with alph$(w)=\Sigma$ is called $k$-subsequence universal if the set of subsequences of length $k$ of $w$ contains…
We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.
A finite word $w$ is called \textit{closed} if it has length at most 1 or it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences in $w$. An infinite word $u$ is called…
We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word $w$ of length $n$ over an alphabet of cardinality $k$, $w$ can be…
A \emph{square} is a finite non-empty word consisting of two identical adjacent blocks. A word is \emph{square-free} if it does not contain a square as a factor. In any finite word one may delete the repeated block of a square, obtaining…
Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…
Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $\sigma$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Let $w$ be an infinite word on an alphabet $A$. We denote by $(n_i)_{i \geq 1}$ the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of $w$. In this text, we give an explicit construction of all words $w$…