Related papers: Algorithmical Aspects of Some Bio Inspired Operati…
We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite…
We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct.
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal…
Two finite words are k-binomially equivalent if each subword (i.e., subsequence) of length at most k occurs the same number of times in both words. The k-binomial complexity of an infinite word is a function that maps the integer $n\geq 0$…
The prefix palindromic length $p_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. This function is surprisingly difficult to…
This work proposes Adaptive Facilitated Mutation, a self-adaptive mutation method for Structured Grammatical Evolution (SGE), biologically inspired by the theory of facilitated variation. In SGE, the genotype of individuals contains a list…
Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors.…
In this paper we define and investigate the binary word operation of strong-$\phi$-bi-catenation (denoted by $\leftrightarrows_\phi$) where $\phi$ is either a morphic or an antimorphic involution. In particular, we concentrate on the…
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…
We consider infinite sequences of symbols, also known as streams, and the decidability question for equality of streams defined in a restricted format. This restricted format consists of prefixing a symbol at the head of a stream, of the…
The prefix palindromic length $PPL_u(n)$ of an infinite word $u$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $u$. In a 2013 paper with Puzynina and Zamboni we stated the conjecture that…
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and…
Covering alignment problems arise from recent developments in genomics; so called pan-genome graphs are replacing reference genomes, and advances in haplotyping enable full content of diploid genomes to be used as basis of sequence…
In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double-cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and…
We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control, PD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PD0L words. We…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holomorphic function; the auxiliary function will be…
This work builds on the notion of breadth-first signature of infinite trees and (prefix-closed) languages introduced by the authors in a previous work. We focus here on periodic signatures, a case coming from the study of rational base…
We study the tandem duplication distance between binary sequences and their roots. In other words, the quantity of interest is the number of tandem duplication operations of the form $\seq x = \seq a \seq b \seq c \to \seq y = \seq a \seq b…
Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…