Related papers: Classifying Rotationally-Closed Languages Having G…
We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a common finite bound for the rank of…
We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem…
We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm…
Let $K$ be a global function field of characteristic $p$ and degree $D$ over $\mathbb F_{p}(t)$. We consider dynamical systems over the projective line $\mathbb P^1(K)$ defined by rational maps with at most one prime of bad reduction. The…
Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a…
Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1992. They have been developed by many authors since, for various combinatorial objects such as…
We show that the coding of rotation by $\alpha$ on $m$ intervals with rationally independent lengths can be recoded over $m$ Sturmian words of angle $\alpha.$ More precisely, for a given $m$ an universal automaton is constructed such that…
We show that for every $n \geq 1$ and over any finite alphabet, there is a word whose circular factors of length $n$ have a one-to-one correspondence with the set of primitive words. In particular, we prove that such a word can be obtained…
We classify rotary (orientably-regular) maps whose underlying graphs are multicycles. For the multicycle $\mathrm{C}_n^{(\lambda)}$ of length $n$ and edge-multiplicity $\lambda$, we determine all rotary embeddings for $n\geqslant 3$ and…
Given a subset of size $k$ of a very large universe a randomized way to find this subset could consist of deleting half of the universe and then searching the remaining part. With a probability of $2^{-k}$ one will succeed. By probability…
Kitaev, Potapov, and Vajnovszki [On shortening u-cycles and u-words for permutations, Discrete Appl. Math, 2019] described how to shorten universal words for permutations, to length $n!+n-1-i(n-1)$ for any $i \in [(n-2)!]$, by introducing…
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…
The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with…
Given a binary word relation $\tau$ onto A * and a finite language X $\subseteq$ A * , a $\tau$-Gray cycle over X consists in a permutation w [i] 0$\le$i$\le$|X|--1 of X such that each word w [i] is an image under $\tau$ of the previous…
The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for…
We investigate the existence of greedy Gray codes, based on the choice of the first element in the code, for two classes of binary words: generalized Fibonacci words and generalized Dyck words.
For a language $L$, we consider its cyclic closure, and more generally the language $C^k(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and…
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed…