相关论文: Counting Subwords in Circular Words and Their Pari…
Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…
We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as…
We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…
The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Serbanuta. Recently, a decade-old conjecture by Serbanuta on the…
The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while…
In this paper, we consider a variant of the classical algorithmic problem of checking whether a given word $v$ is a subsequence of another word $w$. More precisely, we consider the problem of deciding, given a number $p$ (defining a…
Indexed languages are a classical notion in formal language theory. As the language equivalent of second-order pushdown automata, they have received considerable attention in higher-order model checking. Unfortunately, counting properties…
The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its…
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
Parikh matrices have been a powerful tool in arithmetizing words by numerical quantities. However, the dependence on the ordering of the alphabet is inherited by Parikh matrices. Strong M-equivalence is proposed as a canonical alternative…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We consider sigma-words, which are words used by Evdokimov in the construction of the sigma-sequence. We then find the number of occurrences of certain patterns and subwords in these words.
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…
We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as…
Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
Using arch-jumping functions and properties of the arch factorization of words, we propose a new algorithm for computing the subword circular universality index of words. We also introduce the subword universality signature for words, that…
Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…