Related papers: Ranking and Unranking k-subsequence universal word…
We investigate the variance of the length of the longest common subsequences of two independent random words of size $n$, where the letters of one word are i.i.d. uniformly drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m\}$, while the…
Unbounded SubsetSum is a classical textbook problem: given integers $w_1,w_2,\cdots,w_n\in [1,u],~c,u$, we need to find if there exists $m_1,m_2,\cdots,m_n\in \mathbb{N}$ satisfying $c=\sum_{i=1}^n w_im_i$. In its all-target version, $t\in…
Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the…
We investigate the order of the $r$-th, $1\le r < +\infty$, central moment of the length of the longest common subsequence of two independent random words of size $n$ whose letters are identically distributed and independently drawn from a…
We consider the set of finite random words $\mathcal A^\star$, with independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. On a specific subset of $\mathcal A^\star$,…
A finite deterministic (semi)automaton $\mathcal{A} =(Q,\Sigma,\delta)$ is $k$-compressible if there is some word $w\in \Sigma^+$ such that the image of its state set $Q$ under the natural action of $w$ is reduced by at least $k$ states.…
We survey the emerging area of compression-based, parameter-free, similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a…
For an arbitrary word $w$ on an alphabet, we can define the alternating symbol graph, $G(w)$, as the graph in which the edge $(a, b)$ is in $E$ iff the letters $a$ and $b$ alternate in the word $w$. A graph $G = (V, E)$ is said to be…
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 $1<2<3<\dots$…
We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
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…
We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of a rejection-based approach, whose time complexity is shown…
It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a…
Simon's congruence, denoted \sim_n, relates words having the same subwords of length up to n. We show that, over a k-letter alphabet, the number of words modulo \sim_n is in 2^{\Theta(n^{k-1} log n)}.
The notion of Wheeler languages is rooted in the Burrows-Wheeler transform (BWT), one of the most central concepts in data compression and indexing. The BWT has been generalized to finite automata, the so-called Wheeler automata, by Gagie…
The problem of word sense disambiguation (WSD) is considered in the article. Given a set of synonyms (synsets) and sentences with these synonyms. It is necessary to select the meaning of the word in the sentence automatically. 1285…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
Let $S_n$ denote the set of permutations of $[n]$ and let $\sigma=\sigma_1\cdots\sigma_n\in S_n$. For a subsequence $\{\sigma_{i_j}\}_{j=1}^k$ of $\{\sigma_i\}_{i=1}^n$ of length $k\ge2$, construct the ``up/down'' sequence $V_1\cdots…