Related papers: Knuth's Moves on Timed Words
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
We investigate the scattered palindromic subwords in a finite word. We start by characterizing the words with the least number of scattered palindromic subwords. Then, we give an upper bound for the total number of palindromic subwords in a…
We study the shape of the Young diagram \lambda associated via the Robinson-Schensted-Knuth algorithm to a random permutation in S_n such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other…
We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes…
Manacher's algorithm has been shown to be optimal to the longest palindromic substring problem. Many of the existing implementations of this algorithm, however, unanimously required in-memory construction of an augmented string that is…
We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie…
An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine 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…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
We present a method which displays all palindromes of a given length from De Bruijn words of a certain order, and also a recursive one which constructs all palindromes of length $n+1$ from the set of palindromes of length $n$. We show that…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
We consider the generalization ability of algorithms for learning to rank at a query level, a problem also called subset ranking. Existing generalization error bounds necessarily degrade as the size of the document list associated with a…
We present an algorithm that takes an unannotated corpus as its input, and returns a ranked list of probable morphologically related pairs as its output. The algorithm tries to discover morphologically related pairs by looking for pairs…
In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree $n$ over a finite field and their roots in the extension field in quasilinear where $N=n^2$…
We propose a novel convolutional architecture, named $gen$CNN, for word sequence prediction. Different from previous work on neural network-based language modeling and generation (e.g., RNN or LSTM), we choose not to greedily summarize the…
Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to…