Related papers: Generating a Gray code for prefix normal words in …
Starting from a succession rule for Catalan numbers, we define a procedure encoding and listing the objects enumerated by these numbers such that two consecutive codes of the list differ only for one digit. Gray code we obtain can be…
The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints…
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of…
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…
Word segmentation is the task of inserting or deleting word boundary characters in order to separate character sequences that correspond to words in some language. In this article we propose an approach based on a beam search algorithm and…
We show that the equality language of two non-periodic binary morphisms is generated by at most two words. If its rank is two, then the generators start (and end) with different letters. This in particular implies that any binary language…
Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
Symmetric fix-free codes are prefix condition codes in which each codeword is required to be a palindrome. Their study is motivated by the topic of joint source-channel coding. Although they have been considered by a few communities they…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Multiple algorithms are known for efficiently calculating the prefix probability of a string under a probabilistic context-free grammar (PCFG). Good algorithms for the problem have a runtime cubic in the length of the input string. However,…
A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove…
For any integer $n\geq 1$ a middle levels Gray code is a cyclic listing of all $n$-element and $(n+1)$-element subsets of $\{1,2,\ldots,2n+1\}$ such that any two consecutive subsets differ in adding or removing a single element. The…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
An automatic word classification system has been designed which processes word unigram and bigram frequency statistics extracted from a corpus of natural language utterances. The system implements a binary top-down form of word clustering…
A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a `small change'. Such listings are known for many…
We approach the problem of generalizing pre-trained word embeddings beyond fixed-size vocabularies without using additional contextual information. We propose a subword-level word vector generation model that views words as bags of…
We regard a finite word $u=u_1u_2\cdots u_n$ up to word isomorphism as an equivalence relation on $\{1,2,\ldots, n\}$ where $i$ is equivalent to $j$ if and only if $x_i=x_j.$ Some finite words (in particular all binary words) are generated…
An overlap-free (or $\beta$-free) word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ at any position contains an overlap (or a factor of exponent at least $\beta$,…
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…