Search results for "Binary alphabet"
showing 6 items of 6 documents
Balance Properties and Distribution of Squares in Circular Words
2008
We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalised to non periodic infinite words as well.
Balanced Words Having Simple Burrows-Wheeler Transform
2009
The investigation of the "clustering effect" of the Burrows-Wheeler transform (BWT) leads to study the words having simple BWT , i.e. words w over an ordered alphabet $A=\{a_1,a_2,\ldots,a_k\}$, with $a_1 < a_2 < \ldots <a_k$, such that $bwt(w)$ is of the form $a_k^{n_k} a_{k-1}^{n_{k-1}} \cdots a_1^{n_1}$, for some non-negative integers $n_1, n_2, \ldots, n_k$. We remark that, in the case of binary alphabets, there is an equivalence between words having simple BWT, the family of (circular) balanced words and the conjugates of standard words. In the case of alphabets of size greater than two, there is no more equivalence between these notions. As a main result of this paper we prove that, u…
Balancing and clustering of words in the Burrows–Wheeler transform
2011
AbstractCompression algorithms based on Burrows–Wheeler transform (BWT) take advantage of the fact that the word output of BWT shows a local similarity and then turns out to be highly compressible. The aim of the present paper is to study such “clustering effect” by using notions and methods from Combinatorics on Words.The notion of balance of a word plays a central role in our investigation. Empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal BWT compression. Moreover, it is reasonable to assume that the more balanced the input word is, the more local similarity we have after BWT (and therefore the better the compression is).…
A Periodicity Theorem on Words and Applications
1995
We prove a periodicity theorem on words that has strong analogies with the Critical Factorization theorem and we show three applications of it.
Quantum, stochastic, and pseudo stochastic languages with few states
2014
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all th…
Some Decision Results on Nonrepetitive Words
1985
The paper addresses some generalizations of the Thue Problem such as: given a word u, does there exist an infinite nonrepetitive overlap free (or square free) word having u as a prefix? A solution to this as well as to related problems is given for the case of overlap free words on a binary alphabet.