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On Infinite Prefix Normal Words
[article]

2018
*
arXiv
*
pre-print

In this paper, we study

arXiv:1811.06273v1
fatcat:2ojyohhi2raaljuymutx3fkotu
*infinite**prefix**normal**words*and explore their relationship to some known classes of*infinite*binary*words*. ...*Prefix**normal**words*are binary*words*that have no factor with more 1s than the*prefix*of the same length. Finite*prefix**normal**words*were introduced in [Fici and Lipták, DLT 2011]. ... We wish to thank the participants of the Workshop*on**Words*and Complexity (Lyon, February 2018), for interesting discussions and pointers, and to Péter Burcsi, who first got us interested in Sturmian*words*...##
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Bubble-Flip—A new generation algorithm for prefix normal words

2018
*
Theoretical Computer Science
*

We introduce

doi:10.1016/j.tcs.2018.06.021
fatcat:3cpshypcwraklozijkfx4w24j4
*infinite**prefix**normal**words*and show that*one*of the operations used by the algorithm, if applied repeatedly to extend the string, produces an ultimately periodic*infinite**word*, which is ... The new algorithm uses two operations*on*binary strings, which exploit certain properties of*prefix**normal**words*in a smart way. ...*On*finite and*infinite**prefix**normal**words*In this section, we study*infinite**prefix**normal**words*. ...##
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Quasiperiodic and Lyndon episturmian words

2008
*
Theoretical Computer Science
*

Our key tools are morphisms and directive

doi:10.1016/j.tcs.2008.09.056
fatcat:zqhu5um45fbkbgvyfkfwkrir2m
*words*, in particular "*normalized*" directive*words*, which we introduced in an earlier paper. ... Recently the second two authors characterized quasiperiodic Sturmian*words*, proving that a Sturmian*word*is non-quasiperiodic if and only if it is an*infinite*Lyndon*word*. ... Krieger who suggested to the third author the notion of ultimate quasiperiodicity and observed the fact that all Sturmian*words*are ultimately quasiperiodic. ...##
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On periodicity of generalized pseudostandard words
[article]

2015
*
arXiv
*
pre-print

More precisely, we describe how the directive bi-sequence of a generalized pseudostandard

arXiv:1508.02020v1
fatcat:fv6wcghlabazxarisgi6d2f3ny
*word*has to look like in order to correspond to a periodic*word*. ... Generalized pseudostandard*words*were introduced by de Luca and De Luca in 2006. ... Introduction This paper focuses*on*a recent topic of combinatorics*on**words*: generalized pseudostandard*words*. ...##
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On Periodicity of Generalized Pseudostandard Words

2016
*
Electronic Journal of Combinatorics
*

More precisely, we describe how the directive bi-sequence of a generalized pseudostandard

doi:10.37236/4771
fatcat:lnpix5vjpfbaleftsr5uwktaky
*word*has to look like in order to correspond to a periodic*word*. ... Generalized pseudostandard*words*were introduced by de Luca and De Luca in 2006. ... Introduction This paper focuses*on*a recent topic of combinatorics*on**words*: generalized pseudostandard*words*. ...##
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Abelian complexity and abelian co-decomposition

2013
*
Theoretical Computer Science
*

We propose a technique for exploring the abelian complexity of recurrent

doi:10.1016/j.tcs.2012.10.034
fatcat:xk6mqhtwkbbfzcqcujsgkbr7xa
*infinite**words*, focusing particularly*on**infinite**words*associated with Parry numbers. ... Using that technique, we give the affirmative answer to the open question posed by Richomme, Saari and Zamboni, whether the abelian complexity of the Tribonacci*word*attains each value in {4,5,6}*infinitely*... Acknowledgements The author thanks Karel Břinda for a numerical experiment and Edita Pelantová for many valuable comments*on*the manuscript. ...##
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Abelian complexity of infinite words

2018
*
Zenodo
*

In addition, a new toolkit TigrWords, which facilitates study of

doi:10.5281/zenodo.2112128
fatcat:j4gxptknm5dkbg5d65ccjnvmfu
*infinite**words*approximated by their*prefixes*and may serve to discover of new hypotheses, is described. ... This thesis deals with Abelian complexity of*infinite**words*, i.e., function describing complexity of a given*infinite**word*using sets of Parikh vectors of finite factors of the*word*. ... Acknowledgments I thank all members of TIGR (Theoretical Informatics Group) at FNSPE for bringing me into the amazing world of combinatorics*on**words*. ...##
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Fixed points of morphisms among binary generalized pseudostandard words
[article]

2017
*
arXiv
*
pre-print

We conjecture that this class contains all fixed points of primitive morphisms among aperiodic binary generalized pseudostandard

arXiv:1701.04472v1
fatcat:uryio7jvhfgynhqdsheyzcazky
*words*that are not standard Sturmian*words*. ... We introduce a class of fixed points of primitive morphisms among aperiodic binary generalized pseudostandard*words*. ... If a finite*word*w = pvs, where p, v, s ∈ {0, 1} * , then p is called a*prefix*of w and s is called a suffix of w. An*infinite**word*u over {0, 1} is any binary*infinite*sequence. ...##
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Unavoidable Set: Extension and Reduction

1999
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RAIRO - Theoretical Informatics and Applications
*

As u,v j£ e, consider the periodic bi-

doi:10.1051/ita:1999114
fatcat:w6df7dsiqbachhf4uo3yvbjcme
*infinite**word*"vxv? -w u w = "v^, in which the subwords having an occurence of x as*prefix*and the next*one*as sufnx are ail the same s. ... Since every occurence of x in this*word*is invariably followed by the*infinité**word*u w we get that t is a*prefix*of every u^. ...##
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Abelian complexity of infinite words associated with quadratic Parry numbers

2011
*
Theoretical Computer Science
*

We derive an explicit formula for the Abelian complexity of

doi:10.1016/j.tcs.2011.08.016
fatcat:b6nw4jvx5fefzcstlmnnaaccsq
*infinite**words*associated with quadratic Parry numbers. ... Our method consisted in the construction of*infinite**words*v and w whose*prefixes*are factors of the*infinite**word*in question and such that the*prefixes*of v are the richest in A's (among all factors ... Moreover, these cases are the only*ones*among all Parry numbers β (not only the quadratic*ones*) for which the*infinite**word*u β is Sturmian, see [10] . ...##
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Determining Sets of Quasiperiods of Infinite Words

2016
*
International Symposium on Mathematical Foundations of Computer Science
*

Assume by contradiction that n is the least integer such that ψ n (q) is quasiperiodic, and let Q be

doi:10.4230/lipics.mfcs.2016.40
dblp:conf/mfcs/GamardR16
fatcat:viporj3zyfg7fisnhywyzedmfy
*one*of its quasiperiods. Necessarily n ≥ 1. The*word*ψ(a)ba is a*prefix*of ψ n (q). ... Based*on*links between quasiperiods, right special factors and square factors, we introduce a method to determine the set of quasiperiods of a given right*infinite**word*. ... This decomposition is called the left*normal*form (resp. right*normal*form) of the*word*. As observed by Marcus and Monteil [19] this result extends naturally to*infinite**words*. ...##
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On Periodicity and Complexity of Generalized Pseudostandard Words
[article]

2016
*
arXiv
*
pre-print

Vuillon,

arXiv:1408.5210v2
fatcat:vzlfsldlbrevji5ycicye3ehp4
*On*Generalized Pseudostandard*Words*over Binary Alphabet (Journal of Int. ... We present two new results concerning these*words*. The first*one*is a necessary and sufficient condition for their periodicity. ... Introduction This paper focuses*on*an actual topic of combinatorics*on**words*: generalized pseudostandard*words*. ...##
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On Selection Functions that Do Not Preserve Normality
[chapter]

2003
*
Lecture Notes in Computer Science
*

In fact, for both types of languages it is possible to select a constant sequence from a

doi:10.1007/978-3-540-45138-9_54
fatcat:2gvcy2ifqvcfdkmqmbhunjtdr4
*normal**one*. ... We show that there are such languages that are only slightly more complicated than regular*ones*, namely,*normality*is preserved neither by deterministic*one*-counter languages nor by linear languages. ... There is a*normal*sequence N and a deterministic*one*-counter language L such that the sequence selected from N by L is*infinite*and constant. Proof. ...##
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Thompson's group F is 1-counter graph automatic

2016
*
Groups - Complexity - Cryptology
*

We consider two cases, depending

doi:10.1515/gcc-2016-0001
fatcat:hwnibopn5jajdom3iun4kmpp5i
*on*whether wx − is already in*infinite**normal*form, or must be simplified in order to obtain the*infinite**normal*form. ... . (3.5) We again consider subcases, depending*on*whether or not the expression in (3.5) is the*infinite**normal*form for gx − . ...##
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A new estimate on complexity of binary generalized pseudostandard words
[article]

2016
*
arXiv
*
pre-print

Generalized pseudostandard

arXiv:1611.05482v1
fatcat:c7ahkjz5ynhk7e4zhx4fzrld6q
*words*were introduced by de Luca and De Luca in 2006. ... In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard*words*. ... We would like to thank Edita Pelantová for her useful comments and advice concerning in particular complexity of*infinite**words*. ...
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