Bifix codes and Sturmian words

Berstel, Jean; Felice, Clelia De; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina

doi:10.1016/j.jalgebra.2012.07.013

Cited by 32 publications

(121 citation statements)

References 46 publications

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“…Conversely, assume |w | 1 − |w| 1 even and let u = w ⊕ w . According to (2), |u| 1 is also even, moreover according to (1) we obtain w = σ |u| 1 (w): this implies w ∈ σ * 2 (w). According to Lemma 5.5, we have w ∈ σ * k (w): this establishes (ii).…”

Section: 1mentioning

confidence: 82%

Complete Variable-Length Codes: An Excursion into Word Edit Operations

Néraud

2020

Lecture Notes in Computer Science

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Given an alphabet A and a binary relation τ ⊆The language X is complete if any word over A is a factor of some concatenation of words in X. Given a family of languages F containing X, X is maximal in F if no other set of F can stricly contain X. A language X ⊆ A * is a variable-length code if any equation among the words of X is necessarily trivial. The study discusses the relationship between maximality and completeness in the case of τ -independent or τ -closed variable-length codes. We focus to the binary relations by which the images of words are computed by deleting, inserting, or substituting some characters.

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Section: 1mentioning

confidence: 82%

Complete Variable-Length Codes: An Excursion into Word Edit Operations

Néraud

2020

Lecture Notes in Computer Science

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“…We show that the 2-block extension X (2) of X is eventually dendric with threshold 1. Set A 2 = {u, v, w} with f : aa → u, ab → v, ba → w. Since X is dendric, the graph E 1 (w) is a tree for every word w ∈ L(X (2) ) of length at least 1 (but not for w = ε). Thus X (2) is eventually dendric.…”

Section: Conjugacymentioning

confidence: 99%

“…a suffix code) U ⊂ L(X) is called X-maximal if it is not properly contained in a prefix code (resp. suffix code) Y ⊂ L(X) (see, for instance, [2]).…”

Section: Minimal Eventually Dendric Shiftsmentioning

confidence: 99%

Eventually Dendric Shifts

Dolce

Perrin

2019

Computer Science – Theory and Applications

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We define a new class of shift spaces which contains a number of classes of interest, like Sturmian shifts used in discrete geometry. We show that this class is closed under two natural transformations. The first one is called conjugacy and is obtained by sliding block coding. The second one is called the complete bifix decoding, and typically includes codings by non overlapping blocks of fixed length.

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“…. , 10 1 1 1 1 0 1 1 1 1 1 1 0 2 0 1 1 1 2 2 1 1 1 0 2 0 2 0 1 1 1 3 2 2 3 1 1 1 0 3 0 2 0 3 0 1 1 1 3 3 2 2 3 3 1 1 1 0 4 0 2 …”

Section: Numerologymentioning

confidence: 99%

“…The first part of the present article is motivated by the work [10]: a byproduct of the latter article is that the set of factors of given length n in a fixed Sturmian sequence (call such a set a factor set) is a basis of the subgroup of the free group F 2 which is the kernel of the homomorphism sending an element onto its algebraic length (that is, letters are sent onto 1 and their inverses onto −1) taken modulo n. Thus, the fact that a factor set is of cardinality n + 1, known since the work of Morse and Hedlund, appears as a very special case of the Schreier formula (which gives the rank of a subgroup of finite index of a free group). It was therefore tempting to give a more precise description of the factor sets.…”

mentioning

confidence: 99%