Embedding a θ-invariant code into a complete one
Résumé
Let A be a finite or countable alphabet and let θ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short) that is, languages L such that θ (L) is a subset of L.
We establish an extension of the famous defect theorem. With regards to the so-called notion of completeness, we provide a series of examples of finite complete θ-invariant codes.
Moreover, we establish a formula which allows to embed any non-complete θ-invariant code into a complete one.
As a consequence, in the family of the so-called thin θ--invariant codes, maximality and completeness are two equivalent notions.
Mots clés
code
equation
word
involutive
invariant
(anti-)automorphism
antimorphism
maximal
regular
complete
morphism
defect
context-free
bifix
Bernoulli distribution
label
involutive
finite
thin
variable length code
prefix
suffix
defect
antimorphism
anti-automorphism
automorphism
order
overlap
overlapping-free
suffix
thin
tree
θ-invariant
θ-code
uniform
variable-length code
word
Origine : Fichiers produits par l'(les) auteur(s)