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Article Dans Une Revue Theoretical Computer Science Année : 2018

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.
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Dates et versions

hal-01683320 , version 1 (15-01-2018)
hal-01683320 , version 2 (11-08-2018)
hal-01683320 , version 3 (31-08-2018)

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Jean Néraud, Carla Selmi. Embedding a θ-invariant code into a complete one. Theoretical Computer Science, In press, ⟨10.1016/j.tcs.2018.08.022⟩. ⟨hal-01683320v3⟩
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