arXiv subjects

Carla Selmi

Publications and source records attributed to Carla Selmi.

3 recordsLinked to original sources

arXiv2018

Embedding a $θ$-invariant code into a complete one

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.

cs.DM↗

arXiv2017

Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

Let $A$ be a finite or countable alphabet and let $θ$ be literal (anti)morphism 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).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin $θ$-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of $θ$-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular $θ$-invariant code may be embedded into a complete one.

cs.DM↗

arXiv2010

Strategical languages of infinite words

We deal in this paper with strategical languages of infinite words, that is those generated by a nondeterministic strategy in the sense of game theory. We first show the existence of a minimal strategy for such languages, for which we give an explicit expression. Then we characterize the family of strategical languages as that of closed ones, in the topological space of infinite words. Finally, we give a definition of a Nash equilibrium for such languages, that we illustrate with a famous example.

cs.GT↗