Reinterpreting and extending Anatol Vieru's Periodic Sequence through the Celluar Automata formalism : some theoritical, computational and compositional aspects.

Tuesday 29 January 2019, 14:00 à 15:00

Salle des séminaires.

Paul Lanthier

Paul Lanthier est le doctorant de Thierry de la Rue.

The object of study of this work is double: first we extended preexisting results about the action (in the image direction) of one particular cellular automaton on periodic sequences and discovered the existence of a complementarity with an other automaton that we call its dual.    
The main idea is that the study of preimages of one of those two automata is the study of the images of the other one and vice versa.
We show explicitly the form of the preimages for both automata thanks to the existing duality and the evolution of the period.
We tried to understand wether or not the initial periodic sequence was forgotten when considering the preimages, or if some particular elements came back.

Eventualy to illustrate with an example those results and this last question, a composition was made using the two automata both in the image and preimage directions.