Discrétisation automatique de machines à signaux en automates cellulaires

Abstract : In the context of abstract geometrical computation, signal machines have been developed as a continuous counter part of cellular automata capturing the notions of particles, signals and collisions. An important issue is the automatic generation of a cellular automaton mimicking the dynamics of a given signal machine. On the one hand, ad hoc conversions exist.On the other hand, it is not always possible since some signal machines exhibit “purely continuous” behaviors. Therefore, automatically discretizing such structures is often complicated and not always possible. This thesis proposes different ways to automatically discretize signal machines into cellular automata, both with and without handling the possiblity of approximation.The first is concerned with a subcategory of signal machines, which has properties ensuring an exact automatic discretization for any machine of this type. The second is usable on all machines but cannot guarantee the exactness and correction of the result. The third is based on a new expression of the dynamics of a signal machine to propose a discretization.This dynamical expression takes the name of modularity and is described before being used to discretize.
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Tom Besson. Discrétisation automatique de machines à signaux en automates cellulaires. Autre [cs.OH]. Université d'Orléans, 2018. Français. ⟨NNT : 2018ORLE2009⟩. ⟨tel-01975875⟩

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