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Études de la complexité algorithmique des réseaux d'automates

Kévin Perrot 1 
1 CANA - Calcul Naturel
LIS - Laboratoire d'Informatique et Systèmes
Abstract : Automata networks model all finite discrete dynamics. Each automaton has a state, evolving in discrete time steps, according to the states of other automata. The structure of interactions is described by a graph and local transition functions. A global dynamics is obtained with an update schedule, describing which automata apply their local function to change state, deterministically or nondeterministically. This rich expressivity allows to modelize phenomena observed in nature, where the paradigm of going from local rules to global behavior captures the essence of "complex" systems. An automata network is encoded by the (Boolean) circuits of its local functions. Since space is finite, the whole dynamics can be computed. We intend to understand variants of the model, through characterizing the computational complexities of problems: related to computing the graph of interactions, related to the asymptotic dynamics of a given automata network, related to the asymptotic dynamics of all possible networks on a given structure of interactions, and related to update schedules. It indirectly deals with the capacity to embed computation in different aspects of the model. We will draw key elements on the structure of interactions, the principle of locality, the importance of state alphabets, and encodings. This work will result in long term perspectives, on the extension of some partial information on a network, and the statement of "Rice-like" theorems formalized using model theory.
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Submitted on : Thursday, March 17, 2022 - 12:53:57 PM
Last modification on : Friday, March 18, 2022 - 3:35:45 AM
Long-term archiving on: : Saturday, June 18, 2022 - 7:03:19 PM

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Kévin Perrot. Études de la complexité algorithmique des réseaux d'automates. Mathématique discrète [cs.DM]. Aix-Marseille Université, 2022. ⟨tel-03611794⟩

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