Spatialized synchronous computations with Global Transformations

Abstract

This presentation outlines some ideas of my PhD about Global Transformations. These form a general method to describe local and synchronous spatialized dynamical systems such as Cellular Automata and Lindenmayer systems. This work originated from the goal of extending such systems to dynamical graphs. This talk first introduces the categorical formalism, and providing examples of such systems over different structures such as words or graphs. It also give simple instances of many categorical constructions, such as comma categories, colimits and Kan extensions. These tools are then used to relate the local specification of a system and its global behavior. The extension of this formalism to non-deterministic computations is finally considered.

Alexandre Fernandez

Attaché Temporaire d’Enseignement et de Recherche (ATER) in Computer Science

Alexandre Fernandez completed his PhD at University Paris-Est Créteil with a thesis titled “Theory and Practice of Global Transformations”. His research focuses on rule based modeling, category theory and synchronous dynamical systems