CANA : Natural Computation
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Natural computation is a field of computer science. It is based on the links between informatics and other disciplines, mainly physics and biology. On the one hand, it aims at abstracting natural phenomena in order to develop new computational paradigms, or deepening the study of well-known nature-inspired models of computation. On the other hand, it aims at using these models of computation in order to achieve a better understanding of the phenomena at hand, with the hope to unravel some of the underlying fundamental laws.
The CANA research group (CANA is for “CAlcul NAturel”, a French acronym for natural computation), in particular, seeks to capture at the formal level some of the fundamental paradigms of theoretical biology and physics, via the models and approaches of theoretical computer science and discrete mathematics. These approaches and their underlying methods, that we develop also per se, rest on the study of interacting entities. Most often in the models that we study, each of the constitutive entities is elementary and can only take a finite number of states. Moreover, they interact only locally with respect to the network on which they lie in discrete time steps. In spite of their apparent simplicity, these discrete models are able to capture the essence of the dynamics of numerous natural systems, upon which they shed a new light. For instance, thanks to their high level of abstraction, these models provide a qualitative representation of biological regulation networks, of particle propagation in quantum physics, or even of the emergence of waves in sandpiles. Beyond their ability to grasp natural phenomena, the models are also being studied for their own sake, in terms of their intrinsic dynamical, computability and complexity properties.
To define nature-inspired discrete models; to demonstrate their relevance; to tame the complex behaviours that they generate by means of rigorous mathematical results; to use this to better understand real systems: these are the main concerns of CANA research team.
Depending on the situation, the important features of the model can be of static (syntactic) or dynamical (semantic) nature. Moreover, the network of entities may be regular or not, the interaction rules may be deterministic, probabilistic, synchronous or asynchronous… We study these models and their variations both for their representational and computational abilities.
The methods used come from discrete dynamical system theory, combinatorics, complexity and computability theories, and non-monotonic logic, linear algebra, and quantum information.