Section: New Results

Cellular automata as a model of computation

Participant : Nazim Fatès.

The density classification problem is a simple computational problem where a distributed system composed of many cells need to find the majority state in its initial configuration. It is known that no deterministic cellular automaton can solve this problem without making errors. On the other hand, it was shown that a probabilistic mixture of the traffic rule and the majority rule solves the one-dimensional problem correctly with a probability arbitrarily close to one. We investigated the possibility of a similar approach in two dimensions and introduced a companion problem, the particle spacing problem, as an intermediary step. We showed that although this second problem does not have a cellular automaton solution, the use of randomized frameworks, via interacting particle systems, could allow us to have interesting solutions, which were analysed with a theoretical approach and with numerical simulations [18].

In the same direction of research, we studied how to coordinate a team of agents to locate a hidden source on a two-dimensional discrete grid. The challenge here is to find the position of the source with only sporadic detections. This problem arises in various situations, for instance when insects emit pheromones to attract their partners. A search mechanism named infotaxis was previously proposed to explain how agents may progressively approach the source by using only intermittent detections.

We studied the problem of doing a collective infotaxis search with agents that are almost memoryless. We presented a bio-inspired model which mixes stochastic cellular automata and reactive multi-agent systems. The model, inspired by the behaviour of the social amoeba Dictyostelium discoideum, relies on the use of reaction-diffusion waves to guide the agents to the source. The random emissions of waves allows the formation of a group of amoebae, which successively act as emitters of waves or listeners, according to their local perceptions. Our worked showed that the model is worth considering and may provide a simple solution to coordinate a team to perform a distributed form of infotaxis [17].