Section: New Results

Cellular automata with stochastic evolutions

• Participants: Nazim Fatès, Irène Marcovici

In order to explore the computing abilities of simple stochastic cellular automata, we tackle the case of Alesia, a two-player zero-sum game which is quite similar to the rock-paper-scissors game. In this game, two players simultaneously move and do not know what the opponent plays at a given round. The simultaneity of the moves implies that there is no deterministic good strategy in this game, otherwise one would anticipate the moves of the opponent and easily win the game. We explored how to build a family of one-dimensional stochastic cellular automata to play this game by progressively increasing the complexity of the transitions. We showed the possibility to construct a family of rules with interesting results, including good performance when confronted to the Nash-equilibrium strategy [14].

The reversibility of classical cellular automata (CA) was examined for the case where the updates of the system are random. In this context, with B. Sethi and S. Das (IIT Karaghpur, India), we studied a particular form of reversibility: the possibility of returning infinitely often to the initial condition after a random number of time steps. This is the recurrence property of the system. We analyzed this property for the simple rules and described the communication graph of the system [21].

We also contributed to the diffusion of some already-established knowledge on the simulation of complex systems in Biology, more precisely in the case of the formation of swarms [19] and in the case of asynchronous cellular automata [20].