State space properties of Boolean networks trained for sequence tasks

In a recent work, it has been shown that Boolean networks (BN), a well-known genetic regulatory network model, can be utilised to control robots. In this work, we use a genetic algorithm to train robots controlled by a BN so as to accomplish a sequence learning task. We analyse the robots' dynamics by studying the corresponding BNs' phase space. Our results show that a phase space structure emerges enabling the robot to have memory of the past and to exploit this piece of information to choose the next action to perform. This finding is in accordance with previous results on minimally cognitive behaviours and shows that the phase space of Boolean networks can be shaped by the learning process in such a way that the robot can accomplish non-trivial tasks requiring the use of memory.