McCulloch-Pitts Brains and Pseudorandom Functions

In a pioneering classic, Warren McCulloch and Walter Pitts proposed a model of the central nervous system. Motivated by EEG recordings of normal brain activity, Chvátal and Goldsmith asked whether these dynamical systems can be engineered to produce trajectories that are irregular, disorderly, and apparently unpredictable. We show that they cannot build weak pseudorandom functions.