Random Boolean networks (RBN) and Cellular Automata (CA) operate in a very similar way. They update their state with simple deterministic functions called Boolean function or Transition Table (TT), both being essentially the same mechanism under different names. This paper applies a concept most known from CA called Minimum Equivalence (ME). ME is applied to RBN and shows how to calculate the number of unique computations for a given number of neighbours. Crucially, it is shown how RBN rules are even more equivalent than in CA, how the set can be reduced into even fewer unique rules, and how the concept becomes more relevant with larger neighbourhoods. For example, switching transformation alone reduces the number of unique rules in RBN with 4 neighbours from 65 536 to only 3 984 (6.1%) rules. Additionally, this paper examines the ME and transformations in substrates beyond Elementary CA (ECA), such as CA with additional spatial dimensions and number of states.

The human brain is a remarkable computing machine, i.e. vastly parallel, self-organizing, robust, and energy efficient. To gain a better understanding into how the brain works, a cyborg (cybernetic organism, a combination of machine and living tissue) is currently being made in an interdisciplinary effort, known as the Cyborg project. In this paper we describe how living cultures of neurons (biological neural networks) are successfully grown in-vitro over Micro-Electrode Arrays (MEAs), which allow them to be interfaced to a robotic body through electrical stimulation and neural recordings. Furthermore, we describe the bio- and nano-technological procedures utilized for the culture of such dissociated neural networks and the interface software and hardware framework used for creating a closed-loop hybrid neuro-system. A Reservoir Computing (RC) approach is used to harness the computational power of the neuronal culture.