Genetic Systems without Inhibition Rules

Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein) is produced when all activator objects are available in the system, and no inhibitor object is present. Activators are not consumed by the application of such a rule. Objects disappear because of degradation: each object is equipped with a lifetime, and the object decays when such a lifetime expires. It is known that such systems are Turing powerful, either when we consider interleaving semantics (a single action is executed in each computational step) as well as if we consider maximal parallel semantics (all the rules that can be applied at a computational step must be applied). In this paper we investigate the power of inhibiting rules. © 2009 Springer-Verlag Berlin Heidelberg.