Membrane Models of Biological Systems

rewriting systems on multisets (ARMS) are a simple construct in the context of Computational living systems, constituting a class of P systems that have been devised for modelling systems dynamics, with the belief that [177]: Environment + Computational living systems = Computation in agreement with the vision of living beings as computing entities whose computation purpose is keeping themselves alive. The model itself in its basic formulation is composed of a multiset of objects and a set of rewriting rules, while its intuitive meaning can be traced back to the study of abstract chemical machines [24]. As in classic P systems, the multiset of objects models the population of chemicals present into the system while rewriting rules are an abstraction of biochemical reactions. This is consistent with the idea of employing multisets as a representation formalism for undistinguishable floating chemical molecules uniformly distributed and randomly moving in a common environment. Rewriting rules model biochemical reactions between elements of the multiset defining the state of the system at each instant. A rewriting rule r over an alphabet A is a pair r = (α, β) where α, β ∈ A∗, it is denoted as α → β and its meaning is that α is replaced by β. Strings are a representation of multisets, thereby rewriting rules specified in this way can be thought as rewriting rules on multisets, but often strings α and β are substrings of the string representing the multiset encoding the state of the system. Following the terminology of [178], an ARMS is defined as a pair: