Introducing variables in the evolution rules of P systems

Abstract

In membrane systems evolution rules are constructed using only objects from a finite alphabet. In this paper we investigate rules in which variables are used. Namely, we define Variable P systems in which the rules containing variables need to be instantiated at the start of each computational step with values from some predefined sets of sets of objects.

The modelling power of variable P systems is described by simulating some basic arithmetic operations over a (multi)set of positive numbers (addition, multiplication, or a combination of them). The main advantage of using variable P systems consists in the small number of used rules regardless how many numbers are involved in the operation: e.g., the addition requires only 3 rules, while the multiplication only 27 rules.