Generating the n-tuples of Natural Numbers by Enzymatic Numerical P System

Numerical P systems (NP systems) are a class of computing models inspired by both the cell structure and economics. Enzymatic numerical P systems (ENP systems) are a variant of NP systems, which were successfully applied in autonomous robot control. In this work, we design an algorithm using enzymatic numerical P systems to generate all the n-tuples of natural numbers in a well specified order. Specifically, we improve previously known results on generating all the n-tuples of natural numbers. Based on this method, we prove that a numerical P system with one membrane, and the production function used with polynomials of degree 1 with at most 2 variables can reach universality, which optimizes the previous known results. The results also give a positive answer to a problem formulated in [Fundamenta Informaticae, 2006, 73(1): 213-227].