A Linear Solution for Subset Sum Problem with Tissue P Systems with Cell Division

Abstract

Tissue P systems are a computing model in the framework of Membrane Computing where the tree-like membrane structure is replaced by a general graph. Recently, it has been shown that endowing these P systems with cell division, NP-complete problems can be solved in polynomial time. In this paper we present a solution to the Subset Sum problem via a family of such devices, and we also include the formal verification of such solution. This is the first solution to a numerical NP-complete problem by using tissue P systems with cell division.