New applications for an old tool

Abstract

First, the dependency graph technique, not so far from its current application, was developed trying to nd the shortest computations for membrane systems solving instances of SAT. Certain families of membrane systems have been demonstrated to be non-effcient by means of the reduction of nding an accepting computation (respectively, rejecting computation) to the problem of reaching from a node of the dependency graph to another one. In this paper, a novel application to this technique is explained. Supposing that a problem can be solved by means of a kind of membrane systems leads to a contradiction by means of using the dependency graph as a reasoning method. In this case, it is demonstrated that a single system without dissolution, polarizations and cooperation cannot distinguish a single object from more than one object. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.