A new perspective on computational complexity theory in Membrane Computing

A single Turing machine can solve decision problems with an in nite number of instances. On the other hand, in the framework of membrane computing, a \solution" to an abstract decision problem consists of a family of membrane systems (where each system of the family is associated with a nite set of instances of the problem to be solved). An interesting question is to analyze the possibility to nd a single membrane system able to deal with the in nitely many instances of a decision problem. In this context, it is fundamental to de ne precisely how the instances of the problem are introduced into the system. In this paper, two different methods are considered: pre-computed (in polynomial time) resources and non-treated resources. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.