Abstract
A recently introduced variant of P-systems considers membranes which can multiply by division. These systems use two types of division: division for elementary membranes (Le. membranes not containing other membranes inside) and division for non-elementary membranes. In two recent papers it is shown how to solve the Satisfiability problem and the Hamiltonian Path problem (two well known NP complete problems) in linear time with respect to the input length, using both types of division. We show in this paper that P-systems with only division for elementary membranes suffice to solve these two problems in linear time. Is it possible to solve NP complete problems in polynomial time using P-systems without membrane division? We show, moreover, that (if P ≠ NP) deterministic P-systems without membrane division are not able to solve NP complete problems in polynomial time.
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