Replicative - Distribution Rules in P Systems with Active Membranes

P systems (known also as membrane systems) are biologically motivated theoretical models of distributed and parallel computing. The two most interesting questions in the area are completeness (solving every solvable problem) and efficiency (solving a hard problem in feasible time). In this paper we define a general class of P systems covering some biological operations with membranes. We introduce a new operation, called replicative-distribution, into P systems with active membranes. This operation is well motivated from a biological point of view, and elegant from a mathematical point of view. It is both computationally powerful and efficient. More precisely, the P systems with active membranes using replicative-distribution rules can compute exactly what Turing machines can compute, and can solve NP-complete problems, particularly SAT, in linear time.