Complexity classes for membrane systems: A survey

The computational power of membrane systems, in their different variants, can be studied by defining classes of problems that can be solved within given bounds on computation time or space, and comparing them with usual computational complexity classes related to the Turing Machine model. Here we will consider in particular membrane systems with active membranes (where new membranes can be created by division of existing membranes). The problems related to the definition of time/space complexity classes for membrane systems will be discussed, and the resulting hierarchy will be compared with the usual hierarchy of complexity classes, mainly through simulations of Turing Machines by (uniform families of) membrane systems with active membranes.