Constant-Space P Systems with Active Membranes

We continue the investigation of the computational power of space- constrained P systems. We show that only a constant amount of space is needed in order to simulate a polynomial-space bounded Turing machine. Due to this result, we propose an alternative de nition of space complexity for P systems, where the amount of information contained in individual objects and membrane labels is also taken into ac- count. Finally, we prove that, when less than a logarithmic number of membrane labels is available, moving the input objects around the membrane structure without rewriting them is not enough to even distinguish inputs of the same length.