> As a model for computation, P systems offer the attractive possibility of solving NP-complete problems in less-than exponential time. Some P system variants are known to be capable of solving the SAT (boolean satisfiability) problem in linear time and, owing to all NP-complete problems being equivalent, this capability then applies to all such problems. As there is no current method of directly implementing a P system in its own right, their functionality is instead emulated and therefore solving NP-complete problems in linear time remains theoretical. However, it has also been proven that any deterministic P system may be simulated on a Turing Machine in polynomial time.

https://en.wikipedia.org/wiki/P_system

This is not as interesting as it sounds, since you're just trading exponential time for exponential space. It's still not practical or very interesting.