How derivation modes and halting conditions may influence the computational power of P systems

Abstract

In the area of P systems, besides the standard maximally parallel derivation mode, many other derivation modes have been investigated, too. In this overview paper, many variants of hierarchical P systems using different derivation modes are considered and the effects of using different derivation modes, especially the maximally parallel derivation modes and the maximally parallel set derivation modes, on the generative and accepting power are illustrated. Moreover, an overview on some control mechanisms used for P systems is given. Furthermore, besides the standard total halting, we also consider different halting conditions such as unconditional halting and partial halting and explain how the use of different halting conditions may considerably change the computing power of P systems.