Hybrid Transition Modes in (Tissue) P Systems

In addition to the maximally parallel transition mode used from the beginning in the area of membrane computing, many other transition modes for (tissue) P systems have been investigated since then. In this paper we consider (tissue) P systems with hybrid transition modes where each set of a partitioning of the whole set of rules may work in a different transition mode in a first level and all partitions of rules work together at a (second) level of the whole system on the current configuration in a maximally parallel way. With all partitions of noncooperative rules working in the maximally parallel mode, we obtain a characterization of Parikh sets of ET0L-languages, whereas with hybrid systems with either the partitions working in the maximally parallel as well as in the = 1-mode or with all partitions working in the = 1-mode we can simulate catalytic or purely catalytic P systems, respectively, thus obtaining computational completeness.