(Tissue) P systems working in the k-restricted minimally or maximally parallel transition mode

We investigate variants of the maximally and the minimally parallel transition mode, i.e., we allow only a bounded number of rules to be taken from every set of the partitioning of the whole set of rules. The 1-restricted minimally parallel transition mode especially fits to describe the way transitions take place in spiking neural P systems without delays, i.e., in every neuron where a rule is applicable exactly one rule has to be applied. Moreover, purely catalytic P systems working in the maximally parallel transition mode can be described as P systems using the corresponding rules without catalysts, i.e., noncooperative rules, when working in the 1-restricted minimally parallel transition mode. In contrast to these results for computationally complete models of P systems, with the k-restricted maximally parallel transition mode noncooperative rules only allow for the generation of semi-linear sets.