We further investigate the computing power of the recently introduced P systems with Z-multisets (also known as hybrid sets) as generative devices. These systems apply catalytic rules in the maximally parallel way, even consuming absent non-catalysts, thus effectively generating vectors of arbitrary (not just non-negative) integers. The rules may only be made inapplicable by dissolution rules. However, this releases the catalysts into the immediately outer region, where new rules might become applicable to them. We discuss the generative power of this model. Finally, we consider the variant with mobile catalysts.
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