(Tissue) P Systems with Decaying Objects

Objects generated in P systems usually are assumed to survive as long as the computation goes on. In this paper, decaying objects are considered, i.e., objects only surviving a bounded number of computation steps. Variants of (tissue) P systems with decaying objects working in transition modes where the number of rules applied in each computation step is bounded, are shown to be very restricted in their generative power, i.e., if the results are collected in a specified output cell/membrane, then only finite sets of multisets can be generated, and if the results are specified by the objects sent out into the environment, we obtain the regular sets. Only if the decaying objects are regenerated within a certain period of computation steps, i.e., if we allow an unbounded number of rules to be applied, then computational completeness can be obtained, yet eventually more ingredients are needed for the rules than in the case of non-decaying objects, e.g., permitting and/or forbidden contexts. As special variants of P systems, catalytic P systems, P systems using cooperative rules, and spiking neural P systems are investigated.