Cell-like spiking neural P systems with evolution rules

Cell-like spiking neural P systems (abbreviated as cSN P systems) are a class of distributed and parallel computation devices which combine a hierarchical arrangement of membranes in rewriting P systems and evolution rules in spiking neural P systems. The existing results show that cSN P systems are Turing universal with replication target indication or general spiking rules that produce more spikes than the ones consumed. However, with neither the replication target indication nor general spiking rules, cSN P systems can only compute finite set of numbers. In this work, we introduce evolution rules into cSN P systems to compensate the loss of computation power, the application of which depends on the contents of a region. With an evolution rule, every copy of spike evolves to a designate multiset over one kind of objects. We prove that cSN P systems with evolution rules are computationally universal in the case of using traditional spiking rules while avoiding the replication target indication. We also investigate the influence of the target indications on the computation power of cSN P systems with evolution rules. The results show that removing some target indications has no influence on computation power but a corresponding increase in the number of membranes. Besides, the results give a solution to the open problem that seeks alternative methods for the replication of spikes in a cSN P system.