Sequential P Systems with Regular Control

In this article we introduce the regulating mechanism of control languages for the application of rules assigned to the membranes of a sequential P system and the variant of time-varying sets of rules available at different transition steps. Computational completeness can only be achieved when allowing the system to have no rules applicable for a bounded number of steps; in this case we only need one membrane and periodically available sets of non-cooperative rules, i.e., time-varying sequential P systems. On the other hand, even with an arbitrary number of membranes and regular control languages, only Parikh sets of matrix languages can be obtained if the terminal result has to be taken as soon as the system cannot apply any rule anymore.

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