Asynchronous P Systems and P Systems Working in the Sequential Mode

Abstract

In the area of P systems, applying the rules in a maximally parallel way is one of the most common features of many models introduced so far. Whereas the idea of membranes as well as many operations and rules used in membrane systems have a concrete biological background, the universal clock assumed to control the parallel application of rules is unrealistic, but on the other hand relevant for many interesting theoretical results, especially when proving computational completeness and solving computationally hard problems. Based on a quite general definition of tissue P systems, we investigate several models of P systems and compare their computational power in the classic case (i.e., applying the rules in the maximally parallel mode) and in the case of applying the rules in an asynchronous way (i.e., an arbitrary number of rules may be applied in one derivation step) or in the sequential mode (i.e., exactly one rule is applied in one derivation step). Moreover, we also recall some results for (tissue) P systems working in an asynchronous or sequential mode already in the original definition. Finally, we also raise several questions for future research in this subarea of (tissue) P systems working in the asynchronous mode and (tissue) P systems working in the sequential mode.