Limits on P Systems with Proteins and Without Division

In the field of Membrane Computing, computational complexity theory has been widely studied trying to find frontiers of efficiency by means of syntactic or semantical ingredients. The objective of this is to find two kinds of systems, one non-efficient and another one, at least, presumably efficient, that is, that can solve NP-complete problems in polynomial time, and adapt a solution of such a problem in the former. If it is possible, then P = NP. Several borderlines have been defined, and new characterizations of different types of membrane systems have been published. In this work, a certain type of P system, where proteins act as a supporting element for a rule to be fired, is studied. In particular, while division rules, the abstraction of cellular mitosis is forbidden, only problems from class P can be solved, in contrast to the result obtained allowing them.

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