Computational Complexity Theory in Membrane Computing: Seventeen Years After

In this work we revisit the basic concepts, definitions of computational complexity theory in membrane computing. The paper also discusses a novel methodology to tackle the P versus NP problem in the context of the aforementioned theory. The methodology is illustrated with a collection of frontiers of tractability for several classes of P systems.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

The efficiency of tissue P systems with cell separation relies on the environment

The classical definition of tissue P systems includes a distinguished alphabet with the special assumption that its elements are available in an arbitrarily large amount of copies. These objects are shared in a distinguished place of the system, called the environment. This ability of having infinitely many copies of some objects has been widely exploited in the design of efficient solutions to computationally hard problems by means of tissue P systems. This paper deals with computational aspects of tissue P systems with cell separation where there is no such environment as described above. The main result is that only tractable problems can be efficiently solved by using this kind of P systems. Bearing in mind that NP–complete problems can be efficiently solved by using tissue P systems without environment and with cell division, we deduce that in the framework of tissue P systems without environment, the kind of rules (separation versus division) provides a new frontier of the tractability of decision problems.Peer ReviewedPostprint (published version