Abstract
We resume computational complexity aspects of several models of membrane systems, namely P systems with active membranes, P systems with proteins on membranes and tissue P systems both with membrane separation and membrane division. A sequence of common issues is studied in relation to these P system models, and 16 open problems are stated in the text.
We question the role of families of P systems and their necessity to solve computationally hard problems in polynomial time. For each P system model we focus on conditions guaranteeing the polynomial equivalence of families of P systems and Turing machines. The ability of P systems to solve NP/co-NP-complete problems in polynomial time (trading space for time) is a very popular issue. Interesting characterizations of the borderline between tractability and intractability, i.e., P/NP, have been recently shown. Similarly important, although less popular, is the relation between NP/co-NP and further classes as PP, the polynomial hierarchy PH and PSPACE. Several models of P systems has been shown to characterize the class PSPACE which itself characterizes parallel computations with an unlimited number of processors but a limited propagation of data between them.
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Sosík, P. (2014). Active Membranes, Proteins on Membranes, Tissue P Systems: Complexity-Related Issues and Challenges. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Y., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. CMC 2013. Lecture Notes in Computer Science, vol 8340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54239-8_5
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