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P systems attacking hard problems beyond NP: a survey

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Abstract

In the field of membrane computing, a great attention is traditionally paid to the results demonstrating a theoretical possibility to solve NP-complete problems in polynomial time by means of various models of P systems. A bit less common is the fact that almost all models of P systems with this capability are actually stronger: some of them are able to solve PSPACE-complete problems in polynomial time, while others have been recently shown to characterize the class \(\mathbf {P^{\#P}}\) (which is conjectured to be strictly included in PSPACE). A large part of these results has appeared quite recently. In this survey, we focus on strong models of membrane systems which have the potential to solve hard problems belonging to classes containing NP. These include P systems with active membranes, P systems with proteins on membranes and tissue P systems, as well as P systems with symport/antiport and membrane division and, finally, spiking neural P systems. We provide a survey of computational complexity results of these membrane models, pointing out some features providing them with their computational strength. We also mention a sequence of open problems related to these topics.

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Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports Of the Czech Republic from the National Programme of Sustainability (NPU II) project IT4Innovations Excellence in Science—LQ1602, and by the Silesian University in Opava under the Student Funding Scheme, project SGS/11/2019.

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  1. Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601, Opava, Czech Republic

    Petr Sosík

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Sosík, P. P systems attacking hard problems beyond NP: a survey. J Membr Comput 1, 198–208 (2019). https://doi.org/10.1007/s41965-019-00017-y

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