Abstract
In the framework of P systems, it is known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP-complete problems. Nonetheless, it could be sufficient to create an exponential number of membranes in polynomial time. Working with P systems whose membrane structure does not increase in size, it is known that it is not possible to solve computationally hard problems (unless P = NP), basically due to the impossibility of constructing exponential number of membranes, in polynomial time, using only evolution, communication and dissolution rules. In this paper we show how a family of recognizer tissue P systems with symport/antiport rules which solves a decision problem can be efficiently simulated by a family of basic recognizer P systems solving the same problem. This simulation allows us to transfer the result about the limitations in computational power, from the model of basic cell-like P systems to this kind of tissue-like P systems.
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Notes
An informal overview can be found in Păun and Pérez-Jiménez (2003) and further bibliography at P system http://ppage.psystems.eu/.
This method of communication for P systems was introduced in Păun and Păun (2002).
References
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Acknowledgements
The authors acknowledge the support of the project TIN2006-13425 of the Ministerio de Educación y Ciencia of Spain, cofinanced by FEDER funds, and the support of the project of excellence TIC-581 of the Junta de Andalucía.
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Díaz-Pernil, D., Pérez-Jiménez, M.J. & Romero-Jiménez, Á. Efficient simulation of tissue-like P systems by transition cell-like P systems. Nat Comput 8, 797–806 (2009). https://doi.org/10.1007/s11047-008-9102-z
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DOI: https://doi.org/10.1007/s11047-008-9102-z