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Small networks of polarized splicing processors are universal

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Abstract

In this paper, we consider the computational power of a new variant of networks of splicing processors in which each processor as well as the data navigating throughout the network are now considered to be polarized. While the polarization of every processor is predefined (negative, neutral, positive), the polarization of data is dynamically computed by means of a valuation mapping. Consequently, the protocol of communication is naturally defined by means of this polarization. We show that networks of polarized splicing processors (NPSP) of size 2 are computationally complete, which immediately settles the question of designing computationally complete NPSPs of minimal size. With two more nodes we can simulate every nondeterministic Turing machine without increasing the time complexity. Particularly, we prove that NPSP of size 4 can accept all languages in NP in polynomial time. Furthermore, another computational model that is universal, namely the 2-tag system, can be simulated by NPSP of size 3 preserving the time complexity. All these results can be obtained with NPSPs with valuations in the set \(\{-1,0,1\}\) as well. We finally show that Turing machines can simulate a variant of NPSPs and discuss the time complexity of this simulation.

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Acknowledgements

A preliminary version of this work has been presented at TPNC 2017 and has been published in Theory and Practice of Natural Computing–6th International Conference, TPNC 2017, LNCS 10687, pp. 165–177. This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, project number POC P-37-257. Victor Mitrana has also been supported by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Department of Computer Science, University of Potsdam, August-Bebel-Str. 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania

    Victor Mitrana, Maria C. Negru & Andrei Păun

  3. Bioinformatics Department, National Institute for R&D for Biological Sciences, Bucharest, 060031, Romania

    Victor Mitrana, Andrei Păun & Mihaela Păun

  4. Faculty of Administration and Business, University of Bucharest, Queen Elizabeth Bd. 4 - 12, Bucharest, Romania

    Mihaela Păun

Authors
  1. Henning Bordihn
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  2. Victor Mitrana
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  3. Maria C. Negru
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  4. Andrei Păun
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  5. Mihaela Păun
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Correspondence to Victor Mitrana.

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Bordihn, H., Mitrana, V., Negru, M.C. et al. Small networks of polarized splicing processors are universal. Nat Comput 17, 799–809 (2018). https://doi.org/10.1007/s11047-018-9691-0

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