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Universal enzymatic numerical P systems with small number of enzymatic variables

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Abstract

Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired from the structure of living cells and economics. Enzymatic numerical P systems (for short, ENP systems) are a variant of NP systems, which have been successfully applied in designing and implementing controllers for mobile robots. Since ENP systems were proved to be Turing universal, there has been much work to simplify the universal systems, where the complexity parameters considered are the number of membranes, the degrees of polynomial production functions or the number of variables used in the systems. Yet the number of enzymatic variables, which is essential for ENP systems to reach universality, has not been investigated. Here we consider the problem of searching for the smallest number of enzymatic variables needed for universal ENP systems. We prove that for ENP systems as number acceptors working in the all-parallel or one-parallel mode, one enzymatic variable is sufficient to reach universality; while for the one-parallel ENP systems as number generators, two enzymatic variables are sufficient to reach universality. These results improve the best known results that the numbers of enzymatic variables are 13 and 52 for the all-parallel and one-parallel systems, respectively.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61772214, 61320106005, 61033003, 61472154) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province (Grant No. 154200510012). The work of Andrei P˘aun was supported by UEFSCDI Project RemoteForest Project (Grant No. PN-II-PTPCCA-2011-3.2-1710). This paper was written during a three-months stay of Zhiqiang Zhang and Tingfang Wu in Curtea de Arge¸s, Romania, in the fall of 2015.

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Authors and Affiliations

  1. Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhiqiang Zhang, Tingfang Wu & Linqiang Pan

  2. School of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Linqiang Pan

  3. Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Bucuresti, 010014, Romania

    Andrei Păun

  4. Bioinformatics Department, National Institute of Research and Development for Biological Sciences, Bucharest, 060031, Romania

    Andrei Păun

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  1. Zhiqiang Zhang
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  2. Tingfang Wu
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  3. Andrei Păun
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  4. Linqiang Pan
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Correspondence to Linqiang Pan.

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Zhang, Z., Wu, T., Păun, A. et al. Universal enzymatic numerical P systems with small number of enzymatic variables. Sci. China Inf. Sci. 61, 092103 (2018). https://doi.org/10.1007/s11432-017-9103-5

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  • DOI: https://doi.org/10.1007/s11432-017-9103-5

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