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SCIENCE CHINA Information Sciences, Volume 61, Issue 9: 092103(2018) https://doi.org/10.1007/s11432-017-9103-5

Universal enzymatic numerical P systems with small number of enzymatic variables

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  • ReceivedJan 26, 2017
  • AcceptedApr 20, 2017
  • PublishedNov 20, 2017

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.


Acknowledgment

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 Pu 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 Argec s, Romania, in the fall of 2015.


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