Science China Information Sciences

, 61:092103 | Cite as

Universal enzymatic numerical P systems with small number of enzymatic variables

  • Zhiqiang Zhang
  • Tingfang Wu
  • Andrei Păun
  • Linqiang Pan
Research Paper


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.


bio-inspired computing numerical P system mobile robot membrane controller universality 



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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Zhiqiang Zhang
    • 1
  • Tingfang Wu
    • 1
  • Andrei Păun
    • 3
    • 4
  • Linqiang Pan
    • 1
    • 2
  1. 1.Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of AutomationHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of Electric and Information EngineeringZhengzhou University of Light IndustryZhengzhouChina
  3. 3.Department of Computer Science, Faculty of Mathematics and Computer ScienceUniversity of BucharestBucurestiRomania
  4. 4.Bioinformatics DepartmentNational Institute of Research and Development for Biological SciencesBucharestRomania

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