Universal enzymatic numerical P systems with small number of enzymatic variables  

作　　者：Zhiqiang ZHANG Tingfang WU ANDrei PAUN Linqiang PAN 

机构地区：[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 [2]School of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China [3]Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Bucuresti 010014, Romania [4]Bioinformatics Department, National Institute of Research and Development for Biological Sciences, Bucharest 060031, Romania

出　　处：《Science China(Information Sciences)》2018年第9期34-45,共12页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61772214,61320106005,61033003,61472154);Innovation Scientists and Technicians Troop Construction Projects of Henan Province(Grant No.154200510012);Andrei Pǎun was supported by UEFSCDI Project Remote Forest Project(Grant No.PN-II-PTPCCA-2011-3.2-1710)

摘　　要：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.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.

关 键 词：bio-inspired computing numerical P system mobile robot membrane controller UNIVERSALITY 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] TP242[自动化与计算机技术—控制科学与工程]