Numerical P systems with production thresholds

Abstract Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired both from the structure of living cells and from the economic reality, where the values of variables evolve by programs that are composed by production functions and repartition protocols: the value of a production function is distributed to variables according to the corresponding repartition protocol. In this work, we introduce a new method of using evolution programs into NP systems, where thresholds are associated with production functions. The computation power of NP systems with production thresholds is investigated. Specifically, we prove that NP systems with lower-thresholds (the production function value can be distributed only when it is not smaller than a given constant), with one membrane working both in the all-parallel mode and in the sequential mode, are universal. The universal results of NP systems with lower-thresholds are extended to NP systems with upper-thresholds (the production function value can be distributed only when it is not greater than a given constant) by simulating the former with the latter. These universality results show that NP systems with production thresholds have the potential to implement any computer program or robot behavior.

[1]  Catalin Buiu,et al.  Enzymatic numerical P systems - a new class of membrane computing systems , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[2]  Linqiang Pan,et al.  Numerical P Systems with Thresholds , 2016, Int. J. Comput. Commun. Control.

[3]  Andrei Paun,et al.  On the Universality of Axon P Systems , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Alberto Leporati,et al.  Improving Universality Results on Parallel Enzymatic Numerical P Systems , 2013 .

[5]  Hong Peng,et al.  Fuzzy reasoning spiking neural P system for fault diagnosis , 2013, Inf. Sci..

[6]  Xiangxiang Zeng,et al.  Weighted Spiking Neural P Systems with Rules on Synapses , 2014, Fundam. Informaticae.

[7]  Linqiang Pan,et al.  The computational power of enzymatic numerical P systems working in the sequential mode , 2018, Theor. Comput. Sci..

[8]  Catalin Buiu,et al.  Using enzymatic numerical P systems for modeling mobile robot controllers , 2011, Natural Computing.

[9]  Marvin Minsky,et al.  Computation : finite and infinite machines , 2016 .

[10]  Xiangxiang Zeng,et al.  Performing Four Basic Arithmetic Operations With Spiking Neural P Systems , 2012, IEEE Transactions on NanoBioscience.

[11]  Ioan Dumitrache,et al.  Implementing Obstacle Avoidance and Follower Behaviors on Koala Robots Using Numerical P Systems , 2012 .

[12]  Linqiang Pan,et al.  On the Universality and Non-Universality of Spiking Neural P Systems With Rules on Synapses , 2015, IEEE Transactions on NanoBioscience.

[13]  Ioan Dumitrache,et al.  Robot Localization Implemented with Enzymatic Numerical P Systems , 2012, Living Machines.

[14]  Gheorghe Paun.  Some Open Problems about Numerical P Systems , 2013 .

[15]  Linqiang Pan,et al.  Spiking Neural P Systems With Rules on Synapses Working in Maximum Spikes Consumption Strategy , 2015, IEEE Transactions on NanoBioscience.

[16]  Haina Rong,et al.  Automatic Design of Deterministic and Non-Halting Membrane Systems by Tuning Syntactical Ingredients , 2014, IEEE Transactions on NanoBioscience.

[17]  Gheorghe Păun,et al.  Spiking Neural P Systems with Weights , 2010, Neural Computation.

[18]  L. Pan,et al.  Normal Forms of Spiking Neural P Systems With Anti-Spikes , 2012, IEEE Transactions on NanoBioscience.

[19]  Gheorghe Paun,et al.  On the power of enzymatic numerical P systems , 2012, Acta Informatica.

[20]  Gheorghe Paun,et al.  Membrane Computing and Economics: Numerical P Systems , 2006, Fundam. Informaticae.

[21]  Xiangrong Liu,et al.  Implementation of Arithmetic Operations With Time-Free Spiking Neural P Systems , 2015, IEEE Transactions on NanoBioscience.

[22]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[23]  Zhengyou He,et al.  Fault Diagnosis of Electric Power Systems Based on Fuzzy Reasoning Spiking Neural P Systems , 2015, IEEE Transactions on Power Systems.

[24]  Ioan Dumitrache,et al.  Membrane Computing in Robotics , 2013 .

[25]  Xiangxiang Zeng,et al.  Homogeneous Spiking Neural P Systems , 2009, Fundam. Informaticae.

[26]  Xiangxiang Zeng,et al.  Spiking Neural P Systems with Thresholds , 2014, Neural Computation.

[27]  Gabriel Ciobanu,et al.  P systems with minimal parallelism , 2007, Theor. Comput. Sci..

[28]  Catalin Buiu,et al.  A software tool for modeling and simulation of numerical P systems , 2011, Biosyst..

[29]  Hong Peng,et al.  Membrane computing model for IIR filter design , 2016, Inf. Sci..

[30]  Catalin Buiu,et al.  Development of membrane controllers for mobile robots , 2012, Inf. Sci..

[31]  Linqiang Pan,et al.  Normal Forms for Some Classes of Sequential Spiking Neural P Systems , 2013, IEEE Transactions on NanoBioscience.

[32]  Giancarlo Mauri,et al.  Enzymatic Numerical P Systems Using Elementary Arithmetic Operations , 2013, Int. Conf. on Membrane Computing.

[33]  L. Pan,et al.  Spiking Neural P Systems With Rules on Synapses Working in Maximum Spiking Strategy , 2015 .

[34]  Ioan Dumitrache,et al.  Universality of Enzymatic Numerical P systems , 2013, Int. J. Comput. Math..