Universal enzymatic numerical P systems with small number of enzymatic variables

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.

[1]  M. Angels Colomer,et al.  Using a bioinspired model to determine the extinction risk of Calotriton asper populations as a result of an increase in extreme rainfall in a scenario of climatic change , 2014 .

[2]  Oscar H. Ibarra,et al.  On spiking neural P systems , 2006, Natural Computing.

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

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

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

[6]  Miguel Ángel Gutiérrez Naranjo,et al.  The Pole Balancing Problem with Enzymatic Numerical P Systems , 2015 .

[7]  Radu Nicolescu,et al.  P systems and the Byzantine agreement , 2010, J. Log. Algebraic Methods Program..

[8]  Ferrante Neri,et al.  An Optimization Spiking Neural P System for Approximately Solving Combinatorial Optimization Problems , 2014, Int. J. Neural Syst..

[9]  Gheorghe Paun,et al.  Computing with Membranes , 2000, J. Comput. Syst. Sci..

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

[11]  Antoni Margalida,et al.  Modelling the effects of sanitary policies on European vulture conservation , 2012, Scientific Reports.

[12]  Richard S. Sutton,et al.  Neural networks for control , 1990 .

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

[14]  Artiom Alhazov,et al.  Static Sorting P Systems , 2006, Applications of Membrane Computing.

[15]  Gemma Bel Enguix.  Unstable P Systems: Applications to Linguistics , 2004, Workshop on Membrane Computing.

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

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

[18]  Giancarlo Mauri,et al.  Improved Universality Results for Parallel Enzymatic Numerical P Systems , 2013, Int. J. Unconv. Comput..

[19]  Gheorghe Paun,et al.  The Oxford Handbook of Membrane Computing , 2010 .

[20]  Taishin Yasunobu Nishida,et al.  Membrane Algorithms: Approximate Algorithms for NP-Complete Optimization Problems , 2006, Applications of Membrane Computing.

[21]  Gabriel Ciobanu,et al.  Applications of Membrane Computing , 2006, Applications of Membrane Computing.

[22]  Tao Jiang,et al.  Design and implementation of membrane controllers for trajectory tracking of nonholonomic wheeled mobile robots , 2015, Integr. Comput. Aided Eng..

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

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

[25]  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).

[26]  Andrei Paun,et al.  Numerical P systems with migrating variables , 2016, Theor. Comput. Sci..

[27]  Florent Jacquemard,et al.  An Analysis of a Public Key Protocol with Membranes , 2006, Applications of Membrane Computing.

[28]  Ursula Dresdner,et al.  Computation Finite And Infinite Machines , 2016 .

[29]  Eduardo D. Sontag,et al.  Neural Networks for Control , 1993 .

[30]  Grzegorz Rozenberg,et al.  Handbook of Natural Computing , 2011, Springer Berlin Heidelberg.

[31]  Mario de Jesús Pérez Jiménez,et al.  Simulating Large-Scale ENPS Models by Means of GPU , 2012 .

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

[33]  Pierluigi Frisco,et al.  Applications of Membrane Computing in Systems and Synthetic Biology , 2014 .

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