A Survey of Nature-Inspired Computing

Nature-inspired computing is a type of human-designed computing motivated by nature, which is based on the employ of paradigms, mechanisms, and principles underlying natural systems. In this article, a versatile and vigorous bio-inspired branch of natural computing, named membrane computing is discussed. This computing paradigm is aroused by the internal membrane function and the structure of biological cells. We first introduce some basic concepts and formalisms of membrane computing, and then some basic types or variants of P systems (also named membrane systems) are presented. The state-of-the-art computability theory and a pioneering computational complexity theory are presented with P system frameworks and numerous solutions to hard computational problems (especially NP-complete problems) via P systems with membrane division are reported. Finally, a number of applications and open problems of P systems are briefly described.

[1]  Nivat G. Päun,et al.  Handbook of Formal Languages , 2013, Springer Berlin Heidelberg.

[2]  Ying Liu,et al.  An Adaptive Membrane Evolutionary Algorithm for Solving Constrained Engineering Optimization Problems , 2017, J. Univers. Comput. Sci..

[3]  Oscar H. Ibarra,et al.  Asynchronous spiking neural P systems , 2009, Theor. Comput. Sci..

[4]  Xianzhong Duan,et al.  A New Approach to Fault Diagnosis of Power Systems Using Fuzzy Reasoning Spiking Neural P Systems , 2013 .

[5]  Giancarlo Mauri,et al.  On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution , 2008, Fundam. Informaticae.

[6]  Rudolf Freund,et al.  Membrane Systems with Symport/Antiport Rules: Universality Results , 2002, WMC-CdeA.

[7]  Xiangxiang Zeng,et al.  Monodirectional tissue P systems with channel states , 2021, Inf. Sci..

[8]  Andrei Paun,et al.  P systems with proteins on membranes characterize PSPACE , 2013, Theor. Comput. Sci..

[9]  Pierluigi Frisco,et al.  Asynchronous P systems with active membranes , 2012, Theor. Comput. Sci..

[10]  Xiaohui Luo,et al.  Dendrite P systems , 2020, Neural Networks.

[11]  Rudolf Freund,et al.  P systems with active membranes and without polarizations , 2005, Soft Comput..

[12]  Artiom Alhazov,et al.  (Tissue) P Systems with Unit Rules and Energy Assigned to Membranes , 2006, Fundam. Informaticae.

[13]  Linqiang Pan,et al.  Flat maximal parallelism in tissue P systems with promoters , 2017 .

[14]  Petr Sosík.  The Power of Catalysts and Priorities in Membrane Systems , 2003, Grammars.

[15]  Gheorghe Păun,et al.  Tissue P Systems with Cell Division , 2008, Int. J. Comput. Commun. Control.

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

[17]  Henry N. Adorna,et al.  Spiking neural P systems with structural plasticity , 2015, Neural Computing and Applications.

[18]  Andrei Paun,et al.  Results on catalytic and evolution-communication P systems , 2009, New Generation Computing.

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

[20]  Marian Gheorghe,et al.  A Modeling Approach Based on P Systems with Bounded Parallelism , 2006, Workshop on Membrane Computing.

[21]  Mario J. Pérez-Jiménez,et al.  A Linear-Time Solution to the Knapsack Problem Using P Systems with Active Membranes , 2003, Workshop on Membrane Computing.

[22]  Andrei George Florea,et al.  Membrane Computing for Distributed Control of Robotic Swarms: Emerging Research and Opportunities , 2017 .

[23]  Andrei George Florea,et al.  Modelling multi-robot interactions using a generic controller based on numerical P systems and ROS , 2017, 2017 9th International Conference on Electronics, Computers and Artificial Intelligence (ECAI).

[24]  Hua Zhang,et al.  Multi-behaviors coordination controller design with enzymatic numerical P systems for robots , 2021, Integr. Comput. Aided Eng..

[25]  Linqiang Pan,et al.  Sequential spiking neural P systems with exhaustive use of rules , 2012, Biosyst..

[26]  Andrei Paun,et al.  Computing by Communication in Networks of Membranes , 2002, Int. J. Found. Comput. Sci..

[27]  Hong Peng,et al.  Numerical P systems with Boolean condition , 2019, Theor. Comput. Sci..

[28]  Marian Gheorghe,et al.  Computational Completeness of Tissue P Systems with Conditional Uniport , 2006, Workshop on Membrane Computing.

[29]  Artiom Alhazov,et al.  Trading polarizations for labels in P systems with active membranes , 2004, Acta Informatica.

[30]  Linqiang Pan,et al.  The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules , 2018, Complex..

[31]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..

[32]  Alfonso Rodríguez-Patón,et al.  P Systems with Active Membranes Characterize PSPACE , 2006, DNA.

[33]  Mario J. Pérez-Jiménez,et al.  Simulation of Rapidly-Exploring Random Trees in Membrane Computing with P-Lingua and Automatic Programming , 2018, Int. J. Comput. Commun. Control.

[34]  Elisabeth André,et al.  Perception and Interactive Technologies, International Tutorial and Research Workshop, PIT 2006, Kloster Irsee, Germany, June 19-21, 2006, Proceedings , 2006, PIT.

[35]  Rudolf Freund,et al.  Computationally universal P systems without priorities: two catalysts are sufficient , 2005, Theor. Comput. Sci..

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

[37]  Artiom Alhazov,et al.  Solving a PSPACE-Complete Problem by Recognizing P Systems with Restricted Active Membranes , 2003, Fundam. Informaticae.

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

[39]  Mario J. Pérez-Jiménez,et al.  A fast P system for finding a balanced 2-partition , 2005, Soft Comput..

[40]  Mario J. PÉREZ-JIMÉNEZ,et al.  Fault Diagnosis of Metro Traction Power Systems Using A Modified Fuzzy Reasoning Spiking Neural P System , 2016 .

[41]  Giancarlo Mauri,et al.  Complexity classes for membrane systems , 2006, RAIRO Theor. Informatics Appl..

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

[43]  Mario J. Pérez-Jiménez,et al.  Decision P Systems and the P!=NP Conjecture , 2002, WMC-CdeA.

[44]  Marian Gheorghe,et al.  Further results on generalised communicating P systems , 2017, Theor. Comput. Sci..

[45]  Mario J. Pérez-Jiménez,et al.  An Efficient Family of P Systems for Packing Items into Bins , 2004, J. Univers. Comput. Sci..

[46]  Mihai Ionescu,et al.  Replicative - Distribution Rules in P Systems with Active Membranes , 2004, ICTAC.

[47]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[48]  Henry N. Adorna,et al.  On simulating cooperative transition P systems in evolution–communication P systems with energy , 2016, Natural Computing.

[49]  Marian Gheorghe,et al.  A membrane algorithm with quantum-inspired subalgorithms and its application to image processing , 2012, Natural Computing.

[50]  Marian Gheorghe,et al.  Real-life Applications with Membrane Computing , 2017 .

[51]  Linqiang Pan,et al.  Computational efficiency and universality of timed P systems with active membranes , 2015, Theor. Comput. Sci..

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

[53]  Andrei Paun,et al.  On Flip-Flop Membrane Systems with Proteins , 2007, Workshop on Membrane Computing.

[54]  Artiom Alhazov,et al.  Towards a Characterization of P Systems with Minimal Symport/Antiport and Two Membranes , 2006, Workshop on Membrane Computing.

[55]  Linqiang Pan,et al.  Cell-like spiking neural P systems , 2016, Theor. Comput. Sci..

[56]  Linqiang Pan,et al.  The computational power of tissue-like P systems with promoters , 2016, Theor. Comput. Sci..

[57]  Daniel Díaz-Pernil,et al.  A uniform family of tissue P systems with protein on cells solving 3-coloring in linear time , 2016, Natural Computing.

[58]  Peng Shi,et al.  Fault Diagnosis of Power Systems Using Intuitionistic Fuzzy Spiking Neural P Systems , 2018, IEEE Transactions on Smart Grid.

[59]  Christopher G. Langton,et al.  Artificial Life , 2019, Philosophical Posthumanism.

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

[61]  Rudolf Freund,et al.  On String Languages Generated by Spiking Neural P Systems , 2007, Fundam. Informaticae.

[62]  Xiangxiang Zeng,et al.  Spiking Neural P Systems With Scheduled Synapses , 2017, IEEE Transactions on NanoBioscience.

[63]  Linqiang Pan,et al.  Flat maximal parallelism in P systems with promoters , 2016, Theor. Comput. Sci..

[64]  Andrei Paun,et al.  P Systems with Proteins on Membranes and Membrane Division , 2006, Developments in Language Theory.

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

[66]  K. G. Subramanian,et al.  Tissue-like P Systems with Active Membranes for Picture Generation , 2003, Fundam. Informaticae.

[67]  Linqiang Pan,et al.  Numerical P systems with production thresholds , 2017, Theor. Comput. Sci..

[68]  Artiom Alhazov,et al.  Membrane Operations in P Systems with Active Membranes , 2004 .

[69]  Xiangxiang Zeng,et al.  Monodirectional Tissue P Systems With Promoters , 2020, IEEE Transactions on Cybernetics.

[70]  Mario J. Pérez-Jiménez,et al.  Characterizing Tractability by Cell-Like Membrane Systems , 2007, Formal Models, Languages and Applications.

[71]  Qi Meng,et al.  A hybrid approach based on differential evolution and tissue membrane systems for solving constrained manufacturing parameter optimization problems , 2013, Appl. Soft Comput..

[72]  Mario de Jesús Pérez Jiménez,et al.  Complexity Classes in Cellular Computing with Membranes , 2003 .

[73]  Hong Peng,et al.  Coupled Neural P Systems , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[74]  Gexiang Zhang,et al.  A Modified Membrane-Inspired Algorithm Based on Particle Swarm Optimization for Mobile Robot Path Planning , 2015, Int. J. Comput. Commun. Control.

[75]  Mario de Jesús Pérez Jiménez,et al.  Computational Efficiency of Cellular Division in Tissue-like Membrane Systems , 2008 .

[76]  Hendrik Jan Hoogeboom,et al.  Simulating Counter Automata by P Systems with Symport/Antiport , 2002, WMC-CdeA.

[77]  Marian Gheorghe,et al.  Generalized communicating P systems , 2008, Theor. Comput. Sci..

[78]  Tao Wang,et al.  Fault Diagnosis Models for Electric Locomotive Systems Based on Fuzzy Reasoning Spiking Neural P Systems , 2014, Int. Conf. on Membrane Computing.

[79]  Mario J. Pérez-Jiménez,et al.  A polynomial alternative to unbounded environment for tissue P systems with cell division , 2013, Int. J. Comput. Math..

[80]  Mario J. Pérez-Jiménez,et al.  Efficient simulation of tissue-like P systems by transition cell-like P systems , 2008, Natural Computing.

[81]  Linqiang Pan,et al.  Spiking Neural P Systems with Astrocytes , 2012, Neural Computation.

[82]  Linqiang Pan,et al.  Spiking Neural P Systems With Communication on Request and Mute Rules , 2017, IEEE Transactions on Parallel and Distributed Systems.

[83]  Andrei Paun,et al.  The power of communication: P systems with symport/antiport , 2002, New Generation Computing.

[84]  Gheorghe Paun,et al.  Spike Trains in Spiking Neural P Systems , 2006, Int. J. Found. Comput. Sci..

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

[86]  Henry N. Adorna,et al.  Relating Computations in Non-cooperative Transition P Systems and Evolution-Communication P Systems with Energy , 2015, Fundam. Informaticae.

[87]  Mario J. Pérez-Jiménez,et al.  A Polynomial Complexity Class in P Systems Using Membrane Division , 2003, DCFS.

[88]  Erzsébet Csuhaj-Varjú,et al.  Computationally Complete Generalized Communicating P Systems with Three Cells , 2017, Int. Conf. on Membrane Computing.

[89]  Linqiang Pan,et al.  Tissue-like P systems with evolutional symport/antiport rules , 2017, Inf. Sci..

[90]  Alfonso Rodríguez-Patón,et al.  Tissue P systems , 2003, Theor. Comput. Sci..

[91]  Zhiqiang Zhang,et al.  Spiking Neural P Systems With Polarizations , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[92]  Mario J. Pérez-Jiménez,et al.  Attacking the Common Algorithmic Problem by Recognizer P Systems , 2004, MCU.

[93]  Artiom Alhazov,et al.  Solving Graph Problems by P Systems with Restricted Elementary Active Membranes , 2004, Aspects of Molecular Computing.

[94]  Shankara Narayanan Krishna.  On the Computational Power of Flip-Flop Proteins on Membranes , 2007, CiE.

[95]  Linqiang Pan,et al.  Tissue P Systems with Protein on Cells , 2016, Fundam. Informaticae.

[96]  Gexiang Zhang,et al.  Weighted Fuzzy Reasoning Spiking Neural P Systems: Application to Fault Diagnosis in Traction Power Supply Systems of High-Speed Railways , 2015 .

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

[98]  Haiming Chen,et al.  Spiking neural P systems with extended rules: universality and languages , 2006, Natural Computing.

[99]  Ge-Xiang Zhang,et al.  Analyzing radar emitter signals with membrane algorithms , 2010, Math. Comput. Model..

[100]  Hong Peng,et al.  Interval-valued fuzzy spiking neural P systems for fault diagnosis of power transmission networks , 2019, Eng. Appl. Artif. Intell..

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

[102]  Linqiang Pan,et al.  Tissue P Systems With Channel States Working in the Flat Maximally Parallel Way , 2016, IEEE Transactions on NanoBioscience.

[103]  Niall Murphy,et al.  Uniformity is Weaker than Semi-Uniformity for Some Membrane Systems , 2014, Fundam. Informaticae.

[104]  Mario J. Pérez-Jiménez,et al.  A uniform family of tissue P systems with cell division solving 3-COL in a linear time , 2008, Theor. Comput. Sci..

[105]  Andrei George Florea,et al.  A distributed approach to the control of multi-robot systems using XP colonies , 2017, Integr. Comput. Aided Eng..

[106]  Mario J. Pérez-Jiménez,et al.  Application of Fuzzy Reasoning Spiking Neural P Systems to Fault Diagnosis , 2014, Int. J. Comput. Commun. Control.

[107]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[108]  Marian Gheorghe,et al.  Cell communication in tissue P systems: universality results , 2005, Soft Comput..

[109]  Andrei Paun,et al.  P Systems with proteins on Membranes: a Survey , 2011, Int. J. Found. Comput. Sci..

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

[111]  Mario J. Pérez-Jiménez,et al.  Computational complexity of tissue-like P systems , 2010, J. Complex..

[112]  Artiom Alhazov,et al.  Symbol/Membrane Complexity of P Systems with Symport/Antiport Rules , 2005, Workshop on Membrane Computing.

[113]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[114]  Matteo Cavaliere.  Evolution-Communication P Systems , 2002, WMC-CdeA.

[115]  Oscar H. Ibarra,et al.  Deterministic catalytic systems are not universal , 2006, Theor. Comput. Sci..

[116]  Rudolf Freund,et al.  Tissue P systems with channel states , 2005, Theor. Comput. Sci..

[117]  Rudolf Freund,et al.  P Systems with Activated/Prohibited Membrane Channels , 2002, WMC-CdeA.

[118]  Erzsébet Csuhaj-Varjú,et al.  On generalized communicating P systems with minimal interaction rules , 2011, Theor. Comput. Sci..

[119]  Kamala Krithivasan,et al.  P Systems with Membrane Creation: Universality and Efficiency , 2001, MCU.

[120]  Ferrante Neri,et al.  A membrane parallel rapidly-exploring random tree algorithm for robotic motion planning , 2020, Integr. Comput. Aided Eng..

[121]  Giancarlo Mauri,et al.  Solving NP-Complete Problems Using P Systems with Active Membranes , 2000, UMC.

[122]  Artiom Alhazov,et al.  Polarizationless P Systems with Active Membranes , 2004, Grammars.

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

[124]  Andrei Paun,et al.  Universality of Minimal Symport/Antiport: Five Membranes Suffice , 2003, Workshop on Membrane Computing.

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

[126]  Andrei Paun,et al.  P Systems with Proteins on Membranes , 2006, Fundam. Informaticae.

[127]  Andrei George Florea,et al.  Membrane computing models and robot controller design, current results and challenges , 2019, Journal of Membrane Computing.

[128]  Linqiang Pan,et al.  Time-free solution to SAT problem using P systems with active membranes , 2014, Theor. Comput. Sci..

[129]  Pan Zheng,et al.  On the Computational Power of Spiking Neural P Systems with Self-Organization , 2016, Scientific Reports.

[130]  Artiom Alhazov,et al.  Uniform Solution to QSAT Using Polarizationless Active Membranes , 2006 .

[131]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[132]  Mario J. Pérez-Jiménez,et al.  On the Power of Dissolution in P Systems with Active Membranes , 2005, Workshop on Membrane Computing.

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

[134]  Jonathan Timmis,et al.  Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

[135]  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).

[136]  Gheorghe Paun.  P Systems with Active Membranes: Attacking NP-Complete Problems , 2001, J. Autom. Lang. Comb..

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