## On the computational complexity of spiking neural P systems (2008)

Venue: | In 7th International Conference on Unconventional Computation (UC 2008), volume 5204 of LNCS |

Citations: | 3 - 3 self |

### BibTeX

@INPROCEEDINGS{Neary08onthe,

author = {Turlough Neary},

title = {On the computational complexity of spiking neural P systems},

booktitle = {In 7th International Conference on Unconventional Computation (UC 2008), volume 5204 of LNCS},

year = {2008},

pages = {190--206},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. It is shown here that there is no standard spiking neural P system that simulates Turing machines with less than exponential time and space overheads. The spiking neural P systems considered here have a constant number of neurons that is independent of the input length. Following this, we construct a universal spiking neural P system with exhaustive use of rules that simulates Turing machines in linear time and has only 10 neurons. 1

### Citations

409 |
Membrane Computing. An Introduction
- Păun
- 2002
(Show Context)
Citation Context ...piking neural P system with exhaustive use of rules that simulates Turing machines in polynomial time and has only 18 neurons. 1 Introduction Since their inception inside of the last decade P systems =-=[12]-=- have spawned a variety of hybrid systems. One such hybrid, that of spiking neural P system [3], results from a fusion with spiking neural networks. It has been shown that these systems are computatio... |

61 |
Spiking neural P systems
- Păun
- 2006
(Show Context)
Citation Context ... time and has only 18 neurons. 1 Introduction Since their inception inside of the last decade P systems [12] have spawned a variety of hybrid systems. One such hybrid, that of spiking neural P system =-=[3]-=-, results from a fusion with spiking neural networks. It has been shown that these systems are computationally universal. Here the time/space computational complexity of spiking neural P systems is ex... |

20 | P-completeness of cellular automaton rule 110
- Neary, Woods
(Show Context)
Citation Context ...ng the same space. However, it is not unreasonable to expect efficiency from simple universal systems as many of the simplest computationally universal models have polynomial time and space overheads =-=[8,13,10]-=-. A more time efficient simulation of Turing machines may be given by spiking neural P system with exhaustive rules. Using similar techniques it can be shown that for each multi-tape Turing machine M ... |

19 | Small universal register machines - Korec - 1996 |

18 | Păun: Small universal spiking neural P systems
- Păun, Gh
(Show Context)
Citation Context ... second part of the paper we give an extended spiking neural P system with exhaustive use of rules that simulates Turing machines in polynomial time and has only 18 neurons. Previously, Păun and Păun =-=[11]-=- gave a small universal spiking neural P system with 84 neurons and another, that uses extended rules, with 49 neurons. Both of these spiking neural P systems ⋆ The author would like to thank the anon... |

16 |
Spiking Neural P Systems with an Exhaustive Use of Rules
- Ionescu, Pǎun, et al.
- 2007
(Show Context)
Citation Context ...piking neural P systems that have a constant number of neurons independent of the input length. Extended spiking neural P systems with exhaustive use of rules were proved computationally universal in =-=[4]-=-. However, the technique used to prove universality involved the simulation of counter machines and thus suffers from an exponential time overhead. In the second part of the paper we give an extended ... |

16 | On the time complexity of 2-tag systems and small universal turing machines
- Neary, Woods
- 2006
(Show Context)
Citation Context ...ng the same space. However, it is not unreasonable to expect efficiency from simple universal systems as many of the simplest computationally universal models have polynomial time and space overheads =-=[8,13,10]-=-. A more time efficient simulation of Turing machines may be given by spiking neural P system with exhaustive rules. Using similar techniques it can be shown that for each multi-tape Turing machine M ... |

14 |
Counter machines and counter languages
- Fischer, Meyer, et al.
- 1968
(Show Context)
Citation Context ...utational complexity of spiking neural P systems is examined. We begin by showing that counter machines simulate standard spiking neural P systems with linear time and space overheads. Fischer et al. =-=[2]-=- have previously shown that counter machines require exponential time and space to simulate Turing machines. Thus it immediately follows that there is no spiking neural P system that simulates Turing ... |

13 | On the computational power of spiking neural P systems
- Leporati, Zandron, et al.
(Show Context)
Citation Context ...chines but do not have exhaustive use of rules. Chen et al. [1] have shown that with exponential pre-computed resources sat is solvable in constant time with spiking neural P systems. Leporati et al. =-=[6]-=- gave a semi-uniform family of extended spiking neural P systems that solve the Subset Sum problem in constant time. In later work, Leporati et al. [7] gave a uniform family of maximally parallel spik... |

13 | On the efficiency of spiking neural P systems
- Chen, Ionescu, et al.
- 2006
(Show Context)
Citation Context ...cience Foundation Ireland Research Frontiers Programme grant number 07/RFP/CSMF641.require exponential time and space to simulate Turing machines but do not have exhaustive use of rules. Chen et al. =-=[1]-=- have shown that with exponential pre-computed resources sat is solvable in constant time with spiking neural P systems. Leporati et al. [6] gave a semi-uniform family of extended spiking neural P sys... |

13 | Four small universal Turing machines
- Neary, Woods
(Show Context)
Citation Context ...austive use of rules, has only 18 neurons, and simulates Turing machines in polynomial time. The system constructed efficiently simulates the computation of an existing small universal Turing machine =-=[9]-=-. This universal machine has 6 states and 4 symbols and is called U6,4. The following theorem gives the time/space simulation overheads for U6,4. Theorem 3 ([9]). Let M be a single tape Turing machine... |

7 | Solving numerical NP-complete problems with spiking neural P systems
- Leporati, Zandron, et al.
- 2007
(Show Context)
Citation Context ...e with spiking neural P systems. Leporati et al. [6] gave a semi-uniform family of extended spiking neural P systems that solve the Subset Sum problem in constant time. In later work, Leporati et al. =-=[7]-=- gave a uniform family of maximally parallel spiking neural P systems with more general rules that solve the Subset Sum problem in polynomial time. All the above solutions to NP-hard problems rely fam... |

7 | weakly universal Turing machines
- Neary, Woods
- 2009
(Show Context)
Citation Context ...ng the same space. However, it is not unreasonable to expect efficiency from simple universal systems as many of the simplest computationally universal models have polynomial time and space overheads =-=[8,13,10]-=-. A more time efficient simulation of Turing machines may be given by spiking neural P system with exhaustive rules. Using similar techniques it can be shown that for each multi-tape Turing machine M ... |

6 | A two counter machine cannot calculate 2 n - Schroeppel - 1972 |

6 | X.: Small universal spiking neural P systems with anti-spikes - Song, Jiang, et al. - 2013 |

5 | Some Applications of Spiking Neural P Systems
- Ionescu, Suburlan
(Show Context)
Citation Context ...ural P system that solves that particular instance. This is similar to solving problems with uniform circuits families where each input size has a specific circuit that solves it. Ionescu and Drago¸s =-=[5]-=- have shown that spiking neural P systems simulate circuits in linear time. In the next two sections we give definitions for spiking neural P systems and counter machines and explain the operation of ... |

3 | A small universal spiking neural P system - Neary - 2008 |

2 | A boundary between universality and non-universality in spiking neural P systems. arXiv:0912.0741v1 [cs.CC - Neary - 2009 |

1 | Presentation at The International Workshop on Computing with Biomolecules (CBM 2008). Available at http://www.emcc.at/UC2008/Presentations/CBM5.pdf - Neary |

1 | A universal spiking neural P system with 11 neurons - Neary - 2010 |