脉冲神经膜系统的计算性质与应用研究
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摘要
生物计算是计算机科学与生命科学交叉研究领域。生物计算模型具有信息存储使用空间小、计算并行度高、计算高效性、计算具有自组织性与自适应性,以及容错性强等优点。膜计算是生物计算的重要分支之一,膜计算研究的计算模型统称为膜系统。本文研究脉冲神经膜系统,它是一类受生物神经细胞之间的通讯方式启发得到的分布式并行计算模型。
人类大脑中神经元具有匀质性,即每个神经元的结构与功能都是相似的。受这一生物现实的启发,本文研究了带反脉冲的匀质脉冲神经膜系统,其中匀质性的含义体现在系统中所有神经元具有相同的规则集合。在使用“纯激发规则”,并且不使用遗忘规则的情况下,证明了带反脉冲的匀质脉冲神经膜系统具有计算完备性；证明了具有抑制突触的匀质脉冲神经膜系统具有计算完备性。这两个结果表明神经系统的结构对于系统的功能有决定性作用：尽管构成系统的神经元具有匀质性,但是利用神经元之间的相互合作形式的神经网络具有强大的计算能力。
本文研究了带反脉冲的脉冲神经膜系统范式。证明了在使用两类“纯激发规则”的情况下,带反脉冲的脉冲神经膜系统具有计算通用性。对于使用“非纯激发规则”的脉冲神经膜系统而言,判定“非纯激发规则”是否满足使用条件是一个潜在的计算困难问题。因此,构造使用“纯激发规则”的脉冲神经膜系统对于系统计算的可行性有着重要意义。
可逆计算模型都有超低能耗的优点,是量子计算研究的核心计算模型。本文建立了可逆脉冲神经膜系统,证明了可逆脉冲神经膜系统具有与图灵机等价的计算能力。这为量子计算理论与生物计算理论关联提供理论支持,同时也为设计低耗能生物计算模型提供理论模型。
生物神经系统中存在着具有特殊生物功能的模体与功能社团。来自同一个模体或者功能社团的神经元,通过相互协作(一般是同步的工作)实现特殊的生物功能。受这一生物现实的启发,构造了局部同步的异步脉冲神经膜系统；证明了在使用一般神经元或者非限制神经元时,局部同步的异步脉冲神经膜系统是计算通用的；在使用限制神经元时,局部同步的异步脉冲神经膜系统计算能力有所减弱,只能产生自然数的半线性集合。
利用脉冲神经膜系统求解计算困难问题时,通常将神经元中使用激发规则、遗忘规则、神经元分裂,以及神经元芽殖等操作统一地消耗一个单位时间。这种要求脉冲神经膜系统中不同形式的规则都在相等的时间内完成(一个时间单元)并不符合生物现实。针对这个问题,建立了时间无关脉冲神经膜系统,并且构造了一族以非确定地方式求解SAT问题的时间无关脉冲神经膜系统。
人类大脑的最重要的生物功能之一就是维系人类的认知能力,这使得研究脉冲神经膜系统的“认知能力”具有重要意义。本文将学习机制引入脉冲神经膜系统,构造了识别英文手写字母的脉冲神经膜系统。通过分析仿真结果发现,具有学习机制的脉冲神经膜系统可以有效地识别手写英文字母,这显示了脉冲神经膜系统在模式识别研究领域的潜在应用价值。
Bio-computing is a inter-discipline of computer science and bio-science. Bio-computing models have several advantages, such as storing information costing less space,performing computation highly parallel, doing computation in self-assemble and self-adaption manners, and having high fault tolerance in the computation. Membrane com-puting is a new and hot branch of bio-computing. The computing models investigated inmembrane computing are called P systems. In this work, we deal with spiking neural Psystems, which are inspired from the way of biological neuron processing information andcommunicating with each other by means of electrical impulses (spikes).
Homogeneity is a particular property of human brain in sense that each neuron hasthe similar function and structure. We investigate homogeneous spiking neural P systemswith anti-spikes, where each neuron has the same set of rules. Such systems with pure formof spiking rules and without forgetting rules are proved to be universal. In case of usinginhibitory synapse, the equivalence between homogeneous spiking neural P systems withanti-spikes and Turing machine can be achieved. These results have an important sense:the structure of a neural system is crucial for the functioning of the system. Although theindividual neuron is homogeneous, by cooperating with each other, a network of neuronscan be powerful–“complete (Turing) creativity”.
We investigate some normal forms of spiking neural P systems with anti-spikes. Specif-ically, in case of using two categories of pure spiking rules, spiking P systems with anti-spikes can achieve Turing completeness. This result improves a corresponding result pro-posed by Pan, which use three categories of non-pure spiking rules. Note that for spikingneural P systems with anti-spike using non-pure spiking rules, determining whether a rulecan be applied is a potential computational hard problem. So, constructing spiking neu-ral P systems with anti-spike using only pure form of spiking rules will provide feasiblecomputing models in practice.
Reversible computational models are elementary computing devices in Quantum com- puting. The most important advantage of reversible models is that the cost of energy inthe computing processes is low. We construct reversible spiking neural P systems, and it isproved that reversible spiking neural P systems are universal. These results will constructa connection between quantum theory and bio-computing theory, as well as provide some
theoretical low energy costing bio-computing models.There are some typical motifs and communities in biological neural networks. Neuronsfrom the same motif or community can cooperate with each other to achieve some biologicalfunctions. Inspired from this fact, we construct asynchronous spiking neural P systems withlocal synchronization. It is proved that the systems with general neurons can achieve Turingcompleteness, and the systems with limited neurons can only generate semi-linear sets of
natural numbers.In classical spiking neural P systems, each operation, such as application of the spikingrule, forgetting rule, cell division, neuron budding, will cost one time unit. However, thisrestriction that each rule has a precise execution time does not coincide with the biologicalfact, since the execution time of bio-chemical reactions can vary because of external uncon-trollable conditions. To avoid this defect, we construct timed and time-free spiking neuralP systems. We investigate the efficiency of the systems by solving a specific computational
hard problem–SAT problem.The most important function of human brain is maintaining human’s cognitive ability.Spiking neural P systems are neural-like computing models inspired from biological neuralsystems, so it is interesting to investigate the “cognitive ability” the systems. In thiswork, spiking neural P system with learning mechanism is constructed to recognizing handwritten English letters. Simulation results show that spiking neural P systems with learningmechanism performs well in recognizing hand written English characters.
人类大脑中神经元具有匀质性,即每个神经元的结构与功能都是相似的。受这一生物现实的启发,本文研究了带反脉冲的匀质脉冲神经膜系统,其中匀质性的含义体现在系统中所有神经元具有相同的规则集合。在使用“纯激发规则”,并且不使用遗忘规则的情况下,证明了带反脉冲的匀质脉冲神经膜系统具有计算完备性；证明了具有抑制突触的匀质脉冲神经膜系统具有计算完备性。这两个结果表明神经系统的结构对于系统的功能有决定性作用：尽管构成系统的神经元具有匀质性,但是利用神经元之间的相互合作形式的神经网络具有强大的计算能力。
本文研究了带反脉冲的脉冲神经膜系统范式。证明了在使用两类“纯激发规则”的情况下,带反脉冲的脉冲神经膜系统具有计算通用性。对于使用“非纯激发规则”的脉冲神经膜系统而言,判定“非纯激发规则”是否满足使用条件是一个潜在的计算困难问题。因此,构造使用“纯激发规则”的脉冲神经膜系统对于系统计算的可行性有着重要意义。
可逆计算模型都有超低能耗的优点,是量子计算研究的核心计算模型。本文建立了可逆脉冲神经膜系统,证明了可逆脉冲神经膜系统具有与图灵机等价的计算能力。这为量子计算理论与生物计算理论关联提供理论支持,同时也为设计低耗能生物计算模型提供理论模型。
生物神经系统中存在着具有特殊生物功能的模体与功能社团。来自同一个模体或者功能社团的神经元,通过相互协作(一般是同步的工作)实现特殊的生物功能。受这一生物现实的启发,构造了局部同步的异步脉冲神经膜系统；证明了在使用一般神经元或者非限制神经元时,局部同步的异步脉冲神经膜系统是计算通用的；在使用限制神经元时,局部同步的异步脉冲神经膜系统计算能力有所减弱,只能产生自然数的半线性集合。
利用脉冲神经膜系统求解计算困难问题时,通常将神经元中使用激发规则、遗忘规则、神经元分裂,以及神经元芽殖等操作统一地消耗一个单位时间。这种要求脉冲神经膜系统中不同形式的规则都在相等的时间内完成(一个时间单元)并不符合生物现实。针对这个问题,建立了时间无关脉冲神经膜系统,并且构造了一族以非确定地方式求解SAT问题的时间无关脉冲神经膜系统。
人类大脑的最重要的生物功能之一就是维系人类的认知能力,这使得研究脉冲神经膜系统的“认知能力”具有重要意义。本文将学习机制引入脉冲神经膜系统,构造了识别英文手写字母的脉冲神经膜系统。通过分析仿真结果发现,具有学习机制的脉冲神经膜系统可以有效地识别手写英文字母,这显示了脉冲神经膜系统在模式识别研究领域的潜在应用价值。
Bio-computing is a inter-discipline of computer science and bio-science. Bio-computing models have several advantages, such as storing information costing less space,performing computation highly parallel, doing computation in self-assemble and self-adaption manners, and having high fault tolerance in the computation. Membrane com-puting is a new and hot branch of bio-computing. The computing models investigated inmembrane computing are called P systems. In this work, we deal with spiking neural Psystems, which are inspired from the way of biological neuron processing information andcommunicating with each other by means of electrical impulses (spikes).
Homogeneity is a particular property of human brain in sense that each neuron hasthe similar function and structure. We investigate homogeneous spiking neural P systemswith anti-spikes, where each neuron has the same set of rules. Such systems with pure formof spiking rules and without forgetting rules are proved to be universal. In case of usinginhibitory synapse, the equivalence between homogeneous spiking neural P systems withanti-spikes and Turing machine can be achieved. These results have an important sense:the structure of a neural system is crucial for the functioning of the system. Although theindividual neuron is homogeneous, by cooperating with each other, a network of neuronscan be powerful–“complete (Turing) creativity”.
We investigate some normal forms of spiking neural P systems with anti-spikes. Specif-ically, in case of using two categories of pure spiking rules, spiking P systems with anti-spikes can achieve Turing completeness. This result improves a corresponding result pro-posed by Pan, which use three categories of non-pure spiking rules. Note that for spikingneural P systems with anti-spike using non-pure spiking rules, determining whether a rulecan be applied is a potential computational hard problem. So, constructing spiking neu-ral P systems with anti-spike using only pure form of spiking rules will provide feasiblecomputing models in practice.
Reversible computational models are elementary computing devices in Quantum com- puting. The most important advantage of reversible models is that the cost of energy inthe computing processes is low. We construct reversible spiking neural P systems, and it isproved that reversible spiking neural P systems are universal. These results will constructa connection between quantum theory and bio-computing theory, as well as provide some
theoretical low energy costing bio-computing models.There are some typical motifs and communities in biological neural networks. Neuronsfrom the same motif or community can cooperate with each other to achieve some biologicalfunctions. Inspired from this fact, we construct asynchronous spiking neural P systems withlocal synchronization. It is proved that the systems with general neurons can achieve Turingcompleteness, and the systems with limited neurons can only generate semi-linear sets of
natural numbers.In classical spiking neural P systems, each operation, such as application of the spikingrule, forgetting rule, cell division, neuron budding, will cost one time unit. However, thisrestriction that each rule has a precise execution time does not coincide with the biologicalfact, since the execution time of bio-chemical reactions can vary because of external uncon-trollable conditions. To avoid this defect, we construct timed and time-free spiking neuralP systems. We investigate the efficiency of the systems by solving a specific computational
hard problem–SAT problem.The most important function of human brain is maintaining human’s cognitive ability.Spiking neural P systems are neural-like computing models inspired from biological neuralsystems, so it is interesting to investigate the “cognitive ability” the systems. In thiswork, spiking neural P system with learning mechanism is constructed to recognizing handwritten English letters. Simulation results show that spiking neural P systems with learningmechanism performs well in recognizing hand written English characters.
引文
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