Spiking Neural Membrane Computing Models
Abstract
:1. Introduction
- (1)
- The forms of the rules are different; they contain the production functions. Additionally, each neuron contains two data units, including the input value and the threshold value. However, SNP systems contain the number of spikes in integer form.
- (2)
- The execution steps of the rules are different. When the rules start to be executed, SNMC models have the production and comparison steps.
- (3)
- The synapse weights of connecting neurons in SNMC models are divided into inhibitory synapses and excitatory synapses, and the corresponding weights are positive and negative. It can be explained in this manner: if the spike passes through the inhibitory synapse, the spike will be negatively charged.
2. Related Works
2.1. Spiking Neural P Systems
- (1)
- is the alphabet, and is a spike included in neurons;
- (2)
- represents neurons with the form , , where
- (a)
- is the number of spikes in neuron ;
- (b)
- is the finite set of rules, including spiking rules and forgetting rules. The form of spiking rules is , , where indicates the time delay and indicates the regular expression over the alphabet . The form of forgetting rules is , . Additionally indicates the neuron is empty, without spikes.
- (3)
- represents synapses that connect neurons. Additionally, () indicates the synapse between neuron and neuron , where;
- (4)
- is the input neuron;
- (5)
- is the output neuron.
- (1)
- ADD instructions, such as , mean that the number stored in register is increased by 1, and the next instruction is chosen or nondeterministically.
- (2)
- SUB instructions, such as , generate two results according to the number in register . If the value stored in register is greater than 0, the operation of subtracting 1 is performed, and the next instruction is executed. If the value stored in register is equal to 0, no operation is performed on , and the next execution instruction is .
- (3)
- Halting instruction is used to halt calculation.
2.2. Neural Network
3. Spiking Neural Membrane Computing Models
3.1. Definition
- (1)
- is the alphabet, and refers to the spike included in neurons.
- (2)
- is the set of neurons, and neuron has the form , where
- (a)
- is input data in neuron ;
- (b)
- is a threshold of neuron ;
- (c)
- is the production function, which is to compute the total real value of neuron . The total real value is the weighted sum of all inputs minus the threshold;
- (d)
- is the set of firing rules, with the form , . If , neuron is not producing spikes, denoted as .
- (3)
- is the weight on the synapse, which can be positive or negative. A positive weight means an excitatory synapse, and a negative weight means an inhibitory synapse.
- (4)
- is the set of synapses.
- (5)
- and are the input neuron and the output neuron, respectively. The input neuron converts the input data into spikes containing real values. The output neuron outputs the input data as a binary string composed of 0 s and 1 s.
- (1)
- Production step. When neuron receives weighted spikes with real value from connected neurons at time , and the threshold is , the production function works to calculate the total real value by Formula (4).
- (2)
- Comparison step. In this step, the result computed by Formula (4) is compared with the critical value 0. It determines whether the real value output of the next step is 1 or 0.
- (3)
- Outputting step. According to the result of the comparison step, if it has , then , and the rule can be applied to output a spike with the real value of 1. If it has , then and the rule fires. Therefore, no spike can be sent to the connected neurons.
3.2. Illustrative Example
- (1)
- Assuming that the rule is applied, neuron receives a spike from at Time 2, and then the production function executes at Time 3. The value is obtained. Hence, at Time 4, neuron produces and sends an empty to neuron . At the same time, neuron also receives one spike from neuron ; the rule is used. Since its value is 0, neuron sends an empty to neuron . The neuron has not received any spikes, so it produces empty at Time 5, and neuron receives two spikes from neuron . At Time 6, its rule in neuron fires and its , so it produces one spike and sends it out at the same time.
- (2)
- Assuming that the rule is used, then neuron is in the closed state before Time 3 and does not receive any spikes. At Time 3, the production function of neuron performs and produces one spike to send to neurons and . Thus, at Time 3, neuron receives two spikes: one from neuron and the other from neuron . At Time 4, since in , it has , and produces a spike and sends it to neuron . Neuron receives three spikes, and at Time 5, its producing function can be calculated as , so . Meanwhile, neuron receives two spikes from neuron and one negative spike from neuron , so neuron contains one spike. In this way, no spike is generated and sent out at Time 6 because of .
4. Turing Universality of SNMC Models
4.1. Generating Mode
- (1)
- If the rule is applied, neuron receives two spikes and receives one spike at time . The configuration becomes . In neuron , it has and sends one spike to and at time . But due to the delay of one time in , neuron receives the spike at the next time. Thus, the configuration of time is . At time , the rule fires and the production result in neuron is , such that the neuron produced empty, with in the outputting step. In this way, neuron is empty. Since the time delay in neuron , only receives the spikes sent by neurons and at time , so neuron receives two spikes from in total and . Calculate the value , and one spike is generated. Therefore, neuron receives two spikes at time and .
- (2)
- If the rule in neuron is activated, then at time , since there is the time delay in , only neuron receives two spikes and neuron receives one spike. The configuration of time is . The value in neuron is 1, which is greater than 0; thus, sends out a spike at time . Thus, neuron receives two spikes sent by neurons and at time , and . At the next time, neuron receives two spikes sent by neuron . Additionally, neuron receives two spikes from and one spike with a negative charge from neuron , so neuron has one spike at this time, and the configuration is . Therefore, no spike is sent to neuron in time because of in and .
- (1)
- If register of register machine stores a number , it means that neuron contains at least one spike. At time , neuron contains at least two spikes, and so . As its value is 1>0, one spike is generated and sent to neurons and , respectively, at time . At the same time, neuron generates one spike since . Thus, neuron receives two spikes, one from and the other from , and receives one spike because one negatively charged spike and one spike are annihilated. The configuration of time is . At the next time, since of neuron , a spike is generated and two spikes are sent to . Additionally, the value of neuron is 0, so no spike is generated; then, neuron is empty. In this way, the configuration of time is .
- (2)
- Suppose that no number is stored in register at the initial time; that is, neuron is empty. At time , one spike from is received by , and the rule fires. Thus, the configuration is . Since there is only one spike in , and its , neuron produces no spike at time . Meanwhile, the neuron receives one spike from and receives two spikes from . The configuration of time is . At time , the rule in is applied, and the calculation , so no spike is generated. Additionally, according to the rule, generates one spike and neuron obtains two spikes. Therefore, neuron has one spike and neuron is empty. In this way, .
4.2. Accepting Mode
5. Conclusions
- The weight and threshold values are introduced into the SNMC model, and the rule mechanism is improved compared with the SNP system so that the model combines the advantages of membrane computing and neural networks and can extend the application when processing real value information in particular.
- The rules of the SNMC model involve production function, and the calculation method of production function originates from the data processing method of neural networks, so the effective combination of the SNMC model and algorithms can be realized in the future.
- The computing power of the SNMC model has been proven, and it is a kind of Turing universal computational model.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Liu, X.; Ren, Q. Spiking Neural Membrane Computing Models. Processes 2021, 9, 733. https://doi.org/10.3390/pr9050733
Liu X, Ren Q. Spiking Neural Membrane Computing Models. Processes. 2021; 9(5):733. https://doi.org/10.3390/pr9050733
Chicago/Turabian StyleLiu, Xiyu, and Qianqian Ren. 2021. "Spiking Neural Membrane Computing Models" Processes 9, no. 5: 733. https://doi.org/10.3390/pr9050733