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Simulation of Spiking Neural P Systems Using Pnet Lab

Simulation of Spiking Neural P Systems Using Pnet Lab. Authors Padmavati Metta Kamala Krithivasan Deepak Garg. Outline. Spiking Neural P (or SN P) system without delay Petri net SN P system without delay to Petri net Simulation using PNetLab. Spiking Neural P system.

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Simulation of Spiking Neural P Systems Using Pnet Lab

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  1. Simulation of Spiking Neural P Systems Using Pnet Lab Authors Padmavati Metta Kamala Krithivasan Deepak Garg

  2. Outline • Spiking Neural P (or SN P) system without delay • Petri net • SN P system without delay to Petri net • Simulation using PNetLab CMC-12

  3. Spiking Neural P system Ionescu, M., Păun, Gh., Yokomori, T.: Spiking Neural P Systems, Fund. Infor. 71, 279-308 (2006). • Spiking Neural P system is a computational model that has been inspired by neurobiology • Distributed and parallel computing model • Variant of Membrane System (P System) • Uses one type of object called spike (a) • Computationally complete CMC-12

  4. Spiking Neural P system without delay (Contd.) Π=(O, σ1, σ2, σ3 ,. . . , σm , syn , i0) • O = {a}, the alphabet. a is called spike and ā is called anti-spike. • m neurons - σ1, σ2, σ3 ,. . . , σm • Syn - Synapses among the neurons. Spike emitted by a neuron i will pass immediately to all neurons j connected to i through synapses. • i0 – Output neuron CMC-12

  5. SN P systems without delay (contd.) Each neuron σi contains • ni -- initial number of spikes • Ri -- finite set of rules of the form • Spiking Rules • E / ar→ a – used when a neuron has n spikes/anti-spikes such that an ∈ L(E) and n ≥ r where Eis a regular expression over {a} • r ≥ 0, number of spikes are consumed and a spike is sent to all neighbouring neurons. • E is omitted if L(E)=ar CMC-12

  6. SN P system without delay (contd.) • Forgetting Rules • as →λ - used when a neuron has s number of spikes • s ≥ 0, number of spikes are forgotten by the neuron. • as should not be in L(E) for any spiking rule E/ar→ a inRi. Configuration of SN P system The configuration of a system at any time is <n1, n2, …, nm>, where ni is the number of spikes present in neuron σi CMC-12

  7. An SN P System without delay п 1 3 a2 r11 : a2/ a a r12 : a2a r13: a λ a3 r31 : a3a r32 : a2 λ r33: a a Initial Configuration a r21: a  a < 2, 1 , 3> 2 CMC-12

  8. Working of an SN P System • A global clock is there and all neurons work in parallel but each neuron can use one rule at a time. • There can be more than one rule enabled at any time in a neuron, then a rule is chosen in a non-deterministic way. • Using the rules, we pass from one configuration of the system to another configuration. Such a step is called transition. • A computation of an SN P system is finite or infinite sequence of transitions starting from the initial configuration. CMC-12

  9. An SN P System without delay п 3 r12 : a2a r13: aλ a a a a2 a3 a < 2, 1 , 3 > r32 : a2 λ r33: a a r11:a2/ a →a r31 : a3 →a 1 11, 21, 31 < 2, 1 , 2 > a a 2 r21 :a →a Evolution STEP - 1 CMC-12

  10. An SN P System without delay п < 2, 1, 3 > Thus as long as neuron 1uses the rulea2/a →a, it sends a spike to other two neurons. One spikes will remains in it and receives one spike from neurons 2 thus a total of 2 spikes in it and the system will be in the same configuration. 11, 21, 31 < 2, 1 , 2 > 11, 21, 32 Evolution CMC-12

  11. An SN P System without delay п At any moment, neuron 1 can choose the rule a2→a, This means all spikes of neuron 1 are consumed so in the next step, it will have one spike instead of two reaching a configuration < 1, 1, 2> < 2, 1, 3 > 12, 21, 31 11, 21, 31 < 1, 1 , 2 > < 2, 1 , 2 > 12, 21, 32 11, 21, 32 Evolution CMC-12

  12. An SN P System without delay п 3 < 2, 1, 3 > r11:a2/ a →a r12 : a2a a a2 r31 : a3 →a r33: a a 12, 21, 31 11, 21, 31 1 r32 : a2 λ r13: aλ 12, 21, 32 < 1, 1 , 2 > < 2, 1 , 2 > 13, 21, 32 11, 21, 32 < 1, 0 , 1 > a a 2 r21 :a →a NEXT STEP Evolution CMC-12

  13. An SN P System without delay п 3 < 2, 1, 3 > r11:a2/ a →a r12 : a2a a a r31 : a3 →a r32 : a2 λ 12, 21, 31 11, 21, 31 1 r13: aλ 12, 21, 32 < 1, 1 , 2 > < 2, 1 , 2 > r33: a a 13, 21, 32 11, 21, 32 < 1, 0 , 1 > 2 13, 20, 33 r21 :a →a < 0, 0 , 0 > Evolution LAST STEP CMC-12

  14. Petri net with guard P1 P2 2 1 T G(T)=true if #(P1)=3 2 P3 Petri Nets are formal and graphical models to represent concurrent events Consists of set of places and transitions. Arcs connecting transitions and places, have weights Transitions are associated with enabling conditions called guard functions. CMC-12

  15. Petri Net Marking • A transition tjT is enabled when each input place has at least a number of tokens equal to the weight of the arc and guard function associated with tireturns true. • When a transition fires it removes a number of tokens (equal to the weight of each input arc) from each input place and deposits a number of tokens (equal to the weight of each output arc) to each output place. • A marking is an m (no. of places)-vector, containing number of tokens each place. CMC-12

  16. Objective of the Paper To design algorithm for translating SN P systems into equivalent Petri net model. To simulate the obtained model using a Java based Petri net tool called PNetLab . CMC-12

  17. Translation - SN P system and Petri net CMC-12

  18. Translation- Execution Semantics CMC-12

  19. Methodology (SN P System to Petri net) 1 a2 r11: a2/ a →a 2 3 T11 - Transition corresponding to rule r11 P2 Petri Net P1 G(T11)=true if #(P1)=2 P3 P11 P11-synchronizing place for P1 CMC-12

  20. About PNetLab • Java based Petri net tool • Allows parallel execution of transitions after resolving conflicts. • We can write user defined guard functions in C/C++ • Provides step-by-step execution of net in a graphical way • It can find Transition-invariants, Place-invariants, minimal siphons , traps, pre-incidence, post-incidence and incidence matrices and coverability tree. CMC-12

  21. Petri net in PnetLab for SN P System п CMC-12

  22. Specifying conflict management in PnetLab CMC-12

  23. Simulation in PnetLab – Step 1 CMC-12

  24. Simulation in PnetLab – Step 2 CMC-12

  25. Simulation in PnetLab – Step 4 CMC-12

  26. Simulation in PnetLab – Step 5 CMC-12

  27. Markings during Simulation in PnetLab CMC-12

  28. If we consider the sub marking-the marking of first three place we get < 2, 1, 3 > < 2, 1, 3 > 12, 21, 31 11, 21, 31 12, 21, 32 < 1, 1 , 2 > < 2, 1 , 2 > < 1, 1 , 2 > < 2, 1 , 2 > 13, 21, 32 11, 21, 32 < 1, 0 , 1 > < 1, 0 , 1 > 13, 20, 33 < 0, 0 , 0 > < 0, 0 , 0 > Evolution of SN P System Which is same as the evolution of the SN P systems CMC-12

  29. The Significance of the Study To verify and analyze the working of SN P systems without delay. Petri nets can aid in the analysis and verification of SN P systems. Other analytical and verification techniques developed for Petri nets can be deployed to deal with SN P systems. CMC-12

  30. Thank You CMC-12

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