An initial example

This example was initially presented in:

7. Păun and R. Păun, “Membrane Computing and Economics: Numerical P Systems,” Fundamenta Informaticae, vol. 73, no. 1,2. IOS Press, pp. 213–227, 01-Jan-2006.

The PeP input file for this system can also be found at input_files/input_example_3.pep

num_ps = {
    # membrane names (labels)
    H = {m1, m2, m3};

    structure = [m1 [m2 ]m2 [m3 ]m3 ]m1;

    # membrane 1
    m1 = {
        var = {x_1_1}; # variables used in the production function
        #var0 = (15);
        var0 = (0);
    };

    m2 = {
        var = {x_1_2}; # variables used in the production function
        pr = {2*x_1_2 + 1 -> 1|x_1_1};
        #var0 = (0.5);
        var0 = (0);
    };

    m3 = {
        var = {x_1_3}; # variables used in the production function
        pr = {2*(x_1_3 + 1) -> 1|x_1_3 + 1|x_1_2};
        #var0 = (12.6);
        var0 = (0);
    };
}

The following command is used to run this Numerical P system for 5 simulation steps:

./pep.py input_files/input_example_3.pep -n 5

This 5 step execution produces the following output:

INFO     reading input file
INFO     building NumericalPsystem
INFO     building membrane list
INFO     building membrane structure
INFO     building Membrane
INFO     building variable list
INFO     building var0 list
INFO     building Membrane
INFO     building variable list
INFO     building Program
INFO     building production function
INFO     building distribution rule
INFO     building var0 list
INFO     building Membrane
INFO     building variable list
INFO     building Program
INFO     building production function
INFO     building distribution rule
INFO     building var0 list
num_ps = {
    m1:
        var = { x_1_1: 0.00, }
        E = {}
    m2:
        var = { x_1_2: 0.00, }
        E = {}
        pr_0 = { 2 * x_1_2 + 1  ->  1|x_1_1 }
    m3:
        var = { x_1_3: 0.00, }
        E = {}
        pr_0 = { 2 * ( x_1_3 + 1 )  ->  1|x_1_3 + 1|x_1_2 }
}

INFO     Starting simulation step 1
INFO     Simulation step finished succesfully
num_ps = {
  m1:
    var = { x_1_1: 1.00, }
    E = {}
  m2:
    var = { x_1_2: 1.00, }
    E = {}
  m3:
    var = { x_1_3: 1.00, }
    E = {}
}

INFO     Starting simulation step 2
INFO     Simulation step finished succesfully
num_ps = {
  m1:
    var = { x_1_1: 4.00, }
    E = {}
  m2:
    var = { x_1_2: 2.00, }
    E = {}
  m3:
    var = { x_1_3: 2.00, }
    E = {}
}

INFO     Starting simulation step 3
INFO     Simulation step finished succesfully
num_ps = {
  m1:
    var = { x_1_1: 9.00, }
    E = {}
  m2:
    var = { x_1_2: 3.00, }
    E = {}
  m3:
    var = { x_1_3: 3.00, }
    E = {}
}

INFO     Starting simulation step 4
INFO     Simulation step finished succesfully
num_ps = {
  m1:
    var = { x_1_1: 16.00, }
    E = {}
  m2:
    var = { x_1_2: 4.00, }
    E = {}
  m3:
    var = { x_1_3: 4.00, }
    E = {}
}

INFO     Starting simulation step 5
INFO     Simulation step finished succesfully
num_ps = {
  m1:
    var = { x_1_1: 25.00, }
    E = {}
  m2:
    var = { x_1_2: 5.00, }
    E = {}
  m3:
    var = { x_1_3: 5.00, }
    E = {}
}

WARNING  Maximum number of simulation steps exceeded; Simulation stopped
INFO     Simulation finished succesfully after 5 steps and 0.001450 seconds; End state below:
num_ps = {
  m1:
    var = { x_1_1: 25.00, }
    E = {}
  m2:
    var = { x_1_2: 5.00, }
    E = {}
  m3:
    var = { x_1_3: 5.00, }
    E = {}
}

Notice that after reading the entire Numerical P system, an initial print of the system, as read from the file, is shown.

This print contains the programs, P objects and the enzymes of the P system. The initial values of the P objects are also included:

num_ps = {
    m1:
        var = { x_1_1: 0.00, }
        E = {}
    m2:
        var = { x_1_2: 0.00, }
        E = {}
        pr_0 = { 2 * x_1_2 + 1  ->  1|x_1_1 }
    m3:
        var = { x_1_3: 0.00, }
        E = {}
        pr_0 = { 2 * ( x_1_3 + 1 )  ->  1|x_1_3 + 1|x_1_2 }
}

After finishing each simulation step, a simpler print of the system is shown, where the program contents is excluded.