Subset sum - Active membranes

Description

Well-known Subset sum problem, solved with P systems with active membranes.

Model in P-Lingua

The corresponding P-Lingua file is the following:

/*
Pérez-Jiménez, M.J.; Riscos-Núñez, A. Solving the Subset Sum Problem by Active Membranes, New Generation Computing, 23 (4), 2005, 367-384.
*/

@model<membrane_division>

def Sum(n,k)
{
    @mu = [[]'e]'s;
    @ms(s) = z{0};
    @ms(e) = e{0},ab*k;
    [e{i}]'e --> -[q]'e +[e{i}]'e : 0 <= i <= n;
    +[e{i}]'e --> [e{i+1}]'e +[e{i+1}]'e : 0 <= i <= n-1;
    [x{0} --> ab{0}]'e;
    +[x{0} --> l]'e;
    +[x{i} --> x{i-1}]'e : 1 <= i <= n;
    -[q --> q{0}]'e;
    -[ab{0} --> a{0}]'e;
    -[ab --> a]'e;
    -[a{0}]'e --> []f;
    [a]'e --> -[]f;
    -[q{2*j} --> q{2*j+1}]'e : 0 <= j <= k;
    [q{2*j+1} --> q{2*j+2}]'e : 0 <= j <= k-1;
    -[q{2*k+1}]'e --> []Yes;
    [q{2*k+1}]'e --> []#;
    -[q{2*j+1}]'e --> -[]# : 0 <= j <= k-1;
    [z{i} --> z{i+1}]'s : 0 <= i <= 2*n + 2*k + 1;
    [z{2*n+2*k+2} --> d{1},No{0}]'s;
    [d{1}]'s --> +[]d{1};
    +[No{0} --> No]'s;
    +[Yes]'s --> []Yes;
    +[No]'s --> []No;
}

def main()
{
    call Sum(7,8);
    @ms(e) += x{1}*3,x{2}*4,x{3}*5,x{4}*1,x{5}*9,x{6}*10,x{7}*4;
}

Files

• The example does not need input data from any user nor speficic interesting outputs, so it can be run from the general app yet available and pre-loaded in MeCoSim.
• Model file, P-Lingua file with the code above.
• As in the case of the app, no scenario file with specific input is needed, so the general dummy scenario file can also be used.