Knapsack - Active membranes

Description

Well-known Knapsack 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-Núnez, A. A Linear Solution for the Knapsack Problem Using Active Membranes. Lecture Notes in Computer Science, 2933 (2004), 250–268.
*/

@model<membrane_division>

def Knapsack(n,k,c)
{
    @mu = [[]'e]'s;
    @ms(s) = z{0};
    @ms(e) = e{0},ab*k,bb*c;
    [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;
    [y{0} --> bb{0}]'e;
    +[y{0} --> l]'e;
    +[y{i} --> y{i-1}]'e : 1 <= i <= n;
    -[q --> qb,q{0}]'e;
    -[ab{0} --> a{0}]'e;
    -[ab --> a]'e;
    -[bb{0} --> bg{0}]'e;
    -[bb --> bg]'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*j+1}]'e --> +[]f : 0 <= j <= k;
    +[qb --> qb{0}]'e;
    +[bg{0} --> b{0}]'e;
    +[bg --> b]'e;
    +[a --> l]'e;
    +[b{0}]'e -->[]f;
    [b]'e --> +[]f;
    +[qb{2*j} --> qb{2*j+1}]'e : 0 <= j <= c;
    [qb{2*j+1} --> qb{2*j+2}]'e : 0 <= j <= c-1;
    +[qb{2*c+1}]'e --> []Yes;
    [qb{2*c+1}]'e --> []Yes;
    [z{i} --> z{i+1}]'s : 0 <= i <= 2*n + 2*k + 2*c + 5;
    [z{2*n+2*k+2*c+6} --> d{1},No{0}]'s;
    [d{1}]'s --> +[]d{1};
    +[No{0} --> No]'s;
    +[Yes]'s --> []Yes;
    +[No]'s --> []No;
}

def main()
{
    call Knapsack(4,8,20);
    @ms(e) += x{1}*5,y{1}*10,x{2}*3,y{2}*5,x{3}*10,y{3}*5,x{4}*20,y{4}*10;
}

Files

• The example does not need input data from any user nor speficic interesting outputs, so it can 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.