source: branches/HeuristicLab.Problems.GPDL/Examples/EvenParity.txt @ 13687

PROBLEM EvenParity
CODE <<
  const int N = 5;
>>

NONTERMINALS
  Expr<<bool[] d, out bool p>>.
  AND<<bool[] d, out bool p>>.
  OR<<bool[] d, out bool p>>.
  NAND<<bool[] d, out bool p>>.
  NOR<<bool[] d, out bool p>>.

TERMINALS
  D<<out int val>> 
    CONSTRAINTS 
      val IN SET <<Enumerable.Range(0, N);>>
  .

RULES
  Expr<<bool[] d, out bool p>> =                           LOCAL<< int val = 0; >>
    AND<<d, out p>>
    | OR<<d, out p>>
    | NAND<<d, out p>>
    | NOR<<d, out p>>
    | D<<out val>>                                         SEM<< p = d[val]; >>
  .

  AND<<bool[] d, out bool p>> =                            LOCAL << bool p1, p2; >>
    Expr<<d, out p1>> Expr<<d, out p2>>                    SEM << p = p1 & p2; >>
  .

  OR<<bool[] d, out bool p>> =                             LOCAL << bool p1, p2; >>
    Expr<<d, out p1>> Expr<<d, out p2>>                    SEM << p = p1 | p2; >>
  .

  NAND<<bool[] d, out bool p>> =                           LOCAL << bool p1, p2; >>
    Expr<<d, out p1>> Expr<<d, out p2>>                    SEM << p = !(p1 & p2); >>
  .

  NOR<<bool[] d, out bool p>> =                            LOCAL << bool p1, p2; >>
    Expr<<d, out p1>> Expr<<d, out p2>>                    SEM << p = !(p1 | p2); >>
  .

MINIMIZE
  << 
    bool[] d = new bool[N];
    int mistakes = 0;
    for(int i = 0; i < Math.Pow(2, N); i++) {
      // generate bit-vector and count number of 1-bits
      int x = i;
      int nBitsOne = 0;
      for(int j = 0; j < N; j++) {
        if((x % 2) == 1) {
          d[N - j - 1] = true;
          nBitsOne++;
        } else {
          d[N - j - 1] = false;
        }
        x = (x / 2);
      }
      bool target = (nBitsOne % 2) == 0;
      // apply model
      bool p;
      Expr(d, out p);

      if(p != target) mistakes++;
    }
    return mistakes;
  >>
END EvenParity.