Intelligent Problem Solvers in Education: Design Method and Applications - Intelligent Systems - page 133

Algorithm 3.1: Find a solution of the problem HG.

Step 1: Solution  empty;

Step 2: if G  H then begin Solution_found  true; goto step 4; end

else Solution_found  false;

Step 3: Repeat

Hold  H;

Select f  F;

while not Solution_found and (f found) do begin

if (applying f from H produces new facts)

then begin

H  H  M(f); Add f to Solution;

end;

if G  H then

Solution_found  true;

Select new f  F;

end ;  while 

Until Solution_found or (H = Hold);

Step 4: if not Solution_found then

There is no solution found;

else

Solution is a solution of the problem;

Algorithm 3.2: Find a good solution from a solution S = [f 1 , f 2 , ..., f k ] of the problem HG on
computational net (M, F).

Step 1: NewS  []; V  G;
Step 2: for i := k downto 1 do
If v(f k )  V   the Begin
Insert f k at the beginning of NewS;
V  (V - v(f k ))  (u(f k ) - H);
End
Step 3: NewS is a good solution.

On a computational net (M, F), in many cases the problem HG has a solution S in which
there are relations producing some redundancy variables. At those situations, we must
determine necessary variables of each step in the problem solving process. The following
theorem shows the way to analyze the solution to determine necessary variables to compute
at each step.

Theorem 3.2: Given a computational net K = (M, F). Let [f 1 , f 2 , ..., f m ] be a good solution of
the problem HG. denote A 0 = H, A i = [f 1 , f 2 , ..., f i ](H), with i=1, ..., m. Then there exists a
list [B 0 , B 1 , ..., B m-1 , B m ] satisfying the following conditions:

1. B m = G,

2. B i  A i , with i=0, 1, ..., m.

3. For i=1,...,m, [f i ] is a solution of the problem B i-1  B i but not to be a solution of the

problem B  B i , with B is any proper subset B of B i-1 .