internal void Refine(IBooleanAlgebra <S> solver, S newSet)
{
var set_cap_newSet = solver.MkAnd(set, newSet);
if (!solver.IsSatisfiable(set_cap_newSet))
{
return; //set is disjoint from newSet
}
if (solver.AreEquivalent(set, set_cap_newSet))
{
return; //set is a subset of newSet
}
var set_minus_newSet = solver.MkAnd(set, solver.MkNot(newSet));
if (left == null) //leaf
{
left = new PartTree(set_cap_newSet, null, null);
right = new PartTree(set_minus_newSet, null, null);
}
else
{
left.Refine(solver, newSet);
right.Refine(solver, newSet);
}
}
/// <summary>
/// Refines the current partition with respect to the given set.
/// The given set is not required be a subset of the initial set.
/// </summary>
/// <param name="B">given set</param>
public void Refine(S B)
{
var A = partitions.set;
if (!solver.AreEquivalent(A, B))
{
var B_minus_A = solver.MkAnd(B, solver.MkNot(A));
if (solver.IsSatisfiable(B_minus_A)) //new elements are added to the total set
{
var A_union_B = solver.MkOr(A, B);
var A_intersect_B = solver.MkAnd(A, B);
var A_minus_B = solver.MkAnd(A, solver.MkNot(B));
var left = new PartTree(B_minus_A, null, null);
this.partitions = new PartTree(A_union_B, left, this.partitions);
if (solver.IsSatisfiable(A_intersect_B) && solver.IsSatisfiable(A_minus_B))
{
this.partitions.right.Refine(solver, A_minus_B);
}
}
else // B is a subset of A
{
partitions.Refine(solver, B);
}
}
}
internal PartTree(S set, PartTree left, PartTree right)
{
this.set = set;
this.left = left;
this.right = right;
}
/// <summary>
/// Construct a symbolic partition refinement for a given Boolean algebra over S and initial set of elements.
/// </summary>
/// <param name="solver">given Boolean algebra</param>
/// <param name="initialSet">initial set of elements will be one part</param>
public SymbolicPartitionRefinement(IBooleanAlgebra <S> solver, S initialSet)
{
this.solver = solver;
this.partitions = new PartTree(initialSet, null, null);
}