internal void Refine(PRED psi)
{
if (left == null && right == null)
{
#region leaf
var phi_and_psi = solver.MkAnd(phi, psi);
if (solver.IsSatisfiable(phi_and_psi))
{
var phi_min_psi = solver.MkAnd(phi, solver.MkNot(psi));
if (solver.IsSatisfiable(phi_min_psi))
{
left = new PartitonTree <PRED>(solver, nr + 1, this, phi_and_psi, null, null);
right = new PartitonTree <PRED>(solver, nr + 1, this, phi_min_psi, null, null);
}
else // [[phi]] subset of [[psi]]
{
left = new PartitonTree <PRED>(solver, nr + 1, this, phi, null, null); //psi must true
}
}
else // [[phi]] subset of [[not(psi)]]
{
right = new PartitonTree <PRED>(solver, nr + 1, this, phi, null, null); //psi must be false
}
#endregion
}
else if (left == null)
{
right.Refine(psi);
}
else if (right == null)
{
left.Refine(psi);
}
else
{
#region nonleaf
var phi_and_psi = solver.MkAnd(phi, psi);
if (solver.IsSatisfiable(phi_and_psi))
{
var phi_min_psi = solver.MkAnd(phi, solver.MkNot(psi));
if (solver.IsSatisfiable(phi_min_psi))
{
left.Refine(psi);
right.Refine(psi);
}
else // [[phi]] subset of [[psi]]
{
left.ExtendLeft(); //psi is true
right.ExtendLeft();
}
}
else // [[phi]] subset of [[not(psi)]]
{
left.ExtendRight();
right.ExtendRight(); //psi is false
}
#endregion
}
}
PartitonTree(IBooleanAlgebra <PRED> solver, int depth, PartitonTree <PRED> parent, PRED phi, PartitonTree <PRED> left, PartitonTree <PRED> right)
{
this.solver = solver;
this.parent = parent;
this.nr = depth;
this.phi = phi;
this.left = left;
this.right = right;
}
PartitonTree <PRED> right; //complement
internal PartitonTree(IBooleanAlgebra <PRED> solver)
{
this.solver = solver;
nr = -1;
parent = null;
this.phi = solver.True;
this.left = null;
this.right = null;
}
internal IEnumerable <PartitonTree <PRED> > GenerateMintermsHelper(PRED[] preds)
{
var tree = new PartitonTree <PRED>(ba);
foreach (var psi in preds)
{
tree.Refine(psi);
}
return(tree.GetLeaves());
}
private void ExtendLeft()
{
if (left == null && right == null)
{
left = new PartitonTree <PRED>(solver, nr + 1, this, phi, null, null);
}
else if (left == null)
{
right.ExtendLeft();
}
else if (right == null)
{
left.ExtendLeft();
}
else
{
left.ExtendLeft();
right.ExtendLeft();
}
}
/// <summary>
/// Given an array of predidates {p_1, p_2, ..., p_n} where n>=0.
/// Enumerate all satisfiable Boolean combinations Tuple({b_1, b_2, ..., b_n}, p)
/// where p is satisfiable and equivalent to p'_1 & p'_2 & ... & p'_n,
/// where p'_i = p_i if b_i = true and p'_i is Not(p_i) otherwise.
/// If n=0 return Tuple({},True).
/// </summary>
/// <param name="preds">array of predicates</param>
/// <param name="useEquivalenceChecking">optimization flag: if true, uses equivalence checking to cluster equivalent predicates; otherwise does not use equivalence checking</param>
/// <returns>all minterms of the given predicate sequence</returns>
public IEnumerable <Tuple <bool[], PRED> > GenerateMinterms(bool useEquivalenceChecking, params PRED[] preds)
{
if (preds.Length == 0)
{
yield return(new Tuple <bool[], PRED>(new bool[] { }, ba.True));
}
else
{
var count = preds.Length;
List <PRED> nonequivalentSets = new List <PRED>();
//work only with nonequivalent sets as distinct elements
var indexLookup = new Dictionary <int, int>();
var newIndexMap = new Dictionary <EquivClass, int>();
var equivs = new List <List <int> >();
for (int i = 0; i < count; i++)
{
int newIndex;
EquivClass equiv = CreateEquivalenceClass(useEquivalenceChecking, preds[i]);
if (!newIndexMap.TryGetValue(equiv, out newIndex))
{
newIndex = newIndexMap.Count;
newIndexMap[equiv] = newIndex;
nonequivalentSets.Add(preds[i]);
equivs.Add(new List <int>());
}
indexLookup[i] = newIndex;
equivs[newIndex].Add(i);
}
//var pairs = new List<Tuple<IntSet, PRED>>(GenerateMinterms1(nonequivalentSets.ToArray()));
//foreach (var pair in pairs)
//{
// var characteristic = new bool[preds.Length];
// for (int i = 0; i < count; i++)
// if (pair.First.Contains(indexLookup[i]))
// characteristic[i] = true;
// yield return
// new Tuple<bool[], PRED>(characteristic, pair.Second);
//}
var tree = new PartitonTree <PRED>(ba);
foreach (var psi in nonequivalentSets)
{
tree.Refine(psi);
}
foreach (var leaf in tree.GetLeaves())
{
var characteristic = new bool[preds.Length];
foreach (var k in leaf.GetPath())
{
foreach (var n in equivs[k])
{
characteristic[n] = true;
}
}
yield return
(new Tuple <bool[], PRED>(characteristic, leaf.phi));
}
}
}
