/// <summary>
/// Swap the specified variables
/// </summary>
/// <remarks>The two variables shall be adjacent. <c>index</c> shall be
/// followed by<c>index2</c> in the variable order.</remarks>
/// <param name="node">The root node of the BDD.</param>
/// <param name="index">Variable index.<param>
/// <param name="index2">Variable index.</param>
public BDDNode Swap(BDDNode node, int index, int index2)
{
var i = _variable_order.FindIndex(x => x == index) + 1;
if (i >= _variable_order.Count())
{
throw new ArgumentException("'" + index + "' is the last variable in the variable order.");
}
var nextIndex = _variable_order[i];
if (index2 != nextIndex)
{
throw new ArgumentException("Cannot swap variables not adjacents.");
}
// ntm: ignore 008b: read substitution Int32.V_2 => Int32.index2
_variable_order[i - 1] = nextIndex;
_variable_order[i] = index;
BDDNode[] nodesAtIndex;
lock (unique_table_lock)
{
nodesAtIndex = unique_table[index].Nodes().ToArray();
}
foreach (var n in nodesAtIndex)
{
SwapStep(n, index, nextIndex);
}
return(node);
}
/// <summary>
/// Deletes the specified node.
/// </summary>
/// <param name="node">Node to delete.</param>
public void DeleteNode(BDDNode node)
{
if (node.Value != null)
{
return;
}
if (node.RefCount != 0)
{
return;
}
lock (unique_table_lock)
{
unique_table[node.Index].Delete(node);
node.Low.RefCount--;
if (node.Low.RefCount == 0)
{
DeleteNode(node.Low);
}
node.High.RefCount--;
if (node.High.RefCount == 0)
{
DeleteNode(node.High);
}
}
}
/// <summary>
/// Negate the specified node.
/// </summary>
/// <param name="n">The node.</param>
public BDDNode Negate(BDDNode n)
{
if (n.IsZero)
{
return(One);
}
if (n.IsOne)
{
return(Zero);
}
return(Create(n.Index, Negate(n.High), Negate(n.Low)));
}
int GetSize(BDDNode n, ISet <int> visited)
{
if (n == null)
{
return(0);
}
if (visited.Contains(n.Id))
{
return(0);
}
visited.Add(n.Id);
return(GetSize(n.Low, visited) + GetSize(n.High, visited) + 1);
}
/// <summary>
/// Restrict the specified bdd using the <c>positive</c> and
/// <c>negative</c> sets.
/// </summary>
/// <param name="n">Node.</param>
/// <param name="positive">Index of positive variable.</param>
/// <param name="negative">Index of negative variable.</param>
/// <param name="cache">Cache.</param>
public BDDNode Restrict(BDDNode n, int positive, int negative, BDDNode[] cache = null)
{
if (n.Value != null)
{
return(n);
}
BDDNode cached;
if (cache == null)
{
cache = new BDDNode[nextId];
}
else if ((cached = cache[n.Id]) != null)
{
return(cached);
}
BDDNode ret;
if (negative == n.Index)
{
ret = n.Low; // Restrict(n.Low, positive, negative, cache);
}
else if (positive == n.Index)
{
ret = n.High; // Restrict(n.High, positive, negative, cache);
}
else
{
n.Low = Restrict(n.Low, positive, negative, cache);
n.High = Restrict(n.High, positive, negative, cache);
ret = n;
cache[n.Id] = ret;
}
return(ret);
}
/// <summary>
/// Create the BDD Node corresponding to the variable index, with
/// high and low children.
/// </summary>
/// <returns>The create.</returns>
/// <param name="index">Index of the variable.</param>
/// <param name="high">High node, or 1-node.</param>
/// <param name="low">Low node, or 0-node.</param>
public BDDNode Create(int index, BDDNode high, BDDNode low)
{
BDDNode unique;
lock (unique_table_lock)
{
unique = unique_table[index][index, low.Id, high.Id];
if (unique != null)
{
return(unique);
}
}
unique = new BDDNode(index, high, low)
{
Id = nextId++
};
high.RefCount++;
low.RefCount++;
lock (unique_table_lock)
unique_table[index].Put(unique);
return(unique);
}
/// <summary>
/// Returns the size of BDD.
/// </summary>
/// <returns>The size.</returns>
/// <param name="root">The BDD.</param>
public int GetSize(BDDNode root)
{
return(GetSize(root, new HashSet <int>()));
}
/// <summary>
/// Performs the If-Then-Else operation on nodes <c>f</c>, <c>g</c>,
/// <c>h</c>.
/// </summary>
/// <param name="f">Node.</param>
/// <param name="g">Node.</param>
/// <param name="h">Node.</param>
public BDDNode ITE(BDDNode f, BDDNode g, BDDNode h)
{
// ite(f, 1, 0) = f
if (g.IsOne & h.IsZero)
{
return(f);
}
// ite(f, 0, 1) = !f
if (g.IsZero & h.IsOne)
{
return(Negate(f));
}
// ite(1, g, h) = g
if (f.IsOne)
{
return(g);
}
// ite(0, g, h) = h
if (f.IsZero)
{
return(h);
}
// ite(f, g, g) = g
if (g == h)
{
return(g);
}
var cache_key = new Tuple <int, int, int>(f.Id, g.Id, h.Id);
if (_ite_cache.ContainsKey(cache_key))
{
WeakReference wr = _ite_cache[cache_key];
if (wr.IsAlive)
{
return((BDDNode)wr.Target);
}
else
{
_ite_cache.Remove(cache_key);
}
}
int index = f.Index;
if (g.Index < index)
{
index = g.Index;
}
if (h.Index < index)
{
index = h.Index;
}
var fv0 = Restrict(f, -1, index);
var gv0 = Restrict(g, -1, index);
var hv0 = Restrict(h, -1, index);
var fv1 = Restrict(f, index, -1);
var gv1 = Restrict(g, index, -1);
var hv1 = Restrict(h, index, -1);
BDDNode node = Create(index,
ITE(fv1, gv1, hv1),
ITE(fv0, gv0, hv0));
_ite_cache[cache_key] = new WeakReference(node);
return(node);
}
public BDDNode XOR(BDDNode f, BDDNode g)
{
return(ITE(f, g, Negate(g)));
}
/// <summary>
/// Performs the or operation between the specified f and g.
/// </summary>
/// <param name="f">The left node.</param>
/// <param name="g">The right node.</param>
public BDDNode Or(BDDNode f, BDDNode g)
{
return(ITE(f, One, g));
}
public BDDNode Impl(BDDNode f, BDDNode g)
{
return(ITE(f, g, One));
}
/// <summary>
/// Performs the and operation between the specified f and g.
/// </summary>
/// <param name="f">The left node.</param>
/// <param name="g">The right node.</param>
public BDDNode And(BDDNode f, BDDNode g)
{
return(ITE(f, g, Zero));
}
/// <summary>
/// Peform Equal Operator between two nodes.
/// Use XNOR function
/// </summary>
/// <param name="f"></param>
/// <param name="g"></param>
/// <returns></returns>
public BDDNode Equal(BDDNode f, BDDNode g)
{
return(ITE(f, g, Not(g)));
}
/// <summary>
/// Sets the low node and updates the ref count.
/// </summary>
/// <param name="low">Low.</param>
public void SetLow(BDDNode low)
{
Low = low;
low.RefCount++;
}
/// <summary>
/// Returns the dot representation of the given node.
/// </summary>
/// <returns>The dot code.</returns>
public string ToDot(BDDNode root,
Func <BDDNode, string> labelFunction = null,
bool show_all = true)
{
lock (unique_table_lock)
{
var nodes = root.Nodes.Distinct().ToList();
var t = new StringBuilder("digraph G {\n");
if (labelFunction == null)
{
labelFunction = (x) => GetVariableString(x.Index);
}
for (int i = 0; i < N; i++)
{
t.Append($"\tsubgraph cluster_box_{i} {{\n");
t.Append("\tstyle=invis;\n");
//foreach (var n in nodes.Where(x => x.Index == i))
foreach (var n in unique_table[i].Nodes())
{
var color = "grey";
if (nodes.Contains(n))
{
color = "black";
}
if (show_all || nodes.Contains(n))
{
t.Append($"\t\t{n.Id} [label=\"{labelFunction(n)}\", "
+ $"color=\"{color}\"];\n");
}
}
t.Append("\t}\n");
}
t.Append("\tsubgraph cluster_box_sink {\n");
t.Append($"\t{Zero.Id} [shape=box,label=\"0 ({Zero.RefCount})\"];\n");
t.Append($"\t{One.Id} [shape=box,label=\"1 ({One.RefCount})\"];\n");
t.Append("\t}\n");
//foreach (var n in nodes)
for (int i = 0; i < N; i++)
{
foreach (var n in unique_table[i].Nodes())
{
var color = "grey";
if (nodes.Contains(n))
{
color = "black";
}
if (n.Index < N && (show_all || nodes.Contains(n)))
{
t.Append($"\t{n.Id} -> {n.High.Id} [color=\"{color}\"];\n");
t.Append($"\t{n.Id} -> {n.Low.Id} [style=dotted,color=\"{color}\"];\n");
}
}
}
t.Append("}");
return(t.ToString());
}
}
/// <summary>
/// Applies the sifting algorithm to reduce the size of the BDD
/// by changing the variable order.
/// </summary>
/// <returns>The BDD with the new variable order.</returns>
/// <param name="root">The BDD to reduce.</param>
public BDDNode Sifting(BDDNode root)
{
var initial_size = GetSize(root);
var reverse_order = new int[N];
for (int i = 0; i < N; i++)
{
reverse_order[_variable_order[i]] = i;
}
for (int i = 0; i < N; i++)
{
// Move variable xi through the order
int opt_size = GetSize(root);
int opt_pos, cur_pos, startpos = reverse_order[i];
opt_pos = startpos;
cur_pos = startpos;
for (int j = startpos - 1; j >= 0; j--)
{
cur_pos = j;
Swap(root, _variable_order[j], _variable_order[j + 1]);
var new_size = GetSize(root);
if (new_size < opt_size)
{
opt_size = new_size;
opt_pos = j;
}
else if (new_size > MaxGrowth * opt_size)
{
break;
}
}
for (int j = cur_pos + 1; j < N; j++)
{
cur_pos = j;
Swap(root, _variable_order[j - 1], _variable_order[j]);
var new_size = GetSize(root);
if (new_size < opt_size)
{
opt_size = new_size;
opt_pos = j;
}
else if (new_size > MaxGrowth * opt_size)
{
break;
}
}
if (cur_pos > opt_pos)
{
for (int j = cur_pos - 1; j >= opt_pos; j--)
{
Swap(root, _variable_order[j], _variable_order[j + 1]);
}
}
else
{
for (int j = cur_pos + 1; j <= opt_pos; j++)
{
Swap(root, _variable_order[j - 1], _variable_order[j]);
}
}
}
return(root);
}
/// <summary>
/// Create the BDD Node corresponding to the variable index, with
/// high and low children.
/// </summary>
/// <returns>The create.</returns>
/// <param name="index">Index.</param>
/// <param name="high">High.</param>
/// <param name="low">Low.</param>
public BDDNode Create(int index, int high, BDDNode low)
{
return(Create(index, high == 0 ? Zero : One, low));
}
void SwapStep(BDDNode node, int currentIndex, int nextIndex)
{
if (node.Value != null) // ntm: ignore 000d: Or => Xor
{
return;
}
if (node.Index != currentIndex)
{
throw new Exception(
string.Format("Got {0} and should be {1} in the unique table.",
node.Index, currentIndex));
}
if (node.High.Index != nextIndex & node.Low.Index != nextIndex)
{
return;
}
BDDNode f11, f10, f01, f00;
if (node.High.Index == nextIndex)
{
f11 = node.High.High;
f10 = node.High.Low;
}
else
{
f11 = node.High;
f10 = node.High;
}
if (node.Low.Index == nextIndex)
{
f01 = node.Low.High;
f00 = node.Low.Low;
}
else
{
f01 = node.Low;
f00 = node.Low;
}
BDDNode a;
BDDNode b;
if (f11 == f01)
{
a = f11;
}
else
{
a = Create(node.Index, f11, f01);
}
if (f10 == f00)
{
b = f10;
}
else
{
b = Create(node.Index, f10, f00);
}
BDDNode old_low;
BDDNode old_high;
lock (unique_table_lock)
{
unique_table[node.Index].Delete(node);
node.Index = nextIndex;
old_low = node.Low;
old_high = node.High;
old_low.RefCount--;
if (node.Low.RefCount == 0)
{
DeleteNode(node.Low);
}
old_high.RefCount--;
if (node.High.RefCount == 0)
{
DeleteNode(node.High);
}
node.SetHigh(a);
node.SetLow(b);
unique_table[nextIndex].Put(node);
}
}
/// <summary>
/// Create the BDD Node corresponding to the variable index, with
/// high and low children.
/// </summary>
/// <returns>The create.</returns>
/// <param name="index">Index of the variable.</param>
/// <param name="high">High node, or 1-node.</param>
/// <param name="low">Low node, or 0-node.</param>
public BDDNode Create(int index, BDDNode high, int low)
{
return(Create(index, high, low == 0 ? Zero : One));
}
/// <summary>
/// Initializes a new instance of the <see cref="BDDSharp.BDDNode"/> class.
/// </summary>
/// <remarks>
/// Don't use this method to create new nodes, use <see cref="BDDSharp.BDDManager.Create(int, BDDNode, BDDNode)" />.
/// </remarks>
/// <param name="index">Index of the variable the node represents</param>
/// <param name="high">The high node (aka 1-node).</param>
/// <param name="low">The low node (aka 0-node).</param>
public BDDNode(int index, BDDNode high, BDDNode low) : this()
{
this.Index = index;
this.High = high;
this.Low = low;
}
/// <summary>
/// Reduce the specified BDD.
/// </summary>
/// <param name="root">BDD to reduce.</param>
public BDDNode Reduce(BDDNode root)
{
var nodes = root.Nodes.ToArray();
var size = nodes.Length;
var subgraph = new BDDNode[size];
var vlist = new List <BDDNode> [N + 1];
for (int i = 0; i < size; i++)
{
if (vlist[nodes[i].Index] == null)
{
vlist[nodes[i].Index] = new List <BDDNode>();
}
vlist[nodes[i].Index].Add(nodes[i]);
}
int nextid = -1;
for (int k = N; k >= 0; k--)
{
int i = (k == N) ? N : _variable_order[k];
var Q = new List <BDDNode>();
if (vlist[i] == null)
{
continue;
}
foreach (var u in vlist[i])
{
if (u.Index == N)
{
Q.Add(u);
}
else
{
if (u.Low.Id == u.High.Id)
{
u.Id = u.Low.Id;
}
else
{
Q.Add(u);
}
}
}
Q.Sort((x, y) =>
{
var xlk = x.Key.Item1;
var xhk = x.Key.Item2;
var ylk = y.Key.Item1;
var yhk = y.Key.Item2;
int res = xlk.CompareTo(ylk);
return(res == 0 ? xhk.CompareTo(yhk) : res);
});
var oldKey = new Tuple <int, int>(-2, -2);
foreach (var u in Q)
{
if (u.Key.Equals(oldKey))
{
u.Id = nextid;
}
else
{
nextid++;
u.Id = nextid;
subgraph[nextid] = u;
u.Low = u.Low == null ? null : subgraph[u.Low.Id];
u.High = u.High == null ? null : subgraph[u.High.Id];
oldKey = u.Key;
}
}
}
return(subgraph[root.Id]);
}
/// <summary>
/// Sets the high node and updates the ref count.
/// </summary>
/// <param name="high">High.</param>
public void SetHigh(BDDNode high)
{
High = high;
high.RefCount++;
}
/// <summary>
/// Perform Not operation
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public BDDNode Not(BDDNode g)
{
return(ITE(g, Zero, One));
}