private void FindAllPaths(
Vertex vertex, Set <CnfClause <T_Identifier> > cnfClauses, Set <DnfClause <T_Identifier> > dnfClauses,
Set <Literal <T_Identifier> > path)
{
if (vertex.IsOne())
{
// create DNF clause
var clause = new DnfClause <T_Identifier>(path);
dnfClauses.Add(clause);
}
else if (vertex.IsZero())
{
// create CNF clause
var clause = new CnfClause <T_Identifier>(new Set <Literal <T_Identifier> >(path.Select(l => l.MakeNegated())));
cnfClauses.Add(clause);
}
else
{
// keep on walking...
foreach (var successor in _context.GetSuccessors(vertex))
{
path.Add(successor.Literal);
FindAllPaths(successor.Vertex, cnfClauses, dnfClauses, path);
path.Remove(successor.Literal);
}
}
}
private void FindAllPaths(
Vertex vertex,
Set <CnfClause <T_Identifier> > cnfClauses,
Set <DnfClause <T_Identifier> > dnfClauses,
Set <Literal <T_Identifier> > path)
{
if (vertex.IsOne())
{
DnfClause <T_Identifier> element = new DnfClause <T_Identifier>(path);
dnfClauses.Add(element);
}
else if (vertex.IsZero())
{
CnfClause <T_Identifier> element = new CnfClause <T_Identifier>(new Set <Literal <T_Identifier> >(path.Select <Literal <T_Identifier>, Literal <T_Identifier> >((Func <Literal <T_Identifier>, Literal <T_Identifier> >)(l => l.MakeNegated()))));
cnfClauses.Add(element);
}
else
{
foreach (LiteralVertexPair <T_Identifier> successor in this._context.GetSuccessors(vertex))
{
path.Add(successor.Literal);
this.FindAllPaths(successor.Vertex, cnfClauses, dnfClauses, path);
path.Remove(successor.Literal);
}
}
}
/// <summary>
/// Converts the decision diagram (Vertex) wrapped by this converter and translates it into DNF
/// and CNF forms. I'll first explain the strategy with respect to DNF, and then explain how CNF
/// is achieved in parallel. A DNF sentence representing the expression is simply a disjunction
/// of every rooted path through the decision diagram ending in one. For instance, given the
/// following decision diagram:
/// A
/// 0/ \1
/// B C
/// 0/ \1 0/ \1
/// One Zero One
/// the following paths evaluate to 'One'
/// !A, !B
/// A, C
/// and the corresponding DNF is (!A.!B) + (A.C)
/// It is easy to compute CNF from the DNF of the negation, e.g.:
/// !((A.B) + (C.D)) iff. (!A+!B) . (!C+!D)
/// To compute the CNF form in parallel, we negate the expression (by swapping One and Zero sinks)
/// and collect negation of the literals along the path. In the above example, the following paths
/// evaluate to 'Zero':
/// !A, B
/// A, !C
/// and the CNF (which takes the negation of all literals in the path) is (!A+B) . (A+!C)
/// </summary>
private void InitializeNormalForms()
{
if (null == _cnf)
{
// short-circuit if the root is true/false
if (_vertex.IsOne())
{
// And() -> True
_cnf = new CnfSentence <T_Identifier>(Set <CnfClause <T_Identifier> > .Empty);
// Or(And()) -> True
var emptyClause = new DnfClause <T_Identifier>(Set <Literal <T_Identifier> > .Empty);
var emptyClauseSet = new Set <DnfClause <T_Identifier> >();
emptyClauseSet.Add(emptyClause);
_dnf = new DnfSentence <T_Identifier>(emptyClauseSet.MakeReadOnly());
}
else if (_vertex.IsZero())
{
// And(Or()) -> False
var emptyClause = new CnfClause <T_Identifier>(Set <Literal <T_Identifier> > .Empty);
var emptyClauseSet = new Set <CnfClause <T_Identifier> >();
emptyClauseSet.Add(emptyClause);
_cnf = new CnfSentence <T_Identifier>(emptyClauseSet.MakeReadOnly());
// Or() -> False
_dnf = new DnfSentence <T_Identifier>(Set <DnfClause <T_Identifier> > .Empty);
}
else
{
// construct clauses by walking the tree and constructing a clause for each sink
var dnfClauses = new Set <DnfClause <T_Identifier> >();
var cnfClauses = new Set <CnfClause <T_Identifier> >();
var path = new Set <Literal <T_Identifier> >();
FindAllPaths(_vertex, cnfClauses, dnfClauses, path);
_cnf = new CnfSentence <T_Identifier>(cnfClauses.MakeReadOnly());
_dnf = new DnfSentence <T_Identifier>(dnfClauses.MakeReadOnly());
}
}
}