private bool PureLiteral(Cnf cnf, Formula literal)
{
var negation = NegateLiteral(literal);
foreach (var clause in cnf.Clauses)
{
foreach (var l in clause.Literals)
{
if (clause.LiteralEquals(l, negation))
{
return(false);
}
}
}
return(true);
}
private IEnumerable <Formula> PureLiterals(Cnf cnf)
{
var result = new List <Formula>();
foreach (var clause in cnf.Clauses)
{
foreach (var literal in clause.Literals)
{
if (PureLiteral(cnf, literal))
{
result.Add(literal);
}
}
}
return(result);
}
public static void Display()
{
Console.WriteLine(string.Empty);
Console.WriteLine(" Listing 2-12: Creating Formula (p ∨ q ∨ r) ∧ (p ∨ q ∨ ¬r) ∧ (p ∨ ¬q ∨ r) ∧ (p ∨ ¬q ∨ ¬r) ∧ (¬p ∨ q ∨ r) ∧ (¬p ∨ q ∨ ¬r) ∧ (¬p ∨ ¬q ∨ r) and Finding Out If It's Satisfiable Using the DPLL Algorithm");
Console.WriteLine(string.Empty);
var p = new Variable(true)
{
Name = "p"
};
var q = new Variable(true)
{
Name = "q"
};
var r = new Variable(true)
{
Name = "r"
};
var f1 = new Or(p, new Or(q, r));
var f2 = new Or(p, new Or(q, new Not(r)));
var f3 = new Or(p, new Or(new Not(q), r));
var f4 = new Or(p, new Or(new Not(q), new Not(r)));
var f5 = new Or(new Not(p), new Or(q, r));
var f6 = new Or(new Not(p), new Or(q, new Not(r)));
var f7 = new Or(new Not(p), new Or(new Not(q), r));
var formula = new And(f1, new And(f2, new And(f3, new And(f4, new And(f5, new And(f6, f7))))));
var nnf = formula.ToNnf();
Console.WriteLine("NNF: " + nnf);
nnf = nnf.ToCnf();
var cnf = new Cnf(nnf as And);
cnf.SimplifyCnf();
Console.WriteLine("CNF: " + cnf);
Console.WriteLine("SAT: " + cnf.Dpll());
}
private Tuple <Cnf, Cnf> SplittingOnLiteral(Cnf cnf, Formula literal)
{
// List of clauses containing literal
var @in = new List <Clause>();
// List of clauses containing Not(literal)
var inNegated = new List <Clause>();
// List of clauses not containing literal nor Not(literal)
var @out = new List <Clause>();
var negated = NegateLiteral(literal);
foreach (var clause in cnf.Clauses)
{
if (clause.Contains(literal))
{
@in.Add(clause);
}
else if (clause.Contains(negated))
{
inNegated.Add(clause);
}
else
{
@out.Add(clause);
}
}
var inCnf = new Cnf {
Clauses = @in
};
var outCnf = new Cnf {
Clauses = @inNegated
};
inCnf.Join(@out);
outCnf.Join(@out);
return(new Tuple <Cnf, Cnf>(inCnf, outCnf));
}
private Tuple <Cnf, int> OneLiteral(Cnf cnf)
{
var unitLiteral = UnitClause(cnf);
if (unitLiteral == null)
{
return(new Tuple <Cnf, int>(cnf, 1));
}
var newCnf = new Cnf();
while (unitLiteral != null)
{
var clausesToRemove = new List <int>();
var i = 0;
// 1st Loop - Finding clauses where the
// unit literal is, these clauses will not be
// considered in the new Cnf
foreach (var clause in cnf.Clauses)
{
if (clause.Literals.Any(literal => clause.
LiteralEquals(literal, unitLiteral)))
{
clausesToRemove.Add(i);
}
i++;
}
// New Cnf after removing every clause where
// unit literal is
newCnf = new Cnf();
// 2nd Loop - Leave clause that do not include
// the unit literal
for (var j = 0; j < cnf.Clauses.Count; j++)
{
if (!clausesToRemove.Contains(j))
{
newCnf.Clauses.Add(cnf.Clauses[j]);
}
}
// No clauses, which implies SAT
if (newCnf.Clauses.Count == 0)
{
return(new Tuple <Cnf, int>(newCnf, 0));
}
// Remove negation of unit literal from
// remaining clauses
var unitNegated = NegateLiteral(unitLiteral);
var clausesNoLitNeg = new List <Clause>();
foreach (var clause in newCnf.Clauses)
{
var newClause = new Clause();
// Leaving every literal except the unit
// literal negated
foreach (var literal in clause.Literals)
{
if (!clause.LiteralEquals(literal,
unitNegated))
{
newClause.Literals.Add(literal);
}
}
clausesNoLitNeg.Add(newClause);
}
newCnf.Clauses = new List <Clause>(clausesNoLitNeg);
// Resetting variables for next stage
cnf = newCnf;
unitLiteral = UnitClause(cnf);
// Empty clause found
if (cnf.Clauses.Any(c => c.Literals.Count == 0))
{
return(new Tuple <Cnf, int>(newCnf, -1));
}
}
return(new Tuple <Cnf, int>(newCnf, 1));
}