// We assume that the formula is in QBF
// (But no other assumption)
public static bool QBFSAT(FormulaNode formula)
{
// First convert the formula to PNF
formula = formula.NNF().PNF();
// Then convert it to QBCNF
QBCNFormula qbcnf = ConvertToCNF(formula);
return(QBFSolver.Solve(qbcnf));
}
// Write the given QCNF formula into a file in QDIMACS format
public static void CreateQDIMACS(QBCNFormula qbcnf, string filename)
{
using (StreamWriter sw = File.CreateText(filename))
{
// Write preamble
sw.WriteLine("p cnf " + qbcnf.quantifiers.Count +
" " + qbcnf.propositional.Count);
// Write prefix
if (qbcnf.quantifiers.Count > 0)
{
char lastQuant = qbcnf.quantifiers[0][0];
sw.Write(lastQuant + " " + qbcnf.quantifiers[0].Substring(1));
for (int i = 1; i < qbcnf.quantifiers.Count; i++)
{
if (qbcnf.quantifiers[i][0] != lastQuant)
{
sw.Write(" 0");
sw.WriteLine();
sw.Write(qbcnf.quantifiers[i][0] + " ");
lastQuant = qbcnf.quantifiers[i][0];
}
sw.Write(" " + qbcnf.quantifiers[i].Substring(1));
}
sw.Write(" 0");
sw.WriteLine();
}
// Write clauses
foreach (ISet <string> clause in qbcnf.propositional)
{
foreach (string literal in clause)
{
sw.Write(literal + " ");
}
sw.Write("0");
sw.WriteLine();
}
}
}
// Get a PNF formula and return its QBCNF
public static QBCNFormula ConvertToCNF(FormulaNode formula)
{
QBCNFormula res = new QBCNFormula();
FormulaNode node = formula;
ISet <string> addedVars;
res.quantifiers = new List <string>();
while (node.GetLogicOperator() == LogicOperator.EXISTS ||
node.GetLogicOperator() == LogicOperator.ALL)
{
if (node.GetLogicOperator() == LogicOperator.EXISTS)
{
res.quantifiers.Add("e" + node.GetName());
}
else
{
res.quantifiers.Add("a" + node.GetName());
}
node = node[0];
}
if (res.quantifiers.Count != formula.GetVariables().Count)
{
throw new Exception("Non-quantified variables in formula!");
}
res.propositional = TseytinTransformation(node, out addedVars);
//Replace strings with numbers
ISet <string> literals = res.GetLiterals();
Dictionary <string, string> changes = new Dictionary <string, string>();
foreach (string literal in literals)
{
int n;
bool isNum = int.TryParse(literal, out n);
if (!changes.ContainsKey(literal) & !isNum)
{
int ticket = ticketMachine.GetTicket();
if (literal[0] != '-')
{
changes.Add(literal, ticket.ToString());
changes.Add("-" + literal, (-ticket).ToString());
}
else
{
changes.Add(literal, (-ticket).ToString());
changes.Add(literal.Substring(1), ticket.ToString());
}
}
}
res.ReplaceLiterals(changes);
// Quantify the Tseytin variables with EXISTS
foreach (string var in addedVars)
{
res.quantifiers.Add("e" + var);
}
return(res);
}
