// Returns a Variable that appears as a unit clause in the CNF.
// Assigned variables act as if they were removed from the clauses
private Variable GetUnitClause(CNF cnf)
{
foreach (var clause in cnf.Clauses)
{
if (!clause.IsTrue())
{
Variable ret = null;
int count = 0;
foreach (var variable in clause.Variables)
{
if (!variable.IsAssigned)
{
ret = variable;
count++;
if (count > 1)
{
break;
}
}
}
if (count == 1)
{
return(ret);
}
}
}
return(null);
}
// Branch method that creates new CNF formula, sets a variable in the original formula to false
// and sets the variable in the new formula to true and pushes the new formula to the stack (or enqueues it to shared queue in case of parallelism)
private void Branch(Stack <CNF> stack, Variable variable)
{
if (!parallel)
{
CNF branchedCNF = new CNF(stack.Peek()); // Copy the CNF formula
variable.SetValue(stack.Peek(), false); // Try setting the variable to false in the original CNF formula
stack.Push(branchedCNF);
variable.SetValue(stack.Peek(), true); // Try setting the variable to true in the new CNF formula
return; // Try solving the new CNF formula
}
else
{
CNF branchedCNF = new CNF(stack.Peek());
variable.SetValue(stack.Peek(), false);
variable.SetValue(branchedCNF, true);
lock (sharedModelQueue)
{
sharedModelQueue.Enqueue(branchedCNF); // Enqueue and inform about new work
Monitor.Pulse(sharedModelQueue);
}
return;
}
}
public async Task <DPLLResultHolder> SatisfiableParallel(CNF cnf)
{
parallel = true;
sharedModelQueue.Clear();
sharedModelQueue.Enqueue(cnf); // Initial formula (model) to solve
List <Task <DPLLResultHolder> > taskList = new List <Task <DPLLResultHolder> >();
CancellationTokenSource cancellationTokenSource = new CancellationTokenSource();
var token = cancellationTokenSource.Token;
var idleThreadsCounter = new IdleThreadsCounter();
for (int i = 0; i < Environment.ProcessorCount; i++)
{
taskList.Add(Task.Run(() => Solve(this, sharedModelQueue, idleThreadsCounter, token), token));
}
var taskArray = taskList.ToArray();
var finalTask = await Task.WhenAny(taskArray);
cancellationTokenSource.Cancel(); // Cancel other tasks still solving SAT
lock (sharedModelQueue)
{
Monitor.PulseAll(sharedModelQueue); // Wake tasks waiting at the queue, so they can cancel
}
parallel = false;
return(await finalTask);
}
// Sets the value of the variable in the CNF formula.
public void SetValue(CNF cnf, bool Value)
{
foreach (var variable in cnf.VariablesDict[this.Name]) // All variables in the formula with the same name get assigned
{
variable.Value = Value;
variable.IsAssigned = true;
}
}
// Sets the Assigned property for the variable in the whole CNF formula to false.
public void UnsetValue(CNF cnf)
{
if (this.IsAssigned == false)
{
return;
}
foreach (var variable in cnf.VariablesDict[this.Name])
{
variable.IsAssigned = false;
}
}
// Checks if a given CNF formula is SAT or not.
public DPLLResultHolder Satisfiable(CNF cnf)
{
Stack <CNF> stack = new Stack <CNF>();
stack.Push(cnf);
while (stack.Count != 0)
{
List <Clause> clauses = stack.Peek().Clauses;
if (AllClausesTrue(clauses)) // Formula is already satisfiable with current partial model
{
return(new DPLLResultHolder(true, stack.Peek()));
}
if (OneClauseFalse(clauses)) // One clause in the partial model is already false -> unsatisfiable
{
stack.Pop(); // Pops an unsat model and continues solving others on the stack
continue;
}
// Unit propagation
Variable variable = GetUnitClause(stack.Peek());
if (variable != null) // If we have found a unit clause, we can set it so it is true
{
variable.SetValue(stack.Peek(), variable.Sign);
continue;
}
// Pure literal elimination
variable = GetPureVariable(stack.Peek());
if (variable != null) // If we have found a pure literal, we can set it so it is true in all clauses.
{
variable.SetValue(stack.Peek(), variable.Sign);
continue;
}
variable = FindUnassigned(stack.Peek());
if (variable != null) // If we have found an unassigned variable, we are at the decision (branching) point
{
Branch(stack, variable);
continue;
}
else
{
stack.Pop(); // Otherwise no unassigned variable exist and we did not return SAT yet -> this model is UNSAT
}
}
return(new DPLLResultHolder(false, null));
}
// Finds the first unassigned variable and returns it
private Variable FindUnassigned(CNF cnf)
{
foreach (var pair in cnf.VariablesDict)
{
if (!pair.Value[0].IsAssigned)
{
return(pair.Value[0]);
}
}
return(null);
}
static void IndependentSetProblem()
{
PrintIndependentSetUsage();
IndependentSetProblem problem = new IndependentSetProblem();
problem.ReadInput(Console.In);
CNF problemCNF = problem.ConvertToCNF();
DPLL problemDPLL = new DPLL();
Task <DPLLResultHolder> parallelSAT = problemDPLL.SatisfiableParallel(problemCNF);
parallelSAT.Wait();
Console.WriteLine();
Console.WriteLine(problem.InterpretDPLLResult(parallelSAT.Result));
}
static void HamiltonianPathProblem()
{
PrintHamiltonianPathUsage();
HamiltonianPathProblem problem = new HamiltonianPathProblem();
problem.ReadInput(Console.In);
CNF problemCNF = problem.ConvertToCNF();
DPLL problemDPLL = new DPLL();
Task <DPLLResultHolder> parallelSAT = problemDPLL.SatisfiableParallel(problemCNF);
parallelSAT.Wait();
Console.WriteLine();
Console.WriteLine(problem.InterpretDPLLResult(parallelSAT.Result));
}
static void ThreeColorabilityProblem()
{
Print3ColorabilityUsage();
ThreeColorabilityProblem problem = new ThreeColorabilityProblem();
problem.ReadInput(Console.In);
CNF problemCNF = problem.ConvertToCNF();
DPLL problemDPLL = new DPLL();
Task <DPLLResultHolder> parallelSAT = problemDPLL.SatisfiableParallel(problemCNF);
parallelSAT.Wait();
Console.WriteLine();
Console.WriteLine(problem.InterpretDPLLResult(parallelSAT.Result));
}
// Deep copy constructor
// Constructs new CNF type with copied VALUE of clauses, variables, ...
public CNF(CNF cnf)
{
List <Clause> ClauseList = new List <Clause>();
foreach (var clause in cnf.Clauses)
{
List <Variable> VarList = new List <Variable>();
foreach (var variable in clause.Variables)
{
VarList.Add(new Variable(variable.Sign, variable.Value, variable.IsAssigned, variable.Name));
}
ClauseList.Add(new Clause(VarList));
}
Clauses = ClauseList;
VariablesDict = new Dictionary <string, List <Variable> >();
FillVariablesDict(Clauses);
NumberOfVariables = cnf.NumberOfVariables;
NumberOfClauses = cnf.NumberOfClauses;
}
static void SATSolver()
{
PrintSATSolverUsage();
CNF cnf = new CNF();
cnf.ReadFormula(Console.In);
// Sequential solution
/*CNF cnfCopy = new CNF(cnf);
* DPLL sequentialDPLL = new DPLL();
* DPLLResultHolder sequentialResult = sequentialDPLL.Satisfiable(cnfCopy);
* Console.WriteLine();
* Console.WriteLine(sequentialResult);*/
// Parallel solution
DPLL parallelDPLL = new DPLL();
Task <DPLLResultHolder> parallelSAT = parallelDPLL.SatisfiableParallel(cnf);
parallelSAT.Wait();
Console.WriteLine();
Console.WriteLine(parallelSAT.Result);
}
} // Holds the model of the CNF if CNF is satisfiable. If SAT is false, it should not be read (set to null preferably)
public DPLLResultHolder(bool SAT, CNF Model)
{
this.SAT = SAT;
this.Model = Model;
}
// Pure variable is a variable that occurs only with one polarity in the CNF formula.
// This function finds such variable.
private Variable GetPureVariable(CNF cnf)
{
bool IsPositive;
bool IsNegative;
foreach (var variableList in cnf.VariablesDict.Values)
{
if (variableList[0].IsAssigned) // If a variable is assigned we can skip it
{
continue;
}
IsPositive = false;
IsNegative = false;
foreach (var clause in cnf.Clauses)
{
if (!clause.IsTrue()) // If a clause is already true, we can skip it
{
foreach (var clauseVar in clause.Variables)
{
if (clauseVar.Name == variableList[0].Name)
{
if (clauseVar.Sign)
{
IsPositive = true;
}
else
{
IsNegative = true;
}
}
if (IsPositive && IsNegative) // We can skip this variable as it is no pure
{
break;
}
}
if (IsPositive && IsNegative)
{
break;
}
}
}
if (IsPositive && IsNegative)
{
continue;
}
else
{
var ret = new Variable(false, variableList[0].Name);
if (IsPositive)
{
ret.Sign = true;
}
return(ret);
}
}
return(null);
}
