private static ClauseSet.ClauseOperationResult propagateUnitClauses(ClauseSet clauses,
Variables variablesMap)
{
var unitClausuleRuleResult = ClauseSet.ClauseOperationResult.OperationNotUsed;
while (true)
{
var toPropagateUnitClause = clauses.SelectUnitClause(variablesMap);
if (toPropagateUnitClause == null)
{
break;
}
unitClausuleRuleResult = ClauseSet.ClauseOperationResult.OperationSuccess;
var singleLiteral = toPropagateUnitClause.FirstLiteral;
#if PROGRESS_TRACE
Trace.WriteLine($"Trying unit propagation of the clause with literal: {singleLiteral}");
#endif
variablesMap.SetToValue(singleLiteral.Name, singleLiteral.IsTrue);
removeClausulesSatisfiedByLiteral(clauses, singleLiteral);
clauses.AddClause(toPropagateUnitClause);
var deleteLiteralResult = clauses.DeleteLiteralFromClauses(~singleLiteral);
if (deleteLiteralResult == ClauseSet.ClauseOperationResult.MinOneEmptyClausuleFound)
{
return(deleteLiteralResult);
}
}
return(unitClausuleRuleResult);
}
private static Literal?chooseNewLiteral(ClauseSet clauses,
Variables variablesMap)
{
var selectedLiteral = clauses.SelectUnusedLiteral(variablesMap);
return(selectedLiteral);
}
public SolverState(ClauseSet clauses,
Variables variablesMap,
int depth,
bool literalAdded)
{
Clauses = clauses;
VariablesMap = variablesMap;
Depth = depth;
LiteralAdded = literalAdded;
}
private static void removeClausulesSatisfiedByLiteral(ClauseSet clausules,
Literal literal)
{
#if PROGRESS_TRACE
Trace.WriteLine($"Deleting clausules with literal: {literal}");
#endif
clausules.DeleteClausesWithLiteral(literal);
#if PROGRESS_TRACE
Trace.WriteLine($"Remaining ClausulesSet: {clausules.ClausesCount}");
#endif
}
public bool IsModelFor(ClauseSet clauseSet)
{
foreach (var literals in clauseSet.Clauses.Select(clause => clause.Literals))
{
var isClauseSatisfied =
literals.Any(literal => ModelValues.Single(val => val.Name == literal.Name) == literal);
if (!isClauseSatisfied)
{
return(false);
}
}
return(true);
}
private static IEnumerable <ModelValue> generateModelValues(ClauseSet clausesSet,
Variables variablesMap)
{
var modelValues = clausesSet.Clauses.Select(clause =>
{
var literal = clause.FirstLiteral;
return(new ModelValue(literal.Name, literal.IsTrue));
}).Distinct().ToArray();
var retModelValues = modelValues.Concat(variablesMap
.VariableNames().Where(varName => !modelValues.Any(modelValue =>
modelValue
.Name.Equals(varName)))
.Select(varName => new ModelValue(varName, true))).ToArray();
return(retModelValues);
}
public static Model?Solve(ClauseSet clauseSet, Variables variablesMap)
{
var models = generateModels(variablesMap, clauseSet);
#if DUMP_MODELS
foreach (var model in models)
{
if (model.IsModelFor(clauseSet))
{
Console.WriteLine("Found model (dump)...");
Console.WriteLine(model);
}
}
#endif
return(models.FirstOrDefault(model => model.IsModelFor(clauseSet)));
}
private static IEnumerable <Model> generateModels(Variables variablesMap,
ClauseSet clauses)
{
const int VALUATIONS = 2;
BigInteger ONE = 1;
var variablesMapCount = variablesMap.VariablesCount;
var singleLiterals = clauses.Clauses.Where(clause => clause.Literals.Count == 1)
.Select(clause => clause.FirstLiteral)
.ToDictionary(literal => literal.Name);
var numberOfModels = (BigInteger)Math.Pow(VALUATIONS, variablesMapCount);
for (BigInteger modelIndex = 0; modelIndex < numberOfModels; modelIndex++)
{
Console.WriteLine(modelIndex);
var modelValues = new ModelValue[variablesMapCount];
var varIndex = 0;
var haveModel = true;
foreach (var varName in variablesMap.VariableNames())
{
var isVarTrue = (modelIndex & (ONE << varIndex)) != 0;
var modelValue = new ModelValue(varName, isVarTrue);
modelValues[varIndex] = modelValue;
if (singleLiterals.TryGetValue(modelValue.Name, out var literal))
{
if (literal.IsTrue != modelValue.IsTrue)
{
Console.WriteLine($"Declined: {literal.Name}");
haveModel = false;
break;
}
}
varIndex++;
}
if (!haveModel)
{
continue;
}
var model = new Model(modelIndex, modelValues);
Console.WriteLine("Evaluating...");
yield return(model);
}
}
private static bool handlePureLiterals(ClauseSet clauses,
Variables variablesMap)
{
var pureLiteralsInClauses = clauses.GetPureLiterals(variablesMap);
var hasPureLiterals = false;
foreach (var pureLiteral in pureLiteralsInClauses)
{
#if PROGRESS_TRACE
Trace.WriteLine($"Trying pure literal strategy: {pureLiteral}");
#endif
variablesMap.SetToValue(pureLiteral.Name, pureLiteral.IsTrue);
hasPureLiterals = true;
removeClausulesSatisfiedByLiteral(clauses, pureLiteral);
}
return(hasPureLiterals);
}
private static bool isConsistentSetOfLiterals(ClauseSet clauses)
{
return(clauses.IsConsistentSetOfLiterals());
}
private static bool hasEmptyClause(ClauseSet clauses)
{
return(clauses.HasEmptyClause());
}
public static Model?Solve(ClauseSet initialClauses,
Variables variablesMap)
{
if (initialClauses == null)
{
throw new ArgumentNullException(nameof(initialClauses));
}
if (variablesMap == null)
{
throw new ArgumentNullException(nameof(variablesMap));
}
const int INITIAL_LEVEL = 0;
var solverStack = ImmutableStack <SolverState> .Empty;
var initialSolverState = new SolverState(initialClauses,
variablesMap,
INITIAL_LEVEL,
true);
solverStack = solverStack.Push(initialSolverState);
while (!solverStack.IsEmpty)
{
solverStack = solverStack.Pop(out var currentState);
#if PROGRESS_TRACE
Trace.WriteLine($"Iteration depth: {currentState.Depth}");
#endif
var clauses = currentState.Clauses;
var variables = currentState.VariablesMap;
if (isConsistentSetOfLiterals(clauses))
{
#if PROGRESS_TRACE
Trace.WriteLine("Found model...");
#endif
return(new Model(0, generateModelValues(clauses, variables)));
}
if (hasEmptyClause(clauses))
{
#if PROGRESS_TRACE
Trace.WriteLine("Empty clause found. Backtracking...");
#endif
continue;
}
var unitClauseRuleResult = propagateUnitClauses(clauses, variables);
if (unitClauseRuleResult == ClauseSet.ClauseOperationResult.MinOneEmptyClausuleFound)
{
#if PROGRESS_TRACE
Trace.WriteLine("Empty clause (after unit rule) found. Backtracking...");
#endif
continue;
}
handlePureLiterals(clauses, variables);
var chosenLiteral = chooseNewLiteral(clauses,
variables);
if (chosenLiteral == null)
{
if (hasEmptyClause(clauses))
{
#if PROGRESS_TRACE
Trace.WriteLine("Empty clause found. Backtracking...");
#endif
continue;
}
#if PROGRESS_TRACE
Trace.WriteLine("Found model...");
#endif
return(new Model(0, generateModelValues(clauses, variables)));
}
#if PROGRESS_TRACE
Trace.WriteLine($"Chosen literal {chosenLiteral.Name}");
#endif
var newClauseNeg = clauses.CloneWithClause(new Clause(new List <Literal> {
~chosenLiteral
}));
var newClausePos = clauses.CloneWithClause(new Clause(new List <Literal> {
chosenLiteral
}));
solverStack =
solverStack.Push(new
SolverState(newClauseNeg,
variablesMap.Clone(),
currentState.Depth + 1,
true));
solverStack = solverStack.Push(new
SolverState(newClausePos,
variablesMap.Clone(),
currentState.Depth + 1,
true));
}
return(null);
}
