/// <summary>
/// Removes useless symbols from the grammar.
/// Assumes that the language is nonempty.
/// </summary>
public ContextFreeGrammar RemoveUselessSymbols()
{
HashSet <Nonterminal> useful_backwards = new HashSet <Nonterminal>();
//Lemma 4.1, p. 88, Hopcroft-Ullman
#region backward reachability
var variableNodeMap = new Dictionary <Nonterminal, VariableNode>();
foreach (Nonterminal v in this.variables)
{
variableNodeMap[v] = new VariableNode();
}
List <ProductionNode> productionLeaves = new List <ProductionNode>();
foreach (Nonterminal v in this.variables)
{
VariableNode parent = variableNodeMap[v];
foreach (Production p in this.productionMap[v])
{
var children = Array.ConvertAll(new List <Nonterminal>(p.GetVariables()).ToArray(), w => variableNodeMap[w]);
ProductionNode pn = new ProductionNode(parent, children);
if (children.Length == 0)
{
productionLeaves.Add(pn);
}
else
{
foreach (VariableNode child in children)
{
child.parents.Add(pn);
}
}
}
}
foreach (ProductionNode leaf in productionLeaves)
{
leaf.PropagateMark();
}
foreach (Nonterminal v in this.variables)
{
if (variableNodeMap[v].isMarked)
{
useful_backwards.Add(v);
}
}
#endregion
if (!useful_backwards.Contains(this.startSymbol))
{
throw new AutomataException(AutomataExceptionKind.LanguageOfGrammarIsEmpty);
}
ContextFreeGrammar g1 = this.RestrictToVariables(useful_backwards);
HashSet <Nonterminal> useful_forwards = new HashSet <Nonterminal>();
//Lemma 4.2, p. 89, Hopcroft-Ullman
#region forward reachability
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(g1.StartSymbol);
useful_forwards.Add(g1.StartSymbol);
while (stack.Count > 0)
{
Nonterminal v = stack.Pop();
foreach (Production p in g1.GetProductions(v))
{
foreach (Nonterminal u in p.GetVariables())
{
if (!useful_forwards.Contains(u))
{
useful_forwards.Add(u);
stack.Push(u);
}
}
}
}
#endregion
ContextFreeGrammar g2 = g1.RestrictToVariables(useful_forwards);
return(g2);
}