/// <summary>
/// Produces the CNF (Chomsky Normal Form) for the grammar g.
/// It first eliminates epsilons, useless symbols, and unit productions.
/// If Assumes that there are no epsilons, useless symbols or unit productions
/// </summary>
public static ContextFreeGrammar MkCNF(ContextFreeGrammar g, bool removeEpsilonsUselessSymbolsUnitsProductions)
{
if (removeEpsilonsUselessSymbolsUnitsProductions)
{
g = g.RemoveEpsilonsAndUselessSymbols();
g = g.RemoveUnitProductions();
}
var productions = new Dictionary <Nonterminal, List <Production> >();
List <Nonterminal> variables = new List <Nonterminal>(g.variables);
foreach (Nonterminal v in g.variables)
{
productions[v] = new List <Production>();
}
int nonterminalID = 0;
//Implements algo in Theorem 4.5, page 92-93, in Hopcroft-Ullman
#region make productions of the form V --> V0...Vn or V --> a
var freshVarMap = new Dictionary <GrammarSymbol, Nonterminal>();
foreach (Nonterminal v in g.variables)
{
foreach (Production p in g.productionMap[v])
{
if (p.ContainsNoExprinals || p.IsCNF)
{
productions[v].Add(p);
}
else
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
for (int i = 0; i < rhs.Length; i++)
{
if (p.Rhs[i] is Nonterminal)
{
rhs[i] = p.Rhs[i];
}
else
{
Nonterminal u;
if (!freshVarMap.TryGetValue(p.Rhs[i], out u))
{
u = new Nonterminal(nonterminalID++);
freshVarMap[p.Rhs[i]] = u;
variables.Add(u);
var prods = new List <Production>();
prods.Add(new Production(u, p.Rhs[i]));
productions[u] = prods;
}
rhs[i] = u;
}
}
productions[v].Add(new Production(v, rhs));
}
}
}
#endregion
var productionsCNF = new Dictionary <Nonterminal, List <Production> >();
List <Nonterminal> variablesCNF = new List <Nonterminal>(variables);
foreach (Nonterminal v in variablesCNF)
{
productionsCNF[v] = new List <Production>();
}
#region replace V --> V0V1...Vn (n > 2), by V --> V0U0, U0 --> V1U1, ..., Un-2 --> Vn-1Vn
foreach (Nonterminal v in variables)
{
foreach (Production p in productions[v])
{
if (p.IsCNF)
{
productionsCNF[v].Add(p);
}
else
{
Nonterminal x = v;
Nonterminal y = new Nonterminal(nonterminalID++);
variablesCNF.Add(y);
productionsCNF[y] = new List <Production>();
for (int i = 0; i < p.Rhs.Length - 2; i++)
{
productionsCNF[x].Add(new Production(x, p.Rhs[i], y));
if (i < p.Rhs.Length - 3)
{
x = y;
y = new Nonterminal(nonterminalID++);
variablesCNF.Add(y);
productionsCNF[y] = new List <Production>();
}
}
productionsCNF[y].Add(new Production(y, p.Rhs[p.Rhs.Length - 2], p.Rhs[p.Rhs.Length - 1]));
}
}
}
#endregion
ContextFreeGrammar cnf = new ContextFreeGrammar(variablesCNF, g.startSymbol, productionsCNF);
return(cnf);
}
