/// <summary>
/// Removes all productions of the form A->B where A and B are variables.
/// Removes also all the useless symbols after the unit production elimination.
/// Assumes that the grammar has no epsilon productions.
/// </summary>
public ContextFreeGrammar RemoveUnitProductions()
{
var newProductions = new Dictionary <Nonterminal, List <Production> >();
foreach (Nonterminal v in variables)
{
newProductions[v] = new List <Production>();
}
foreach (Nonterminal v in variables)
{
foreach (Nonterminal u in GetUnitClosure(v))
{
foreach (Production p in productionMap[u])
{
if (!p.IsUnit)
{
newProductions[v].Add(new Production(v, p.Rhs));
}
}
}
}
ContextFreeGrammar g = new ContextFreeGrammar(variables, startSymbol, newProductions);
ContextFreeGrammar g1 = g.RemoveUselessSymbols();
return(g1);
}
/// <summary>
/// Removes epsilon productions and then removes useless symbols.
/// Assumes that the grammar does not accept the empty string and that the language is nonempty.
/// </summary>
public ContextFreeGrammar RemoveEpsilonsAndUselessSymbols()
{
//--- eliminate epsilon productions
//based on algo in Theorem 4.3, p. 90-91, Hopcroft-Ullman
HashSet <Nonterminal> nullables = GetNullables();
Dictionary <Nonterminal, List <Production> > prodMap = new Dictionary <Nonterminal, List <Production> >();
foreach (Nonterminal v in this.variables)
{
prodMap[v] = new List <Production>(EliminateNullables(v, nullables));
}
ContextFreeGrammar g1 = new ContextFreeGrammar(this.variables, this.StartSymbol, prodMap);
ContextFreeGrammar g2 = g1.RemoveUselessSymbols();
return(g2);
}
/// <summary>
/// Produces the EGNF (Extended Greibach Normal Form) for the grammar g.
/// Implements a variation of the Blum-Koch algorithm.
/// (Inf. and Comp. vol.150, pp.112-118, 1999)
/// </summary>
/// <param name="g">the grammar to be normalized</param>
/// <param name="removeEpsilonsAndUselessSymbols">if true, first removes epsilons and useless symbols, otherwise assumes that epsilons do not occur</param>
/// <returns>Extended Greibach Normal Form of g</returns>
public static ContextFreeGrammar MkEGNF(ContextFreeGrammar g, bool removeEpsilonsAndUselessSymbols)
{
if (removeEpsilonsAndUselessSymbols)
{
g = g.RemoveEpsilonsAndUselessSymbols();
}
if (g.IsInGNF())
{
return(g);
}
var leavesP = new List <Production>();
var revP = new Dictionary <Nonterminal, List <Pair <GrammarSymbol[], Nonterminal> > >();
int nonterminalID = 0;
#region compute leavesP and revP
foreach (Nonterminal v in g.variables)
{
revP[v] = new List <Pair <GrammarSymbol[], Nonterminal> >();
}
foreach (Production p in g.GetProductions())
{
if (!(p.First is Nonterminal))
{
leavesP.Add(p);
}
else
{
revP[(Nonterminal)p.First].Add(new Pair <GrammarSymbol[], Nonterminal>(p.Rest, p.Lhs));
}
}
#endregion
var W = new Dictionary <Nonterminal, HashSet <Nonterminal> >();
var startSymbol = new Dictionary <Nonterminal, Nonterminal>();
#region create new start symbols and compute unit closures
foreach (Nonterminal v in g.variables)
{
W[v] = g.GetUnitClosure(v);
startSymbol[v] = new Nonterminal(nonterminalID++);
}
#endregion
var P = new Dictionary <Nonterminal, List <Production> >();
#region construct intermediate productions in P for each variable B
foreach (Nonterminal B in g.variables)
{
var S_B = startSymbol[B];
var W_B = W[B]; //unit closure of B
var Bvar = new Dictionary <Nonterminal, Nonterminal>();
Stack <Nonterminal> stack = new Stack <Nonterminal>();
HashSet <Nonterminal> visited = new HashSet <Nonterminal>();
var S_B_list = new List <Production>();
P[S_B] = S_B_list;
foreach (Production p in leavesP)
{
S_B_list.Add(new Production(S_B, p.Rhs, Lookup(Bvar, p.Lhs, ref nonterminalID)));
if (visited.Add(p.Lhs))
{
stack.Push(p.Lhs);
}
if (W_B.Contains(p.Lhs))
{
S_B_list.Add(new Production(S_B, p.Rhs));
}
}
while (stack.Count > 0)
{
Nonterminal C = stack.Pop();
Nonterminal C_B = Lookup(Bvar, C, ref nonterminalID);
List <Production> C_B_list;
if (!P.TryGetValue(C_B, out C_B_list))
{
C_B_list = new List <Production>();
P[C_B] = C_B_list;
}
foreach (var t in revP[C])
{
Nonterminal D = t.Second;
Nonterminal D_B = Lookup(Bvar, D, ref nonterminalID);
C_B_list.Add(new Production(C_B, t.First, D_B));
if (t.First.Length > 0 && W_B.Contains(D))
{
C_B_list.Add(new Production(C_B, t.First));
}
if (visited.Add(D))
{
stack.Push(D);
}
}
}
}
#endregion
//produce the union of P and g.productionMap in H
//and replace each production 'A ::= B alpha' by 'A ::= S_B alpha"
var Hprods = new Dictionary <Nonterminal, List <Production> >();
#region compute Hprods
foreach (Nonterminal A in g.variables)
{
var A_prods = new List <Production>();
Hprods[A] = A_prods;
foreach (Production p in g.productionMap[A])
{
if (p.First is Nonterminal && !p.IsUnit)
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
rhs[0] = startSymbol[(Nonterminal)p.First];
Array.Copy(p.Rhs, 1, rhs, 1, rhs.Length - 1);
Production q = new Production(p.Lhs, rhs);
A_prods.Add(q);
}
else
{
A_prods.Add(p);
}
}
}
foreach (Nonterminal A in P.Keys)
{
var A_prods = new List <Production>();
Hprods[A] = A_prods;
foreach (Production p in P[A])
{
if (p.First is Nonterminal && !p.IsUnit)
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
rhs[0] = startSymbol[(Nonterminal)p.First];
Array.Copy(p.Rhs, 1, rhs, 1, rhs.Length - 1);
Production q = new Production(p.Lhs, rhs);
A_prods.Add(q);
}
else
{
A_prods.Add(p);
}
}
}
#endregion
ContextFreeGrammar H = new ContextFreeGrammar(new List <Nonterminal>(Hprods.Keys), g.startSymbol, Hprods);
//Console.WriteLine("--------- H:");
//H.Display(Console.Out);
//eliminate useless symbols from H
//this may dramatically decrease the number of productions
ContextFreeGrammar H1 = H.RemoveUselessSymbols();
//Console.WriteLine("---------- H1:");
//H1.Display(Console.Out);
List <Nonterminal> egnfVars = new List <Nonterminal>();
Dictionary <Nonterminal, List <Production> > egnfProds = new Dictionary <Nonterminal, List <Production> >();
Stack <Nonterminal> egnfStack = new Stack <Nonterminal>();
HashSet <Nonterminal> egnfVisited = new HashSet <Nonterminal>();
egnfStack.Push(H1.startSymbol);
egnfVisited.Add(H1.startSymbol);
egnfVars.Add(H1.startSymbol);
egnfProds[H1.startSymbol] = new List <Production>();
#region eliminate temp start symbols and produce the EGNF form
while (egnfStack.Count > 0)
{
var A = egnfStack.Pop();
List <Production> A_prods = egnfProds[A];
foreach (Production p in H1.productionMap[A])
{
if (!(p.First is Nonterminal) || p.IsUnit)
{
A_prods.Add(p);
foreach (Nonterminal x in p.GetVariables())
{
if (egnfVisited.Add(x))
{
egnfStack.Push(x);
egnfVars.Add(x);
egnfProds[x] = new List <Production>();
}
}
}
else
{
Nonterminal S_B = (Nonterminal)p.First; //here we know that S_B is a temp start symbol
foreach (Production t in H1.productionMap[S_B])
{
int k = t.Rhs.Length;
GrammarSymbol[] rhs = new GrammarSymbol[k + p.Rhs.Length - 1];
for (int i = 0; i < k; i++)
{
rhs[i] = t.Rhs[i];
}
for (int i = 1; i < p.Rhs.Length; i++)
{
rhs[k + i - 1] = p.Rhs[i];
}
Production q = new Production(A, rhs);
A_prods.Add(q);
foreach (Nonterminal x in q.GetVariables())
{
if (egnfVisited.Add(x))
{
egnfStack.Push(x);
egnfVars.Add(x);
egnfProds[x] = new List <Production>();
}
}
}
}
}
}
#endregion
ContextFreeGrammar egnf = new ContextFreeGrammar(egnfVars, H1.startSymbol, egnfProds);
return(egnf);
}