/// <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>
/// Restrict the grammar to the given variables.
/// </summary>
public ContextFreeGrammar RestrictToVariables(HashSet <Nonterminal> varSet)
{
Dictionary <Nonterminal, List <Production> > productions = new Dictionary <Nonterminal, List <Production> >();
foreach (Nonterminal v in varSet)
{
productions[v] = new List <Production>();
}
List <Nonterminal> varList = new List <Nonterminal>();
foreach (Nonterminal v in variables)
{
if (varSet.Contains(v))
{
varList.Add(v);
foreach (Production p in productionMap[v])
{
if (p.AreVariablesContainedIn(varSet))
{
productions[v].Add(p);
}
}
}
}
if (!productions.ContainsKey(startSymbol) || productions[startSymbol].Count == 0)
{
throw new ArgumentException("Start symbol is not the LHS of any production.");
}
ContextFreeGrammar g = new ContextFreeGrammar(varList, startSymbol, productions);
return(g);
}
/// <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>
/// Returns MkCNF(g, true)
/// </summary>
public static ContextFreeGrammar MkCNF(ContextFreeGrammar g)
{
return MkCNF(g, true);
}
/// <summary>
/// Restrict the grammar to the given variables.
/// </summary>
public ContextFreeGrammar RestrictToVariables(HashSet<Nonterminal> varSet)
{
Dictionary<Nonterminal, List<Production>> productions = new Dictionary<Nonterminal, List<Production>>();
foreach (Nonterminal v in varSet)
productions[v] = new List<Production>();
List<Nonterminal> varList = new List<Nonterminal>();
foreach (Nonterminal v in variables)
if (varSet.Contains(v))
{
varList.Add(v);
foreach (Production p in productionMap[v])
if (p.AreVariablesContainedIn(varSet))
productions[v].Add(p);
}
if (!productions.ContainsKey(startSymbol) || productions[startSymbol].Count == 0)
throw new ArgumentException("Start symbol is not the LHS of any production.");
ContextFreeGrammar g = new ContextFreeGrammar(varList, startSymbol, productions);
return g;
}
/// <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 GNF (Greibach Normal Form) for the grammar g.
/// If g is not already in GNF, first makes CNF.
/// Implements a variation of the Koch-Blum algorithm. (STACS 97, pp. 47-54)
/// </summary>
/// <param name="g"></param>
/// <param name="removeEpsilonsUselessSymbolsUnitsProductions"></param>
/// <returns></returns>
public static ContextFreeGrammar MkGNF(ContextFreeGrammar g, bool removeEpsilonsUselessSymbolsUnitsProductions)
{
if (removeEpsilonsUselessSymbolsUnitsProductions)
g = g.RemoveEpsilonsAndUselessSymbols().RemoveUnitProductions();
if (g.IsInGNF())
return g;
ContextFreeGrammar cnf = MkCNF(g,false);
var Vars = cnf.variables;
int nonterminalID = 0;
var M = new Dictionary<Nonterminal, Automaton<GrammarSymbol>>();
#region construct the automata M[B] for all variables B
int id = 0;
var initStateMap = new Dictionary<Nonterminal, int>();
var finalStateMap = new Dictionary<Nonterminal, int>();
foreach (Nonterminal B in Vars)
{
initStateMap[B] = id++;
finalStateMap[B] = id++;
}
var movesOfM = new Dictionary<Nonterminal, List<Move<GrammarSymbol>>>();
foreach (Nonterminal B in Vars)
movesOfM[B] = new List<Move<GrammarSymbol>>();
#region construct the moves of the automata
foreach (Nonterminal B in Vars)
{
var variableToStateMap = new Dictionary<Nonterminal, int>();
Stack<Nonterminal> stack = new Stack<Nonterminal>();
stack.Push(B);
int initState = initStateMap[B];
variableToStateMap[B] = finalStateMap[B];
while (stack.Count > 0)
{
Nonterminal C = stack.Pop();
foreach (Production p in cnf.GetProductions(C))
{
if (p.IsSingleExprinal)
movesOfM[B].Add(Move<GrammarSymbol>.Create(initState, variableToStateMap[C], p.First));
else
{
Nonterminal D = (Nonterminal)p.First; //using the fact that the grammar is in CNF
if (!variableToStateMap.ContainsKey(D))
{
//visit all variables reachable that have not already been visited
variableToStateMap.Add(D,id++);
stack.Push(D);
}
GrammarSymbol E = p.Rhs[1];
movesOfM[B].Add(Move<GrammarSymbol>.Create(variableToStateMap[D], variableToStateMap[C], E));
}
}
}
}
#endregion
foreach (Nonterminal B in Vars)
M[B] = Automaton<GrammarSymbol>.Create(null, initStateMap[B], new int[] {finalStateMap[B]}, movesOfM[B]);
#endregion
var G_ = new Dictionary<Nonterminal, ContextFreeGrammar>();
#region construct corresponding intermediate grammars G_[B] corresponding to M[B]
foreach (Nonterminal B in Vars)
{
var MB = M[B];
bool MBfinalStateHasVariableMoves = FinalStateHasVariableMoves(MB);
var productions = new Dictionary<Nonterminal, List<Production>>();
Nonterminal startSymbol = new Nonterminal(nonterminalID++);
var vars = new List<Nonterminal>();
vars.Add(startSymbol);
productions[startSymbol] = new List<Production>();
foreach (var move in MB.GetMovesFrom(MB.InitialState))
{
if (move.TargetState == MB.FinalState)
productions[startSymbol].Add(new Production(startSymbol, move.Label));
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
var C = new Nonterminal("Q" + move.TargetState);
productions[startSymbol].Add(new Production(startSymbol, move.Label, C));
if (!productions.ContainsKey(C))
{
productions[C] = new List<Production>();
vars.Add(C);
}
}
}
foreach (int state in MB.States)
if (state != MB.InitialState)
foreach (Move<GrammarSymbol> move in MB.GetMovesFrom(state))
{
Nonterminal D = new Nonterminal("Q" + state);
Nonterminal C = new Nonterminal("Q" + move.TargetState);
if (!productions.ContainsKey(D))
{
productions[D] = new List<Production>();
vars.Add(D);
}
Nonterminal E = (Nonterminal)move.Label;
if (move.TargetState == MB.FinalState)
productions[D].Add(new Production(D, E));
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
productions[D].Add(new Production(D, E, C));
//we pretend here that E is a terminal
if (!productions.ContainsKey(C))
{
productions[C] = new List<Production>();
vars.Add(C);
}
}
}
G_[B] = new ContextFreeGrammar(vars, startSymbol, productions);
}
#endregion
var G = new Dictionary<Nonterminal, ContextFreeGrammar>();
#region construct the corresponding temporary G[B]'s
foreach (Nonterminal B in Vars)
{
var G_B = G_[B];
var productions = new Dictionary<Nonterminal, List<Production>>();
//var vars = new List<Variable>();
Nonterminal startSymbol = G_B.startSymbol;
productions[startSymbol] = G_B.productionMap[startSymbol];
foreach (Nonterminal D in G_B.variables)
if (!D.Equals(startSymbol))
{
var productions_D = new List<Production>();
productions[D] = productions_D;
foreach (Production p in G_B.productionMap[D])
{
Nonterminal E = (Nonterminal)p.First;
var G_E = G_[E];
if (p.IsUnit)
foreach (Production q in G_E.productionMap[G_E.startSymbol])
productions_D.Add(new Production(D, q.Rhs));
else
foreach (Production q in G_E.productionMap[G_E.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = p.Rhs[1];
productions_D.Add(new Production(D, symbols));
}
}
}
//ignore the variable list, it is not used
G[B] = new ContextFreeGrammar(null, startSymbol, productions);
}
#endregion
#region construct the final GNF from the G[B]'s
var productionsGNF = new List<Production>();
foreach (Nonterminal A in cnf.variables)
{
foreach (Production p in cnf.productionMap[A])
{
if (p.IsSingleExprinal)
productionsGNF.Add(p);
else
{
Nonterminal B = (Nonterminal)p.Rhs[0];
Nonterminal C = (Nonterminal)p.Rhs[1];
var GB = G[B];
foreach (Production q in GB.productionMap[GB.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = C;
productionsGNF.Add(new Production(A, symbols));
}
}
}
}
foreach (Nonterminal B in Vars)
{
var GB = G[B];
foreach (var kv in GB.productionMap)
if (!kv.Key.Equals(GB.startSymbol))
productionsGNF.AddRange(kv.Value);
}
#endregion
ContextFreeGrammar gnf = new ContextFreeGrammar(cnf.startSymbol, productionsGNF);
return gnf;
}
/// <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;
}
/// <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().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;
}
/// <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 <Tuple <GrammarSymbol[], Nonterminal> > >();
int nonterminalID = 0;
#region compute leavesP and revP
foreach (Nonterminal v in g.variables)
{
revP[v] = new List <Tuple <GrammarSymbol[], Nonterminal> >();
}
foreach (Production p in g.GetProductions())
{
if (!(p.First is Nonterminal))
{
leavesP.Add(p);
}
else
{
revP[(Nonterminal)p.First].Add(new Tuple <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.Item2;
Nonterminal D_B = Lookup(Bvar, D, ref nonterminalID);
C_B_list.Add(new Production(C_B, t.Item1, D_B));
if (t.Item1.Length > 0 && W_B.Contains(D))
{
C_B_list.Add(new Production(C_B, t.Item1));
}
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);
}
/// <summary>
/// Produces the EGNF (Extended Greibach Normal Form) for the grammar g.
/// The grammar g can be arbitrary. First removes epsilons and useless symbols from 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>
/// <returns>Extended Greibach Normal Form of g</returns>
public static ContextFreeGrammar MkEGNF(ContextFreeGrammar g)
{
return(MkEGNF(g, true));
}
/// <summary>
/// Produces the GNF (Greibach Normal Form) for the grammar g.
/// If g is not already in GNF, first makes CNF.
/// Implements a variation of the Koch-Blum algorithm. (STACS 97, pp. 47-54)
/// </summary>
/// <param name="g"></param>
/// <param name="removeEpsilonsUselessSymbolsUnitsProductions"></param>
/// <returns></returns>
public static ContextFreeGrammar MkGNF(ContextFreeGrammar g, bool removeEpsilonsUselessSymbolsUnitsProductions)
{
if (removeEpsilonsUselessSymbolsUnitsProductions)
{
g = g.RemoveEpsilonsAndUselessSymbols().RemoveUnitProductions();
}
if (g.IsInGNF())
{
return(g);
}
ContextFreeGrammar cnf = MkCNF(g, false);
var Vars = cnf.variables;
int nonterminalID = 0;
var M = new Dictionary <Nonterminal, Automaton <GrammarSymbol> >();
#region construct the automata M[B] for all variables B
int id = 0;
var initStateMap = new Dictionary <Nonterminal, int>();
var finalStateMap = new Dictionary <Nonterminal, int>();
foreach (Nonterminal B in Vars)
{
initStateMap[B] = id++;
finalStateMap[B] = id++;
}
var movesOfM = new Dictionary <Nonterminal, List <Move <GrammarSymbol> > >();
foreach (Nonterminal B in Vars)
{
movesOfM[B] = new List <Move <GrammarSymbol> >();
}
#region construct the moves of the automata
foreach (Nonterminal B in Vars)
{
var variableToStateMap = new Dictionary <Nonterminal, int>();
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(B);
int initState = initStateMap[B];
variableToStateMap[B] = finalStateMap[B];
while (stack.Count > 0)
{
Nonterminal C = stack.Pop();
foreach (Production p in cnf.GetProductions(C))
{
if (p.IsSingleExprinal)
{
movesOfM[B].Add(Move <GrammarSymbol> .Create(initState, variableToStateMap[C], p.First));
}
else
{
Nonterminal D = (Nonterminal)p.First; //using the fact that the grammar is in CNF
if (!variableToStateMap.ContainsKey(D))
{
//visit all variables reachable that have not already been visited
variableToStateMap.Add(D, id++);
stack.Push(D);
}
GrammarSymbol E = p.Rhs[1];
movesOfM[B].Add(Move <GrammarSymbol> .Create(variableToStateMap[D], variableToStateMap[C], E));
}
}
}
}
#endregion
foreach (Nonterminal B in Vars)
{
M[B] = Automaton <GrammarSymbol> .Create(null, initStateMap[B], new int[] { finalStateMap[B] }, movesOfM[B]);
}
#endregion
var G_ = new Dictionary <Nonterminal, ContextFreeGrammar>();
#region construct corresponding intermediate grammars G_[B] corresponding to M[B]
foreach (Nonterminal B in Vars)
{
var MB = M[B];
bool MBfinalStateHasVariableMoves = FinalStateHasVariableMoves(MB);
var productions = new Dictionary <Nonterminal, List <Production> >();
Nonterminal startSymbol = new Nonterminal(nonterminalID++);
var vars = new List <Nonterminal>();
vars.Add(startSymbol);
productions[startSymbol] = new List <Production>();
foreach (var move in MB.GetMovesFrom(MB.InitialState))
{
if (move.TargetState == MB.FinalState)
{
productions[startSymbol].Add(new Production(startSymbol, move.Label));
}
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
var C = new Nonterminal("Q" + move.TargetState);
productions[startSymbol].Add(new Production(startSymbol, move.Label, C));
if (!productions.ContainsKey(C))
{
productions[C] = new List <Production>();
vars.Add(C);
}
}
}
foreach (int state in MB.States)
{
if (state != MB.InitialState)
{
foreach (Move <GrammarSymbol> move in MB.GetMovesFrom(state))
{
Nonterminal D = new Nonterminal("Q" + state);
Nonterminal C = new Nonterminal("Q" + move.TargetState);
if (!productions.ContainsKey(D))
{
productions[D] = new List <Production>();
vars.Add(D);
}
Nonterminal E = (Nonterminal)move.Label;
if (move.TargetState == MB.FinalState)
{
productions[D].Add(new Production(D, E));
}
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
productions[D].Add(new Production(D, E, C));
//we pretend here that E is a terminal
if (!productions.ContainsKey(C))
{
productions[C] = new List <Production>();
vars.Add(C);
}
}
}
}
}
G_[B] = new ContextFreeGrammar(vars, startSymbol, productions);
}
#endregion
var G = new Dictionary <Nonterminal, ContextFreeGrammar>();
#region construct the corresponding temporary G[B]'s
foreach (Nonterminal B in Vars)
{
var G_B = G_[B];
var productions = new Dictionary <Nonterminal, List <Production> >();
//var vars = new List<Variable>();
Nonterminal startSymbol = G_B.startSymbol;
productions[startSymbol] = G_B.productionMap[startSymbol];
foreach (Nonterminal D in G_B.variables)
{
if (!D.Equals(startSymbol))
{
var productions_D = new List <Production>();
productions[D] = productions_D;
foreach (Production p in G_B.productionMap[D])
{
Nonterminal E = (Nonterminal)p.First;
var G_E = G_[E];
if (p.IsUnit)
{
foreach (Production q in G_E.productionMap[G_E.startSymbol])
{
productions_D.Add(new Production(D, q.Rhs));
}
}
else
{
foreach (Production q in G_E.productionMap[G_E.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = p.Rhs[1];
productions_D.Add(new Production(D, symbols));
}
}
}
}
}
//ignore the variable list, it is not used
G[B] = new ContextFreeGrammar(null, startSymbol, productions);
}
#endregion
#region construct the final GNF from the G[B]'s
var productionsGNF = new List <Production>();
foreach (Nonterminal A in cnf.variables)
{
foreach (Production p in cnf.productionMap[A])
{
if (p.IsSingleExprinal)
{
productionsGNF.Add(p);
}
else
{
Nonterminal B = (Nonterminal)p.Rhs[0];
Nonterminal C = (Nonterminal)p.Rhs[1];
var GB = G[B];
foreach (Production q in GB.productionMap[GB.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = C;
productionsGNF.Add(new Production(A, symbols));
}
}
}
}
foreach (Nonterminal B in Vars)
{
var GB = G[B];
foreach (var kv in GB.productionMap)
{
if (!kv.Key.Equals(GB.startSymbol))
{
productionsGNF.AddRange(kv.Value);
}
}
}
#endregion
ContextFreeGrammar gnf = new ContextFreeGrammar(cnf.startSymbol, productionsGNF);
return(gnf);
}
/// <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().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);
}
/// <summary>
/// Return all useful nonterminal symbols. If checkBackwardsOnly is true, assume that all symbols are reachable from the start symbol.
/// </summary>
public HashSet <string> GetUsefulNonterminals(bool checkBackwardsOnly)
{
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
//returns the empty set because the language is empty
if (!useful_backwards.Contains(this.startSymbol))
{
return(new HashSet <string>());
}
//don't bother to check forward
if (checkBackwardsOnly)
{
var res = new HashSet <string>();
foreach (var nt in useful_backwards)
{
res.Add(nt.Name);
}
return(res);
}
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
HashSet <string> usefulSymbols = new HashSet <string>();
foreach (var nt in useful_forwards)
{
if (useful_backwards.Contains(nt))
{
usefulSymbols.Add(nt.Name);
}
}
return(usefulSymbols);
}
/// <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);
}
