/// <summary>
/// Generates a CNF that accepts the prefix closure of a given grammar.
/// </summary>
/// <param name="g">the original grammar</param>
/// <returns>the prefix closure</returns>
public static ContextFreeGrammar getCNFPrefixClosure(ContextFreeGrammar g)
{
if (g == null)
{
return(g);
}
if (!g.IsInCNF())
{
g = getEquivalentCNF(g);
}
if (g == null)
{
return(g);
}
var prefixClosure = getPrefixClosure(g);
prefixClosure = getEquivalentCNF(prefixClosure); // !!ATTENTION!! this may remove old productions
var productions = g.GetProductions();
productions = productions.Concat(prefixClosure.GetProductions());
return(new ContextFreeGrammar(prefixClosure.StartSymbol, productions));
}
public static Tuple <int, IEnumerable <String> > gradeFindDerivation(ContextFreeGrammar grammar, String word, List <GrammarSymbol[]> derivation, int maxGrade, int derivationType = Derivation.DERIVATION_ALL)
{
var comp = new DerivationComparator();
List <String> feedback = new List <String>();
if (derivation.Count == 0) //empty
{
feedback.Add("The derivation was empty... The first step is always the start symbol.");
return(Tuple.Create(0, (IEnumerable <String>)feedback));
}
if (!comp.Equals(derivation[0], new GrammarSymbol[] { grammar.StartSymbol }))
{
feedback.Add("The first step of the derivation has to be the start symbol!");
return(Tuple.Create(0, (IEnumerable <String>)feedback));
}
bool correct = true;
int points = 0;
for (int i = 1; i < derivation.Count; i++)
{
bool b = Derivation.isValidDerivationStep(grammar.GetProductions(), derivation[i - 1], derivation[i], derivationType);
if (!b)
{
correct = false;
feedback.Add(String.Format("There is no rule that leads from '{0}' to '{1}'", Derivation.partialWordToString(derivation[i - 1]).Replace(" ", ""), Derivation.partialWordToString(derivation[i]).Replace(" ", "")));
if (derivationType != Derivation.DERIVATION_ALL && Derivation.isValidDerivationStep(grammar.GetProductions(), derivation[i - 1], derivation[i]))
{
feedback.Add(String.Format("Make sure to give a derivation of the correct type (e.g. leftmost / rightmost)!", Derivation.partialWordToString(derivation[i - 1]), Derivation.partialWordToString(derivation[i])));
}
break;
}
points++;
}
String lastStep = Derivation.partialWordToString(derivation[derivation.Count - 1]);
if (!lastStep.Equals(word))
{
correct = false;
feedback.Add(String.Format("The last step should be '{0}'", word));
}
if (correct) //perfekt
{
feedback.Add("Correct!");
return(Tuple.Create(maxGrade, (IEnumerable <String>)feedback));
}
return(Tuple.Create(0, (IEnumerable <String>)feedback));
}
/// <summary>
/// Genereates warnings for useless variables.
/// </summary>
/// <param name="g">the grammar</param>
/// <returns></returns>
public static List <string> getGrammarWarnings(ContextFreeGrammar g)
{
List <string> res = new List <string>();
HashSet <string> variables = new HashSet <string>();
foreach (var n in g.Variables)
{
variables.Add(n.ToString());
}
var productiv = g.GetUsefulNonterminals(true);
var unproductiv = variables.Except(productiv);
if (unproductiv.Count() > 0)
{
res.Add(string.Format("Warning: There are unproductive variables! ({0})", string.Join(", ", unproductiv)));
}
var reachable = new HashSet <string>();
//Lemma 4.2, p. 89, Hopcroft-Ullman
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(g.StartSymbol);
reachable.Add(g.StartSymbol.ToString());
while (stack.Count > 0)
{
Nonterminal v = stack.Pop();
foreach (Production p in g.GetProductions(v))
{
foreach (Nonterminal u in p.GetVariables())
{
if (!reachable.Contains(u.ToString()))
{
reachable.Add(u.ToString());
stack.Push(u);
}
}
}
}
var unreachable = variables.Except(reachable);
if (unproductiv.Count() > 0)
{
res.Add(string.Format("Warning: There are unreachable variables! ({0})", string.Join(", ", unreachable)));
}
return(res);
}
/// <summary>
/// Generates a CFG that accepts the prefix closure of a given grammar.
/// </summary>
/// <param name="g">the original grammar</param>
/// <returns>the prefix closure</returns>
public static ContextFreeGrammar getPrefixClosure(ContextFreeGrammar g)
{
Func <Nonterminal, Nonterminal> prefixFor = delegate(Nonterminal x)
{
return(new Nonterminal(x.Name + "PREFIX"));
};
if (g == null)
{
return(g);
}
if (!g.IsInCNF())
{
g = getEquivalentCNF(g);
}
if (g == null)
{
return(g);
}
Nonterminal prefixStart = prefixFor(g.StartSymbol);
var prefixProductions = new List <Production>();
foreach (Production p in g.GetProductions())
{
//add original
prefixProductions.Add(p);
Nonterminal prefixNT = prefixFor(p.Lhs);
if (p.Rhs.Length == 2) // case: X->AB ==> X' ->A' | AB'
{
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { p.Rhs[0], prefixFor((Nonterminal)p.Rhs[1]) }));
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { prefixFor((Nonterminal)p.Rhs[0]) }));
}
else // case: X->a ==> X'->a
{
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { p.Rhs[0] }));
}
}
var res = new ContextFreeGrammar(prefixStart, prefixProductions);
res.setAcceptanceForEmptyString(true);
return(res);
}
private static HashSet <string> generateWordsWithLength(ContextFreeGrammar cnf, int length, Dictionary <Nonterminal, Dictionary <int, HashSet <string> > > dp)
{
HashSet <string> res = new HashSet <string>();
if (cnf == null)
{
return(res); //empty grammar -> can't generate any words
}
if (length == 0) //case: length = 0
{
if (cnf.acceptsEmptyString())
{
res.Add("");
}
}
else if (length == 1) //case: length = 1
{
foreach (Nonterminal nt in cnf.Variables)
{
//init dp[nt]
Dictionary <int, HashSet <string> > curDP = new Dictionary <int, HashSet <string> >();
dp.Add(nt, curDP);
//find words of length 1
HashSet <string> l = new HashSet <string>();
foreach (Production p in cnf.GetProductions(nt))
{
if (p.IsSingleExprinal)
{
l.Add(p.Rhs[0].ToString());
}
}
curDP.Add(1, l);
if (nt.Equals(cnf.StartSymbol))
{
res = l;
}
}
}
else //case: length > 1
{
foreach (KeyValuePair <Nonterminal, Dictionary <int, HashSet <string> > > entry in dp)
{
Nonterminal cur = entry.Key;
Dictionary <int, HashSet <string> > curDP = entry.Value;
HashSet <string> curSet = new HashSet <string>();
curDP.Add(length, curSet);
if (cur.Equals(cnf.StartSymbol))
{
res = curSet;
}
foreach (Production p in cnf.GetProductions(entry.Key))
{
if (p.Rhs.Length != 2)
{
continue; //ignore productions that don't have form X->AB
}
Nonterminal left = (Nonterminal)p.Rhs[0];
Dictionary <int, HashSet <string> > leftDP = null;
dp.TryGetValue(left, out leftDP);
Nonterminal right = (Nonterminal)p.Rhs[1];
Dictionary <int, HashSet <string> > rightDP = null;
dp.TryGetValue(right, out rightDP);
for (int leftPart = 1; leftPart < length; leftPart++)
{
int rightPart = length - leftPart;
HashSet <string> leftPossibilities = null;
leftDP.TryGetValue(leftPart, out leftPossibilities);
HashSet <string> rightPossibilities = null;
rightDP.TryGetValue(rightPart, out rightPossibilities);
foreach (string leftString in leftPossibilities)
{
foreach (string rightString in rightPossibilities)
{
curSet.Add(leftString + rightString);
}
}
}
}
}
}
return(res);
}
/// <summary>
/// Performs the CYK-algorithm
/// </summary>
/// <param name="grammar">the grammar (in CNF)</param>
/// <param name="word">the word (not null)</param>
/// <returns>the filled table of the cyk-algorithm</returns>
public static Tuple <HashSet <Nonterminal>, List <Tuple <Production, int> > >[][] cyk(ContextFreeGrammar grammar, string word)
{
/*
* Every entry in the table consists of 2 parts:
* 1. The HasSet of all Nonterminals that produce the corresponding subword
* 2. All possible subtrees encodes as pair (p,x)
* where p is the applicable production and
* x is the lengt of the word produced by the first grammarsymbol on the right hand side of p
*/
//prepare CYK table
int n = word.Length;
Tuple <HashSet <Nonterminal>, List <Tuple <Production, int> > >[][] cyk = new Tuple <HashSet <Nonterminal>, List <Tuple <Production, int> > > [n][];
for (int i = 0; i < n; i++)
{
cyk[i] = new Tuple <HashSet <Nonterminal>, List <Tuple <Production, int> > > [n - i];
for (int j = 0; j < n - i; j++)
{
cyk[i][j] = new Tuple <HashSet <Nonterminal>, List <Tuple <Production, int> > >(new HashSet <Nonterminal>(), new List <Tuple <Production, int> >());
}
}
//prepare lookups (productions for a given NT or pair of NTs)
Dictionary <Tuple <Nonterminal, Nonterminal>, HashSet <Production> > lookupNT = new Dictionary <Tuple <Nonterminal, Nonterminal>, HashSet <Production> >();
Dictionary <string, HashSet <Production> > lookupT = new Dictionary <string, HashSet <Production> >();
foreach (Production p in grammar.GetProductions())
{
if (p.IsSingleExprinal) //form: X -> a
{
HashSet <Production> hashset = null;
if (!lookupT.TryGetValue(p.Rhs[0].Name, out hashset))
{
hashset = new HashSet <Production>();
lookupT.Add(p.Rhs[0].Name, hashset);
}
hashset.Add(p);
}
else if (p.Rhs.Length == 2)//form: X -> A B
{
HashSet <Production> hashset = null;
var tuple = new Tuple <Nonterminal, Nonterminal>((Nonterminal)p.Rhs[0], (Nonterminal)p.Rhs[1]);
if (!lookupNT.TryGetValue(tuple, out hashset))
{
hashset = new HashSet <Production>();
lookupNT.Add(tuple, hashset);
}
hashset.Add(p);
}
}
//CYK algorithm
//first row (check for Productions X -> a)
for (int i = 0; i < n; i++)
{
HashSet <Production> applicable = null;
if (lookupT.TryGetValue(word.Substring(i, 1), out applicable))
{
foreach (Production p in applicable)
{
cyk[0][i].Item1.Add(p.Lhs);
cyk[0][i].Item2.Add(new Tuple <Production, int>(p, 1));
}
}
}
//fill rest
for (int length = 1; length < n; length++)
{
for (int start = 0; start + length < n; start++)
{
//to_fill: cyk[length][start]
for (int part1 = 0; part1 < length; part1++)
{
var left = cyk[part1][start].Item1;
var right = cyk[length - 1 - part1][start + 1 + part1].Item1;
if (left.Count > 0 && right.Count > 0)
{
foreach (Nonterminal leftNT in left)
{
foreach (Nonterminal rightNT in right)
{
var tuple = new Tuple <Nonterminal, Nonterminal>(leftNT, rightNT);
HashSet <Production> applicable = null;
if (lookupNT.TryGetValue(new Tuple <Nonterminal, Nonterminal>(leftNT, rightNT), out applicable))
{
foreach (Production p in applicable)
{
cyk[length][start].Item1.Add(p.Lhs);
cyk[length][start].Item2.Add(new Tuple <Production, int>(p, part1 + 1));
}
}
}
}
}
}
}
}
return(cyk);
}
/// <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 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(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>
/// 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);
}