/// <summary>
/// Generates a CNF for a given grammar or returns null if the Grammar doesn't produce any words.
/// </summary>
/// <param name="g">the original grammar</param>
/// <returns>the CNF or null</returns>
public static ContextFreeGrammar getEquivalentCNF(ContextFreeGrammar g)
{
if (g == null)
{
return(null);
}
if (g.IsInCNF())
{
return(g);
}
try
{
ContextFreeGrammar res = ContextFreeGrammar.MkCNF(g);
//handle empty string
res.setAcceptanceForEmptyString(g.acceptsEmptyString());
return(res);
}
catch (AutomataException e)
{
if (g.acceptsEmptyString())
{
var res = new ContextFreeGrammar(new Nonterminal("S"), new Production[] { new Production(new Nonterminal("S"), new GrammarSymbol[] { new Nonterminal("S"), new Nonterminal("S") }) });
res.setAcceptanceForEmptyString(true);
return(res);
}
return(null);
}
}
/// <summary>
/// Checks if a word is recognized by the given grammar. (CYK-algorithm)
/// </summary>
/// <param name="grammar">the grammar</param>
/// <param name="word">the word</param>
/// <returns>true, if there exists a dereviation from the startsymbol to the word</returns>
public static bool isWordInGrammar(ContextFreeGrammar grammar, string word)
{
if (word == null || grammar == null)
{
return(false);
}
if (!grammar.IsInCNF())
{
grammar = getEquivalentCNF(grammar);
}
if (grammar == null)
{
return(false);
}
//empty word
if (word.Length == 0)
{
return(grammar.acceptsEmptyString());
}
//CYK
var cyk_table = cyk(grammar, word);
return(cyk_table[word.Length - 1][0].Item1.Contains(grammar.StartSymbol));
}
/// <summary>
/// Finds the longest prefix of a given word that is still recognized by a given grammar. (CYK algorithm with prefix closure)
/// </summary>
/// <param name="grammar">the grammar</param>
/// <param name="word">the word</param>
/// <returns>-1 if the grammar is empty; -2 if the word is in the grammar; n (if the substring up to index n is the longest prefix)</returns>
public static int longestPrefixLength(ContextFreeGrammar grammar, string word)
{
if (word == null || grammar == null)
{
return(-1);
}
if (!grammar.IsInCNF())
{
grammar = getEquivalentCNF(grammar);
}
if (grammar == null)
{
return(-1);
}
//empty word
if (word.Length == 0)
{
if (grammar.acceptsEmptyString())
{
return(-2);
}
return(0);
}
//prefix closure
var prefixGrammar = getCNFPrefixClosure(grammar);
//CYK
var cyk_table = cyk(prefixGrammar, word);
//check if word was in original grammar
if (cyk_table[word.Length - 1][0].Item1.Contains(grammar.StartSymbol))
{
return(-2);
}
//check for startsymbol in first row
for (int i = word.Length - 1; i >= 0; i--)
{
if (cyk_table[i][0].Item1.Contains(prefixGrammar.StartSymbol))
{
return(i + 1);
}
}
return(0);
}
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);
}
