//Static method for NDFA -> DFA
public static DFA <string> toDFA(NDFA <string> ndfa)
{
DFA <string> dfa = new DFA <string>(ndfa.symbols);
string combinedName = "";
SortedSet <string> completeStartState = new SortedSet <string>();
foreach (string startState in ndfa.startStates)
{
eClosure(startState, ndfa, ref completeStartState);
}
foreach (string s in completeStartState)
{
combinedName += s + "_";
}
combinedName = combinedName.TrimEnd('_');
Convert(combinedName, ref dfa, ref ndfa);
dfa.addStartState(combinedName);
if (dfa.states.Contains("F"))
{
foreach (char route in dfa.symbols)
{
dfa.addTransition(new Transition <string>("F", route, "F"));
}
}
return(dfa);
}
//Used Ref for pointer use and prevent overflows...
private static bool deltaE(ref string toState, string[] states, char symbol, NDFA <string> ndfa)
{
bool isFinalState = false;
SortedSet <string> newStates = new SortedSet <string>();
foreach (string state in states)
{
List <Transition <string> > trans = ndfa.GetTransition(state);
foreach (Transition <string> t in trans)
{
if (t.symbol == symbol)
{
eClosure(t.toState, ndfa, ref newStates);
if (ndfa.finalStates.Contains(t.toState))
{
isFinalState = true;
}
}
}
}
foreach (string subState in newStates)
{
toState += subState + "_";
}
toState = toState.TrimEnd('_');
return(isFinalState);
}
public static NDFA <String> getTestNDFA52()
{
char[] alphabet = { 'a', 'b' };
NDFA <string> m = new NDFA <string>(alphabet);
m.addTransition(new Transition <String>("A", 'a', "C"));
m.addTransition(new Transition <String>("A", 'b', "C"));
m.addTransition(new Transition <String>("A", 'b', "B"));
m.addTransition(new Transition <String>("B", '$', "C"));
m.addTransition(new Transition <String>("B", 'b', "C"));
m.addTransition(new Transition <String>("C", 'a', "D"));
m.addTransition(new Transition <String>("C", 'b', "D"));
m.addTransition(new Transition <String>("D", 'a', "C"));
m.addTransition(new Transition <String>("D", 'a', "B"));
m.addTransition(new Transition <String>("C", 'a', "E"));
m.addTransition(new Transition <String>("E", '$', "D"));
m.addTransition(new Transition <String>("E", 'b', "E"));
m.addStartState("A");
m.addFinalState("C");
m.addFinalState("E");
return(m);
}
public static NDFA <String> getExample1()
{
char[] alphabet = { 'a', 'b' };
NDFA <String> m = new NDFA <String>(alphabet);
m.addTransition(new Transition <String>("q0", '$', "q1"));
m.addTransition(new Transition <String>("q0", '$', "q2"));
m.addTransition(new Transition <String>("q1", 'b', "q3"));
m.addTransition(new Transition <String>("q1", '$', "q5"));
m.addTransition(new Transition <String>("q3", 'b', "q4"));
m.addTransition(new Transition <String>("q2", 'a', "q5"));
m.addTransition(new Transition <String>("q2", '$', "q6"));
m.addTransition(new Transition <String>("q5", 'a', "q6"));
m.addTransition(new Transition <String>("q4", '$', "q7"));
m.addTransition(new Transition <String>("q6", '$', "q7"));
// only on start state in a dfa:
m.addStartState("q0");
// two final states:
m.addFinalState("q7");
m.addFinalState("q3");
return(m);
}
public static DFA <String> getTestNDFA00()
{
char[] alphabet = { 'a', 'b' };
NDFA <string> m = new NDFA <string>(alphabet);
m.addTransition(new Transition <string>("0", '$', "1"));
m.addTransition(new Transition <string>("0", '$', "7"));
m.addTransition(new Transition <string>("1", '$', "2"));
m.addTransition(new Transition <string>("1", '$', "4"));
m.addTransition(new Transition <string>("2", 'a', "3"));
m.addTransition(new Transition <string>("3", '$', "6"));
m.addTransition(new Transition <string>("4", 'b', "5"));
m.addTransition(new Transition <string>("5", '$', "6"));
m.addTransition(new Transition <string>("6", '$', "7"));
m.addTransition(new Transition <string>("6", '$', "1"));
m.addTransition(new Transition <string>("7", 'a', "8"));
m.addTransition(new Transition <string>("8", 'b', "9"));
m.addTransition(new Transition <string>("9", 'b', "10"));
m.addStartState("0");
m.addFinalState("10");
DFA <string> epsilonDFA = NDFA <string> .toDFA(m);
return(epsilonDFA);
}
//Used Ref for pointer use and prevent overflows...
private static void eClosure(string state, NDFA <string> ndfa, ref SortedSet <string> subStateList)
{
subStateList.Add(state);
List <Transition <string> > trans = ndfa.GetTransition(state);
foreach (Transition <string> t in trans)
{
if (t.symbol == '$' && !subStateList.Contains(t.toState))
{
eClosure(t.toState, ndfa, ref subStateList);
}
}
}
public bool Equals(NDFA <T> other)
{
if (other == null)
{
return(false);
}
else if (this.symbols == other.symbols && this.transitions == other.transitions && this.startStates == other.startStates && this.finalStates == other.finalStates)
{
return(true);
}
else
{
return(false);
}
}
//Used Ref for pointer use and prevent overflows...
private static void Convert(string inputState, ref DFA <String> dfa, ref NDFA <String> ndfa)
{
if (dfa.GetTransition(inputState).Count == ndfa.symbols.Length)
{
return;
}
string[] states = inputState.Split('_');
foreach (char symbol in ndfa.symbols)
{
if (CheckExistingRouteForChar(inputState, symbol, dfa))
{
return;
}
int correctAmountOfRoutes = CheckAvailableRoutes(states, symbol, ndfa);
string toState = "";
if (correctAmountOfRoutes == 0)
{
dfa.addTransition(new Transition <string>(inputState, symbol, "F"));
}
else
{
bool isFinalState = deltaE(ref toState, states, symbol, ndfa);
dfa.addTransition(new Transition <string>(inputState, symbol, toState));
if (ndfa.finalStates.Contains(inputState))
{
dfa.addFinalState(inputState);
}
if (isFinalState)
{
dfa.addFinalState(toState);
}
if (inputState != toState)
{
Convert(toState, ref dfa, ref ndfa);
}
}
}
}
public static DFA <string> toDFA(NDFA <string> ndfa)
{
DFA <string> dfa = new DFA <string>(ndfa.symbols);
foreach (string startState in ndfa.states)
{
ConvertAutomata(startState, ref dfa, ref ndfa);
dfa.addStartState(startState);
}
if (dfa.states.Contains("F"))
{
foreach (char route in dfa.symbols)
{
dfa.addTransition(new Transition <string>("F", route, "F"));
}
}
return(dfa);
}
private static int CheckAvailableRoutes(string[] states, char symbol, NDFA <string> ndfa)
{
//array which shows how many possible routes there are for each sub-state
int[] possibleRoutesPerState = new int[states.Length];
// value that shows the amount of routes the ndfa has for all the substates combined.
int correctAmountOfRoutes = 0;
//reads ndfa for possible routes, saves maximum amount of accessible routes to correctAmountOfRoutes
foreach (string state in states)
{
if (ndfa.GetTransition(state).Count(transition => transition.symbol == symbol) > correctAmountOfRoutes)
{
correctAmountOfRoutes = ndfa.GetTransition(state).Count(transition => transition.symbol == symbol);
}
}
return(correctAmountOfRoutes);
}
public static NDFA <String> getMinimizeExample()
{
char[] alphabet = { 'a', 'b' };
NDFA <String> m = new NDFA <String>(alphabet);
m.addTransition(new Transition <String>("q0", 'a', "q1"));
m.addTransition(new Transition <String>("q0", 'b', "q2"));
m.addTransition(new Transition <String>("q1", 'a', "q0"));
m.addTransition(new Transition <String>("q1", 'b'));
m.addTransition(new Transition <String>("q2", 'a', "q0"));
m.addTransition(new Transition <String>("q2", 'b'));
// only one start state in a dfa:
m.addStartState("q0");
// two final states:
m.addFinalState("q1");
m.addFinalState("q2");
return(m);
}
private static void ConvertAutomata(string currentState, ref DFA <string> dfa, ref NDFA <string> ndfa)
{
if (dfa.GetTransition(currentState).Count == ndfa.symbols.Length)
{
return;
}
string[] states = currentState.Split('_');
foreach (char symbol in ndfa.symbols)
{
List <Transition <string> > currentTrans = dfa.GetTransition(currentState);
foreach (Transition <string> t in currentTrans)
{
if (t.symbol == symbol)
{
return;
}
}
int[] counts = new int[states.Length];
for (int i = 0; i < states.Length; i++)
{
counts[i] = ndfa.GetTransition(states[i]).Count(transition => transition.symbol == symbol);
}
int amountOfRoutes = 0;
foreach (int i in counts)
{
if (i > amountOfRoutes)
{
amountOfRoutes = i;
}
}
if (amountOfRoutes == 0)
{
dfa.addTransition(new Transition <string>(currentState, symbol, "F"));
}
string toState = "";
bool isFinalState = false;
SortedSet <String> newState = new SortedSet <string>();
if (amountOfRoutes >= 1)
{
foreach (string state in states)
{
List <Transition <string> > trans = ndfa.GetTransition(state);
foreach (Transition <string> t in trans)
{
if (t.symbol == symbol)
{
newState.Add(t.toState);
if (ndfa.finalStates.Contains(t.toState))
{
isFinalState = true;
}
}
}
}
foreach (string subState in newState)
{
toState += subState;
toState += "_";
}
if (newState.Count >= 1)
{
toState = toState.TrimEnd('_');
}
dfa.addTransition(new Transition <string>(currentState, symbol, toState));
if (ndfa.finalStates.Contains(currentState))
{
dfa.addFinalState(currentState);
}
if (isFinalState)
{
dfa.addFinalState(toState);
}
if (currentState != toState)
{
ConvertAutomata(toState, ref dfa, ref ndfa);
}
}
}
}
