static public Automata <String> getExampleSlide8Lesson2()
{
char[] alphabet = { 'a', 'b' };
Automata <String> automata = new Automata <string>(alphabet);
automata.AddTransition(new Transition <String>("q0", "q1", 'a'));
automata.AddTransition(new Transition <String>("q0", "q4", 'b'));
automata.AddTransition(new Transition <String>("q1", "q4", 'a'));
automata.AddTransition(new Transition <String>("q1", "q2", 'b'));
automata.AddTransition(new Transition <String>("q2", "q3", 'a'));
automata.AddTransition(new Transition <String>("q2", "q4", 'b'));
automata.AddTransition(new Transition <String>("q3", "q1", 'a'));
automata.AddTransition(new Transition <String>("q3", "q2", 'b'));
// the error state, loops for a and b:
automata.AddTransition(new Transition <String>("q4", 'a'));
automata.AddTransition(new Transition <String>("q4", 'b'));
// only on start state in a dfa:
automata.DefineAsStartState("q0");
// two final states:
automata.DefineAsFinalState("q2");
automata.DefineAsFinalState("q3");
return(automata);
}
/// <summary>
/// Turns a <see cref="RegExp"/> into a <see cref="Automata{string}"/>, which is a NDFA.
/// </summary>
/// <param name="expressionToTranslate">The <see cref="RegExp"/> to translate.</param>
/// <returns>A <see cref="Automata{string}"/>, which is a NDFA or null if there was a problem</returns>
public Automata <string> GenerateNDFA(RegExp expressionToTranslate)
{
HashSet <char> alphabet = new HashSet <char>();
String regexAsString = expressionToTranslate.ToString();
foreach (char c in regexAsString)
{
if (IsUsableCharacter(c))
{
alphabet.Add(c);
}
}
;
ThompsonPart completeNdfaAsThompson = GenerateThompsonPart(regexAsString);
if (completeNdfaAsThompson.Equals(new ThompsonPart()))
{
return(null);
}
Automata <string> NDFA = new Automata <string>(alphabet.ToArray());
foreach (Transition <string> thompsonTransition in completeNdfaAsThompson.transitions)
{
NDFA.AddTransition(thompsonTransition);
}
NDFA.DefineAsStartState(completeNdfaAsThompson.startState);
NDFA.DefineAsFinalState(completeNdfaAsThompson.finalState);
return(NDFA);
}
/// <summary>
/// Generates the dfa for the given dictionary of states
/// </summary>
private void GenerateDFA()
{
dfa = new Automata <T>(ndfa.Symbols);
//Start building the DFA as normal, with the state names being the combined states to be reached in one string, with a - as delimiter.
//Starting with the start state, foreach symbol create two string builder objects, build up the string in the state + - format
//Create a transition with the symbol and the states.
//Should we reach an empty collection, create the $ state, and for each symbol in the alphabet make a transition to this state
//Begin with the start state and all transitions
List <Transition <T> > dfaStart = GenerateDfaStart();
//Keep track of states that we still need to visit
HashSet <T> statesToTraverse = new HashSet <T>();
foreach (Transition <T> transition in dfaStart)
{
dfa.AddTransition(transition);
if (!transition.FromState.Equals(transition.ToState))
{
statesToTraverse.Add(transition.ToState);
}
}
//Sets all the transitions for the following states
GenerateOtherTransitions(statesToTraverse);
//After that, for all states check if it's a start state or end state.
MarkStatesAsStartOrEnd();
}
/// <summary>
/// This makes sure only a single - will end up between states.
/// </summary>
/// <param name="dfaToRemap">The dfa to remap the states for</param>
/// <returns>A re mapped version of the given automata</returns>
private Automata <T> RemapStates(Automata <T> dfaToRemap)
{
Dictionary <T, T> stateMap = new Dictionary <T, T>();
for (int i = 0; i < dfaToRemap.States.Count; i++)
{
string newState = "q" + i;
T newStateT = (T)Convert.ChangeType(newState, typeof(T));
stateMap.Add(dfaToRemap.States.ElementAt(i), newStateT);
}
Console.WriteLine("Now printing the remap dictionary:");
foreach (KeyValuePair <T, T> map in stateMap)
{
Console.WriteLine("Mapped {0} as {1}", map.Key, map.Value);
}
Console.WriteLine("-----------------------------------------");
Automata <T> remappedDfa = new Automata <T>(dfaToRemap.Symbols);
foreach (Transition <T> transition in dfaToRemap.Transitions)
{
remappedDfa.AddTransition(new Transition <T>(stateMap[transition.FromState], stateMap[transition.ToState], transition.Identifier));
}
foreach (T startState in dfaToRemap.StartStates)
{
remappedDfa.DefineAsStartState(stateMap[startState]);
}
foreach (T finalState in dfaToRemap.FinalStates)
{
remappedDfa.DefineAsFinalState(stateMap[finalState]);
}
return(remappedDfa);
}
/// <summary>
/// Turns a dfa into a form in which the original is not accepted.
/// </summary>
/// <param name="originalDfa">The dfa to make a reverse of</param>
/// <returns>A dfa that is a reverse of the original dfa</returns>
public Automata <T> ReverseDfa(Automata <T> originalDfa)
{
if (!originalDfa.IsDfa())
{
throw new ArgumentException("Given automata is not a DFA.");
}
Automata <T> reversedDfa = new Automata <T>(originalDfa.Symbols);
//Every transition is swapped as follows: new transition(original end state, symbol, original start state)
foreach (Transition <T> transition in originalDfa.Transitions)
{
reversedDfa.AddTransition(new Transition <T>(transition.ToState, transition.FromState, transition.Identifier));
}
//All start states become end states
foreach (T startState in originalDfa.StartStates)
{
reversedDfa.DefineAsFinalState(startState);
}
//All end states become start states
foreach (T endState in originalDfa.FinalStates)
{
reversedDfa.DefineAsStartState(endState);
}
return(reversedDfa);
}
/// <summary>
/// Turns a dfa into a form in which the original is not accepted.
/// </summary>
/// <param name="originalDfa">The dfa to "invert"</param>
/// <returns>A dfa that is !the original dfa</returns>
public Automata <T> NotDfa(Automata <T> originalDfa)
{
if (!originalDfa.IsDfa())
{
throw new ArgumentException("Given automata is not a DFA.");
}
Automata <T> notDfa = new Automata <T>(originalDfa.Symbols);
//Alles wat geen end state is word een end, en omgekeerd.
//Filter all end states from all the states
IEnumerable <T> newEndStates = originalDfa.States.Except(originalDfa.FinalStates);
//Set everthing in the new dfa
foreach (Transition <T> transition in originalDfa.Transitions)
{
notDfa.AddTransition(transition);
}
foreach (T startState in originalDfa.StartStates)
{
notDfa.DefineAsStartState(startState);
}
foreach (T finalState in newEndStates)
{
notDfa.DefineAsFinalState(finalState);
}
return(notDfa);
}
/// <summary>
/// Traverses the <see cref="Dictionary{TKey, TValue}"/> to generate a dfa. This recursively happen untill there are no more states to traverse.
/// </summary>
/// <param name="combinedDfa">The combined dfa, modified and passed every loop.</param>
/// <param name="statesToTraverse">The next states to traverse.</param>
private void GenerateCombinedDfa(Automata <T> combinedDfa, List <T> statesToTraverse)
{
List <T> statesToTraverseNext = new List <T>();
//Add all the new transitions to the combined dfa.
foreach (T state in statesToTraverse)
{
List <KeyValuePair <char, T> > transitionsFromThisState = combinedTransitionsMap[state];
foreach (KeyValuePair <char, T> symbolAndToState in transitionsFromThisState)
{
if (DfaContainsStateCombinedDfa(combinedDfa, symbolAndToState.Value))
{
combinedDfa.AddTransition(new Transition <T>(state, symbolAndToState.Value, symbolAndToState.Key));
continue;
} //Skip this state if it is already in the dfa. But do add a transition
if (state.Equals(symbolAndToState.Value))
{
combinedDfa.AddTransition(new Transition <T>(state, symbolAndToState.Key));
}
else
{
combinedDfa.AddTransition(new Transition <T>(state, symbolAndToState.Value, symbolAndToState.Key));
statesToTraverseNext.Add(symbolAndToState.Value);
}
}
}
//And a zero means that we have reached the end.
if (statesToTraverseNext.Count <= 0)
{
return;
}
else
{
GenerateCombinedDfa(combinedDfa, statesToTraverseNext);
}
}
static public Automata <String> ndfaToDfaTest()
{
char[] alphabet = { 'a', 'b' };
Automata <String> automata = new Automata <String>(alphabet);
automata.AddTransition(new Transition <string>("A", "B", 'a'));
automata.AddTransition(new Transition <string>("A", "C", 'b'));
automata.AddTransition(new Transition <string>("B", "D", 'a'));
automata.AddTransition(new Transition <string>("C", "B", 'b'));
automata.AddTransition(new Transition <string>("C", "D"));
automata.AddTransition(new Transition <string>("D", "A", 'b'));
automata.AddTransition(new Transition <string>("D", "E", 'a'));
automata.AddTransition(new Transition <string>("E", "C"));
automata.AddTransition(new Transition <string>("E", "F", 'a'));
automata.DefineAsStartState("A");
automata.DefineAsFinalState("F");
return(automata);
}
/// <summary>
/// Uses the given dictionary and the given list of states to get more transitions
/// </summary>
/// <param name="statesToLoopThrough">The states to loop through</param>
/// <returns></returns>
private void GenerateOtherTransitions(HashSet <T> statesToLoopThrough)
{
List <Transition <T> > transitions = new List <Transition <T> >();
HashSet <T> statesToTraverseNext = new HashSet <T>();
foreach (T currentStateLoopingThrough in statesToLoopThrough)
{
if (currentStateLoopingThrough.Equals(emptyStateT))
{
foreach (char symbol in ndfa.Symbols)
{
transitions.Add(new Transition <T>(emptyStateT, symbol));
}
continue;
}
//For the state (which may be a composite) get all single states
string[] splitStates = currentStateLoopingThrough.ToString().Split('-');
List <T> splitStatesT = new List <T>(); //List of all states contained in this state
foreach (string stateAsString in splitStates)
{
T stateT = (T)Convert.ChangeType(stateAsString, typeof(T));
splitStatesT.Add(stateT);
}
foreach (char symbol in ndfa.Symbols)
{
HashSet <T> reachableStatesWithThisSymbol = new HashSet <T>();
foreach (T stateToLookFor in splitStatesT)
{
//Then gather all states this can go to
HashSet <T> statesReachedByGivenState = reachableStates[stateToLookFor].Find(x => x.Key == symbol).Value; //Find the states reached with this state-symbol combination
foreach (T foundState in statesReachedByGivenState)
{
reachableStatesWithThisSymbol.Add(foundState);
}
}
//For which the collection forms a single to state
StringBuilder toState = new StringBuilder();
if (reachableStatesWithThisSymbol.Count == 0)
{
toState.Append("$");
} //Create the empty to state
else
{
foreach (T reachableState in reachableStatesWithThisSymbol)
{
//Append to the string
toState.Append(reachableState.ToString() + '-');
}
//And remove last
toState.Remove(toState.Length - 1, 1);
}
T toStateT = (T)Convert.ChangeType(toState.ToString(), typeof(T));
if (StatesAreEqual(currentStateLoopingThrough, toStateT))
{
//Should the toState and the current state be equal, we can point to ourself
transitions.Add(new Transition <T>(currentStateLoopingThrough, symbol));
}
else
{
//Which then gives us the transition of:
//state as the from state,
//The collection as the to state
//And the symbol as the identifier
statesToTraverseNext.Add(toStateT);
transitions.Add(new Transition <T>(currentStateLoopingThrough, toStateT, symbol));
}
}
}
foreach (Transition <T> transition in transitions)
{
dfa.AddTransition(transition);
}
//Check if there still are states left to traverse, which we haven't traversed yet
HashSet <T> statesAlreadyTraversed = new HashSet <T>();
foreach (Transition <T> transition in dfa.Transitions)
{
statesAlreadyTraversed.Add(transition.FromState);
}
//Quick filter all states that happen to be the exact same (for example, C-D-E might be in the to traverse and the already traversed as the same string)
statesToTraverseNext = new HashSet <T>(statesToTraverseNext.Except(statesAlreadyTraversed));
//Since this method adds states anyway, only continue if we still need to traverse states.
if (statesToTraverseNext.Count > 0)
{
GenerateOtherTransitions(statesToTraverseNext);
}
}
static public Automata <String> dfaMutationTestL1()
{
char[] alphabet = { 'a', 'b' };
Automata <String> automata = new Automata <String>(alphabet);
automata.AddTransition(new Transition <string>("A", "B", 'b'));
automata.AddTransition(new Transition <string>("B", "C", 'a'));
automata.AddTransition(new Transition <string>("C", "D", 'b'));
automata.AddTransition(new Transition <string>("D", "E", 'a'));
automata.AddTransition(new Transition <string>("E", "F", 'a'));
automata.AddTransition(new Transition <string>("A", "G", 'a'));
automata.AddTransition(new Transition <string>("B", "G", 'b'));
automata.AddTransition(new Transition <string>("C", "G", 'a'));
automata.AddTransition(new Transition <string>("D", "G", 'b'));
automata.AddTransition(new Transition <string>("E", "G", 'b'));
//End point shenenigans so testing goes a bit smoother
automata.AddTransition(new Transition <string>("F", 'a'));
automata.AddTransition(new Transition <string>("F", 'b'));
automata.AddTransition(new Transition <string>("G", 'a'));
automata.AddTransition(new Transition <string>("G", 'b'));
automata.DefineAsStartState("A");
automata.DefineAsFinalState("F");
return(automata);
}
static public Automata <String> getExampleSlide14Lesson2()
{
char[] alphabet = { 'a', 'b' };
Automata <String> automata = new Automata <String>(alphabet);
automata.AddTransition(new Transition <String>("A", "C", 'a'));
automata.AddTransition(new Transition <String>("A", "B", 'b'));
automata.AddTransition(new Transition <String>("A", "C", 'b'));
automata.AddTransition(new Transition <String>("B", "C", 'b'));
automata.AddTransition(new Transition <String>("B", "C"));
automata.AddTransition(new Transition <String>("C", "D", 'a'));
automata.AddTransition(new Transition <String>("C", "E", 'a'));
automata.AddTransition(new Transition <String>("C", "D", 'b'));
automata.AddTransition(new Transition <String>("D", "B", 'a'));
automata.AddTransition(new Transition <String>("D", "C", 'a'));
automata.AddTransition(new Transition <String>("E", 'a'));
automata.AddTransition(new Transition <String>("E", "D"));
// only on start state in a dfa:
automata.DefineAsStartState("A");
// two final states:
automata.DefineAsFinalState("C");
automata.DefineAsFinalState("E");
return(automata);
}