/// <summary>
/// Concatinates two NDFA's.
/// </summary>
/// <param name="m1">The second NDFA to concatinate with.</param>
/// <returns>The new graph that is this and m1 concatinated.</returns>
public Graph Concat(Graph m1)
{
var m = new Graph ();
var m2 = this;
var m1FinalStates = m1.FindFinalStates (m1.StartState);
foreach (var finalState in m1FinalStates) {
//create a new connection to m2 initial state
var m1FinalTom2Initial = new GraphStateConnection () {
Start = finalState,
End = m2.StartState,
ConnectedBy =
Word.Epsilon
};
//make the connection
finalState.Out.Add (m1FinalTom2Initial);
//kill m1 final states and leave m2 as finals for m
finalState.IsFinal = false;
}
//update state count for new graph
m.StartState = m1.StartState;
m.StateCount = m1.StateCount + m2.StateCount;
if (updateStateNumber) {
RenumberStates (m.StartState);
}
return m;
}
public void CreatesCorrectConnection()
{
var m1Start = new GraphState () {
StateNumber = 0,
IsFinal = true
};
var m2Start = new GraphState () {
StateNumber = 1,
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Concat (m2);
ndfa.StartState.Out[0].Start.Should ().Be (m2Start);
ndfa.StartState.Out[0].End.Should ().Be (m1Start);
ndfa.StartState.Out[0].ConnectedBy.Letter.Should ().Be (Word.Epsilon.Letter);
ndfa.StartState.Out[0].ConnectedBy.Mapping.Should ().Be (Word.Epsilon.Mapping);
}
Graph ProcessOperation(Graph initGraph, Operation op, Stack<Word> opStack)
{
// create base graph if not done already.
if(initGraph == null){
//start of our graph
initGraph = Graph.CreateNewGraph(opStack.Pop());
}
//if kleene operation, do it here.
if (op.Mapping == OperationType.Kleene) {
initGraph = initGraph.Kleene ();
}
//now process each operation
while(opStack.Count != 0){
//get next letter to work with.
var wordToAdd = opStack.Pop();
//depending on the mapped type, do operation on graph
//with the new letter.
if(op.Mapping == OperationType.Concat)
initGraph = initGraph.Concat(wordToAdd);
else if(op.Mapping == OperationType.Union)
initGraph = initGraph.Union(wordToAdd);
}
//return the created graph.
return initGraph;
}
/// <summary>
/// Parses a given expression into a graph.
/// </summary>
/// <returns>The built graph.</returns>
/// <param name="expression">The expression to create the graph from.</param>
/// <param name="initGraph">The graph to append too. Used for recursion.</param>
public Graph ParseExpression(string expression, Graph initGraph = null)
{
var lang = new Language ();
var ops = new Operations ();
expression = expression.Trim ();
var opStack = new Stack<Word>();
foreach (char letter in expression) {
//find the language mapping
var inLanguage = lang
.DefaultIfEmpty(null)
.FirstOrDefault (w => w.Letter == letter);
//find the operation mapping
var inOps = ops
.DefaultIfEmpty(null)
.FirstOrDefault(w => w.Letter == letter);
//not in the language or operators
if(inLanguage == null && inOps == null){
throw new InvalidLanguageException("Invalid input: " + letter);
}
//it is valid language input, so add it to the list.
if(inLanguage != null){
opStack.Push(inLanguage);
continue;
}
else{
//not a letter, so must be an operation
//verify that it has the correct arg count for that type of operation.
if (opStack.Count != inOps.MinArgCount && initGraph == null) {
throw new InvalidLanguageException (
string.Format(
"Unbalanced arguement count for operation (expected {0}, but got {1}.",
inOps.MinArgCount, opStack.Count
));
}
//operation, so stop, and process graph
initGraph = ProcessOperation(initGraph, inOps, opStack);
}
}
//expression was given with no operation, so error out.
if (opStack.Count > 0) {
throw new InvalidLanguageException ("No operation was specified in the given expression.");
}
//once done with graph, renumber the states.
initGraph.RenumberStates ();
//return the completed graph.
return initGraph;
}
public void Print(Graph toPrint)
{
//if state has been visited, don't do it again to avoid SO
List<GraphState> visited = new List<GraphState> ();
List<string> output = new List<string> ();
//output start state
Console.WriteLine ("Start state is: q" + toPrint.StartState.StateNumber);
//find all state strings to output.
PrintStatesOutputs (toPrint.StartState, visited, output);
//now print each row.
foreach (var row in output.OrderBy (s => s)) {
Console.WriteLine (row);
}
}
public void CreatesOneConnection()
{
var m1Start = new GraphState () {
StateNumber = 0,
IsFinal = true
};
var m2Start = new GraphState () {
StateNumber = 1,
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Concat (m2);
ndfa.StartState.Out.Count.Should ().Be (1);
}
public void HasLoopConnection()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var ndfa = m1.Kleene();
var self = ndfa.StartState.Out [0].End.Out [0].End;
self.Should ().Be (ndfa.StartState);
}
public void HasCorrectFinalStates()
{
var m1Start = new GraphState () {
StateNumber = 0,
IsFinal = true
};
var m2Start = new GraphState () {
StateNumber = 1,
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Concat (m2);
var finals = ndfa.FindFinalStates (ndfa.StartState);
finals.Count.Should ().Be (1);
finals [0].Should ().Be (m1Start);
}
public void HasCorrectStateCount()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m2Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Union (m2);
ndfa.StateCount.Should ().Be (4);
}
public void StateNumbersCorrect()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m2Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Union (m2);
ndfa.StartState.StateNumber.Should ().Be (0);
ndfa.StartState.Out [0].End.StateNumber.Should ().Be (1);
}
public void CreatesCorrectEpsilonConnections()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m2Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var finalState = new GraphState {
StateNumber = 2,
IsFinal = true
};
var ndfa = m1.Union (m2);
ndfa.StartState.Out[0].Start.Should ().Be (ndfa.StartState);
ndfa.StartState.Out[0].End.Should ().Be (m1Start);
ndfa.StartState.Out[0].ConnectedBy.Letter.Should ().Be (Word.Epsilon.Letter);
ndfa.StartState.Out[0].ConnectedBy.Mapping.Should ().Be (Word.Epsilon.Mapping);
ndfa.StartState.Out[1].Start.Should ().Be (ndfa.StartState);
ndfa.StartState.Out[1].End.Should ().Be (m2Start);
ndfa.StartState.Out[1].ConnectedBy.Letter.Should ().Be (Word.Epsilon.Letter);
ndfa.StartState.Out[1].ConnectedBy.Mapping.Should ().Be (Word.Epsilon.Mapping);
//epsilons to final state
var firstFinal = ndfa.StartState.Out[0].End;
var secondFinal = ndfa.StartState.Out [1].End;
var finalConnection1 = firstFinal.Out [0];
finalConnection1.ConnectedBy.Should ().Be (Word.Epsilon);
finalConnection1.Start.Should ().Be (firstFinal);
var finalConnection2 = secondFinal.Out [0];
finalConnection2.ConnectedBy.Should ().Be (Word.Epsilon);
finalConnection2.Start.Should ().Be (secondFinal);
//now check the final state
finalConnection1.End.Should ().Be (finalState);
finalConnection2.End.Should ().Be (finalState);
}
public void CreatesFourConnections()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m2Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Union (m2);
ndfa.StartState.Out.Count.Should ().Be (2);
ndfa.StartState.Out [0].End.Out.Count.Should ().Be (1);
ndfa.StartState.Out [1].End.Out.Count.Should ().Be (1);
}
/// <summary>
/// Performs the Union on two NDFA's.
/// </summary>
/// <param name="m2">The NDFA to Union with.</param>
/// <returns>>A new NDFA that is the union of the two graphs.</returns>
public Graph Union(Graph m2)
{
var m = new Graph ();
var m1 = this;
//new start state
m.StartState = new GraphState ();
//new q0
var newFinalState = new GraphState () {
IsFinal = true
};
//connection from q0 to q1 over epsilon
var q0Toq1 = new GraphStateConnection () {
ConnectedBy = Word.Epsilon,
Start = m.StartState,
End = m1.StartState
};
//connection from q0 to q2
var q0Toq2 = new GraphStateConnection () {
ConnectedBy = Word.Epsilon,
Start = m.StartState,
End = m2.StartState
};
//attach states.
m.StartState.Out.Add (q0Toq1);
m.StartState.Out.Add (q0Toq2);
var m1Finals = FindFinalStates (m1.StartState);
var m2Finals = FindFinalStates (m2.StartState);
foreach (var final in m1Finals) {
final.IsFinal = false;
var finalConnection = new GraphStateConnection () {
Start = final,
End = newFinalState,
ConnectedBy = Word.Epsilon
};
final.Out.Add (finalConnection);
}
foreach (var final in m2Finals) {
final.IsFinal = false;
var finalConnection = new GraphStateConnection () {
Start = final,
End = newFinalState,
ConnectedBy = Word.Epsilon
};
final.Out.Add (finalConnection);
}
//update the total state count
m.StateCount = m1.StateCount + m2.StateCount + 2;
if (updateStateNumber) {
RenumberStates (m.StartState);
}
return m;
}
public void StateNumbersCorrect()
{
var m1 = new Graph () {
StartState = new GraphState () {
IsFinal = false,
StateNumber = 0
}
};
m1.StartState.Out.Add (new GraphStateConnection () {
ConnectedBy = new Word('a'),
Start = m1.StartState,
End = new GraphState() {
StateNumber = 1
}
});
var ndfa = m1.Kleene ();
ndfa.StartState.Out [0].End.StateNumber.Should ().Be (0);
ndfa.StartState.Out [0].End.Out[0].End.StateNumber.Should ().Be (1);
ndfa.StartState.StateNumber.Should ().Be (2);
}
/// <summary>
/// Helper method to create a new graph based on a specified word.
/// Creates a two node graph that is connected by the specified word.
/// </summary>
/// <returns>The new graph.</returns>
/// <param name="fromConnection">The word to connect by.</param>
internal static Graph CreateNewGraph(Word fromConnection)
{
var graph = new Graph () {
StartState = new GraphState() { StateNumber = 0 }
};
graph.StartState.Out.Add (new GraphStateConnection () {
Start = graph.StartState,
End = new GraphState() { StateNumber = 1, IsFinal = true },
ConnectedBy = fromConnection
});
graph.StateCount = 2;
return graph;
}
public void HasCorrectTwoStateCount()
{
var m1Start = new GraphState () {
StateNumber = 0,
IsFinal = true
};
var m2Start = new GraphState () {
StateNumber = 1,
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var m2 = new Graph () {
StartState = m2Start
};
var ndfa = m1.Concat (m2);
ndfa.StateCount.Should ().Be (2);
}
public void HasCorrectSingleFinalState()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var finals = m1.FindFinalStates (m1.StartState);
finals [0].Should ().Be (m1Start);
}
public void HasCorrectCount()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var finals = m1.FindFinalStates (m1.StartState);
finals.Count.Should ().Be (1);
}
public void CountsOnlyOneFinal()
{
var m1Start = new GraphState () {
IsFinal = true
};
var secondFinal = new GraphState () {
IsFinal = true
};
var thirdFinal = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var epsilonConnection1 = new GraphStateConnection {
Start = m1Start,
End = secondFinal,
ConnectedBy = Word.Epsilon
};
var epsilonConnection2 = new GraphStateConnection {
Start = secondFinal,
End = thirdFinal,
ConnectedBy = Word.Epsilon
};
m1.StartState.Out.Add (epsilonConnection1);
secondFinal.Out.Add (epsilonConnection2);
var finals = m1.FindFinalStates (m1.StartState);
finals.Count.Should ().Be (3);
}
public void NewInitialShouldBeFinal()
{
var m1Start = new GraphState () {
IsFinal = true
};
var m1 = new Graph () {
StartState = m1Start
};
var ndfa = m1.Kleene ();
ndfa.StartState.IsFinal.Should ().BeTrue ();
}
/// <summary>
/// Perfoms a Kleene operation on the graph.
/// </summary>
/// <returns>The new graph after the Kleene operation.</returns>
public Graph Kleene()
{
var m = new Graph ();
var m1 = this;
var finals = FindFinalStates (m1.StartState);
var oldInitial = m1.StartState;
//create new init and final state.
var newInitial = new GraphState (){
IsFinal = true,
StateNumber = m1.StateCount + 1
};
//create connection from new initial to the old initial through epsilon
var initialEpsilonConnection = new GraphStateConnection {
End = oldInitial,
Start = newInitial,
ConnectedBy = Word.Epsilon
};
//add the connection to the states.
newInitial.Out.Add (initialEpsilonConnection);
foreach (var finalState in finals) {
//now create epsilon connections from final to original start state
var finalToOldInitialConnection = new GraphStateConnection {
End = newInitial,
Start = finalState,
ConnectedBy = Word.Epsilon
};
finalState.IsFinal = false;
//now connect them
finalState.Out.Add(finalToOldInitialConnection);
}
//now attach the new init state to the graph
m.StartState = newInitial;
m.StateCount = m1.StateCount + 1;
return m;
}