/////////////////////////////////////////////////////////////////
//
// NFA building functions
//
// Using Thompson Construction, build NFAs from basic inputs or
// compositions of other NFAs.
//
/// <summary>
/// Builds a basic, single input NFA
/// </summary>
/// <param name="in"></param>
/// <returns></returns>
public static NFA BuildNFABasic(input @in)
{
NFA basic = new NFA(2, 0, 1);
basic.AddTrans(0, 1, @in);
return(basic);
}
public NFA(NFA nfa)
{
initial = nfa.initial;
final = nfa.final;
size = nfa.size;
inputs = nfa.inputs;
transTable = nfa.transTable;
}
/// <summary>
/// Fills states 0 up to other.size with other's states.
/// </summary>
/// <param name="other"></param>
public void FillStates(NFA other)
{
for (state i = 0; i < other.size; ++i)
{
for (state j = 0; j < other.size; ++j)
{
transTable[i][j] = other.transTable[i][j];
}
}
SCG.IEnumerator <input> cE = other.inputs.GetEnumerator();
while (cE.MoveNext())
{
inputs.Add(cE.Current);
}
}
public void FillStates(NFA other)
{
for (state i = 0; i < other.size; ++i)
{
for (state j = 0; j < other.size; ++j)
{
transTable[i][j] = other.transTable[i][j];
}
}
for (int i = 0; i < other.inputs.Count; i++)
{
if (!inputs.Contains(other.inputs[i]))
{
inputs.Add(other.inputs[i]);
}
}
}
/// <summary>
/// The main entry point of the Console Application
/// </summary>
/// <param name="args"></param>
static void Main(string[] args)
{
if (args.Length != 3)
{
Console.WriteLine("Call with the regex as an argument.");
Environment.Exit(1);
}
RegexParser myRegexParser = new RegexParser();
// Passing the regex to be preprocessed.
myRegexParser.Init(args[1]);
// Creating a parse tree with the preprocessed regex
ParseTree parseTree = myRegexParser.Expr();
// Checking for a string termination character after
// parsing the regex
if (myRegexParser.Peek() != '\0')
{
Console.WriteLine("Parse error: unexpected char, got {0} at #{1}",
myRegexParser.Peek(), myRegexParser.GetPos());
Environment.Exit(1);
}
PrintTree(parseTree, 1);
NFA nfa = NFA.TreeToNFA(parseTree);
nfa.Show();
DFA dfa = SubsetMachine.SubsetConstruct(nfa);
dfa.Show();
Console.Write("\n\n");
Console.Write("Result: {0}", dfa.Simulate(args[2]));
Console.ReadKey();
}
/// <summary>
/// Builds a star (kleene closure) of nfa (nfa*)
/// How this is done: First will come the new initial state, then NFA, then the
/// new final state
/// </summary>
/// <param name="nfa"></param>
/// <returns></returns>
public static NFA BuildNFAStar(NFA nfa)
{
// Makes room for the new initial state
nfa.ShiftStates(1);
// Makes room for the new final state
nfa.AppendEmptyState();
// Adds new transitions
nfa.AddTrans(nfa.final, nfa.initial, (char)Constants.Epsilon);
nfa.AddTrans(0, nfa.initial, (char)Constants.Epsilon);
nfa.AddTrans(nfa.final, nfa.size - 1, (char)Constants.Epsilon);
nfa.AddTrans(0, nfa.size - 1, (char)Constants.Epsilon);
nfa.initial = 0;
nfa.final = nfa.size - 1;
return(nfa);
}
/// <summary>
/// Builds an alternation of nfa1 and nfa2 (nfa1|nfa2)
/// </summary>
/// <param name="nfa1"></param>
/// <param name="nfa2"></param>
/// <returns></returns>
public static NFA BuildNFAConcat(NFA nfa1, NFA nfa2)
{
// How this is done: First will come nfa1, then nfa2 (its initial state replaced
// with nfa1's final state)
nfa2.ShiftStates(nfa1.size - 1);
// Creates a new NFA and initialize it with (the shifted) nfa2
NFA newNFA = new NFA(nfa2);
// nfa1's states take their places in newNFA
// note: nfa1's final state overwrites nfa2's initial state,
// thus we get the desired merge automagically (the transition
// from nfa2's initial state now transits from nfa1's final state)
newNFA.FillStates(nfa1);
// Sets the new initial state (the final state stays nfa2's final state,
// and was already copied)
newNFA.initial = nfa1.initial;
return(newNFA);
}
/// <summary>
/// Builds an alternation of nfa1 and nfa2 (nfa1|nfa2)
/// </summary>
/// <param name="nfa1"></param>
/// <param name="nfa2"></param>
/// <returns></returns>
public static NFA BuildNFAAlter(NFA nfa1, NFA nfa2)
{
// How this is done: the new nfa must contain all the states in
// nfa1 and nfa2, plus a new initial and final states.
// First will come the new initial state, then nfa1's states, then
// nfa2's states, then the new final state
// make room for the new initial state
nfa1.ShiftStates(1);
// make room for nfa1
nfa2.ShiftStates(nfa1.size);
// create a new nfa and initialize it with (the shifted) nfa2
NFA newNFA = new NFA(nfa2);
// nfa1's states take their places in new_nfa
newNFA.FillStates(nfa1);
// Set new initial state and the transitions from it
newNFA.AddTrans(0, nfa1.initial, (char)Constants.Epsilon);
newNFA.AddTrans(0, nfa2.initial, (char)Constants.Epsilon);
newNFA.initial = 0;
// Make up space for the new final state
newNFA.AppendEmptyState();
// Set new final state
newNFA.final = newNFA.size - 1;
newNFA.AddTrans(nfa1.final, newNFA.final, (char)Constants.Epsilon);
newNFA.AddTrans(nfa2.final, newNFA.final, (char)Constants.Epsilon);
return(newNFA);
}
/// <summary>
/// Builds the Epsilon closure of states for the given NFA
/// </summary>
/// <param name="nfa"></param>
/// <param name="states"></param>
/// <returns></returns>
static Set <state> EpsilonClosure(NFA nfa, Set <state> states)
{
// Push all states onto a stack
SCG.Stack <state> uncheckedStack = new SCG.Stack <state>(states);
// Initialize EpsilonClosure(states) to states
Set <state> epsilonClosure = states;
while (uncheckedStack.Count != 0)
{
// Pop state t, the top element, off the stack
state t = uncheckedStack.Pop();
int i = 0;
// For each state u with an edge from t to u labeled Epsilon
foreach (input input in nfa.transTable[t])
{
if (input == (char)NFA.Constants.Epsilon)
{
state u = Array.IndexOf(nfa.transTable[t], input, i);
// If u is not already in epsilonClosure, add it and push it onto stack
if (!epsilonClosure.Contains(u))
{
epsilonClosure.Add(u);
uncheckedStack.Push(u);
}
}
i = i + 1;
}
}
return(epsilonClosure);
}
/// <summary>
/// Subset machine that employs the powerset construction or subset construction algorithm.
/// It creates a DFA that recognizes the same language as the given NFA.
/// </summary>
public static DFA SubsetConstruct(NFA nfa)
{
DFA dfa = new DFA();
// Sets of NFA states which is represented by some DFA state
Set <Set <state> > markedStates = new Set <Set <state> >();
Set <Set <state> > unmarkedStates = new Set <Set <state> >();
// Gives a number to each state in the DFA
HashDictionary <Set <state>, state> dfaStateNum = new HashDictionary <Set <state>, state>();
Set <state> nfaInitial = new Set <state>();
nfaInitial.Add(nfa.initial);
// Initially, EpsilonClosure(nfa.initial) is the only state in the DFAs states
// and it's unmarked.
Set <state> first = EpsilonClosure(nfa, nfaInitial);
unmarkedStates.Add(first);
// The initial dfa state
state dfaInitial = GenNewState();
dfaStateNum[first] = dfaInitial;
dfa.start = dfaInitial;
while (unmarkedStates.Count != 0)
{
// Takes out one unmarked state and posteriorly mark it.
Set <state> aState = unmarkedStates.Choose();
// Removes from the unmarked set.
unmarkedStates.Remove(aState);
// Inserts into the marked set.
markedStates.Add(aState);
// If this state contains the NFA's final state, add it to the DFA's set of
// final states.
if (aState.Contains(nfa.final))
{
dfa.final.Add(dfaStateNum[aState]);
}
SCG.IEnumerator <input> iE = nfa.inputs.GetEnumerator();
// For each input symbol the NFA knows...
while (iE.MoveNext())
{
// Next state
Set <state> next = EpsilonClosure(nfa, nfa.Move(aState, iE.Current));
// If we haven't examined this state before, add it to the unmarkedStates,
// and make up a new number for it.
if (!unmarkedStates.Contains(next) && !markedStates.Contains(next))
{
unmarkedStates.Add(next);
dfaStateNum.Add(next, GenNewState());
}
KeyValuePair <state, input> transition = new KeyValuePair <state, input>();
transition.Key = dfaStateNum[aState];
transition.Value = iE.Current;
dfa.transTable[transition] = dfaStateNum[next];
}
}
return(dfa);
}
