public void Char()
{
NFA nfa = NFA.Char('a');
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsTrue(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("bbb"));
}
public void Empty()
{
NFA nfa = NFA.Empty();
DFA dfa = nfa.ToDfa();
Assert.IsTrue(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("aaaa"));
Assert.IsFalse(dfa.IsMatch("bbb"));
}
public void Sequence_1_a()
{
NFA nfa = NFA.Sequence(NFA.Char('a'));
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsTrue(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("bb"));
Assert.IsFalse(dfa.IsMatch("ba"));
Assert.IsFalse(dfa.IsMatch("aaa"));
}
public void Concat()
{
NFA nfa = NFA.Concat(NFA.Char('a'), NFA.Char('b'));
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsTrue(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("bb"));
Assert.IsFalse(dfa.IsMatch("ba"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("aba"));
Assert.IsFalse(dfa.IsMatch("abb"));
}
public void a()
{
DFA.State s1 = new DFA.State();
DFA.State s2 = new DFA.State() { IsFinal = true };
s1.AddTransition('a', s2);
DFA dfa = new DFA(s1);
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsTrue(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ba"));
}
public void Misc()
{
NFA nfa = NFA.Sequence(NFA.Star(NFA.Or(NFA.Char('a'), NFA.Char('b'))), NFA.Char('a'), NFA.Char('b'), NFA.Char('b')); // (a|b)*abb
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsTrue(dfa.IsMatch("abb"));
Assert.IsTrue(dfa.IsMatch("aabb"));
Assert.IsTrue(dfa.IsMatch("babb"));
Assert.IsTrue(dfa.IsMatch("ababb"));
Assert.IsTrue(dfa.IsMatch("aaabb"));
Assert.IsTrue(dfa.IsMatch("bbabb"));
Assert.IsTrue(dfa.IsMatch("abababb"));
}
public void NfaToDfaExample() // http://web.cecs.pdx.edu/~harry/compilers/slides/LexicalPart3.pdf
{
NFA nfa = new NFA();
NFA.State[] states = new NFA.State[11];
for (int i = 0; i < states.Length; i++)
{
states[i] = new NFA.State();
}
states[0].AddEmptyTransition(states[1]);
states[0].AddEmptyTransition(states[7]);
states[1].AddEmptyTransition(states[2]);
states[1].AddEmptyTransition(states[4]);
states[2].AddTransition('a', states[3]);
states[3].AddEmptyTransition(states[6]);
states[4].AddTransition('b', states[5]);
states[5].AddEmptyTransition(states[6]);
states[6].AddEmptyTransition(states[1]);
states[6].AddEmptyTransition(states[7]);
states[7].AddTransition('a', states[8]);
states[8].AddTransition('b', states[9]);
states[9].AddTransition('b', states[10]);
states[10].IsFinal = true;
nfa.Start = states[0];
nfa.Exit = states[10];
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsTrue(dfa.IsMatch("abb"));
Assert.IsTrue(dfa.IsMatch("aabb"));
Assert.IsTrue(dfa.IsMatch("babb"));
Assert.IsTrue(dfa.IsMatch("ababb"));
Assert.IsTrue(dfa.IsMatch("aaabb"));
Assert.IsTrue(dfa.IsMatch("bbabb"));
Assert.IsTrue(dfa.IsMatch("abababb"));
}
public void Or_3_abc()
{
NFA nfa = NFA.Or(NFA.Char('a'), NFA.Char('b'), NFA.Char('c'));
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsTrue(dfa.IsMatch("a"));
Assert.IsTrue(dfa.IsMatch("b"));
Assert.IsTrue(dfa.IsMatch("c"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("bb"));
Assert.IsFalse(dfa.IsMatch("ba"));
Assert.IsFalse(dfa.IsMatch("cc"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("aba"));
Assert.IsFalse(dfa.IsMatch("abb"));
Assert.IsFalse(dfa.IsMatch("ccc"));
}
public void Sequence_3_abc()
{
NFA nfa = NFA.Sequence(NFA.Char('a'), NFA.Char('b'), NFA.Char('c'));
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("bb"));
Assert.IsFalse(dfa.IsMatch("ba"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("aba"));
Assert.IsFalse(dfa.IsMatch("abb"));
Assert.IsTrue(dfa.IsMatch("abc"));
Assert.IsFalse(dfa.IsMatch("abcc"));
Assert.IsFalse(dfa.IsMatch("abcd"));
}
public void a()
{
DFA.State s1 = new DFA.State();
DFA.State s2 = new DFA.State()
{
IsFinal = true
};
s1.AddTransition('a', s2);
DFA dfa = new DFA(s1);
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsTrue(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("ab"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("ba"));
}
public void Date()
{
CharRange digit = new CharRange('0', '9');
CharRange dash = new CharRange('-');
// NFA nfa = NFA.Sequence(NFA.Repeat(NFA.Char(digit), 4), NFA.Char(dash), NFA.Repeat(NFA.Char(digit), 2), NFA.Char(dash), NFA.Repeat(NFA.Char(digit), 2));
NFA nfa = NFA.Sequence(
NFA.Char(digit), NFA.Char(digit), NFA.Char(digit), NFA.Char(digit),
NFA.Char(dash),
NFA.Char(digit), NFA.Char(digit),
NFA.Char(dash),
NFA.Char(digit), NFA.Char(digit)
);
DFA dfa = nfa.ToDfa();
Assert.IsTrue(dfa.IsMatch("2014-01-03"));
Assert.IsTrue(dfa.IsMatch("0000-00-00"));
}
public void Plus()
{
NFA nfa = NFA.Plus(NFA.Sequence(NFA.Char('a'), NFA.Char('b')));
DFA dfa = nfa.ToDfa();
Assert.IsFalse(dfa.IsMatch(""));
Assert.IsFalse(dfa.IsMatch("a"));
Assert.IsFalse(dfa.IsMatch("b"));
Assert.IsFalse(dfa.IsMatch("aa"));
Assert.IsFalse(dfa.IsMatch("bb"));
Assert.IsFalse(dfa.IsMatch("ba"));
Assert.IsFalse(dfa.IsMatch("cc"));
Assert.IsFalse(dfa.IsMatch("aaa"));
Assert.IsFalse(dfa.IsMatch("aba"));
Assert.IsFalse(dfa.IsMatch("abb"));
Assert.IsTrue(dfa.IsMatch("ab"));
Assert.IsTrue(dfa.IsMatch("abab"));
Assert.IsTrue(dfa.IsMatch("ababab"));
}
public void DateTime()
{
CharRange digit = new CharRange('0', '9');
CharRange dash = new CharRange('-');
CharRange colon = new CharRange(':');
CharRange seperator = new CharRange(' ');
// NFA date = NFA.Sequence(NFA.Repeat(NFA.Char(digit), 4), NFA.Char(dash), NFA.Repeat(NFA.Char(digit), 2), NFA.Char(dash), NFA.Repeat(NFA.Char(digit), 2));
// NFA time = NFA.Sequence(NFA.Repeat(NFA.Char(digit), 2), NFA.Char(colon), NFA.Repeat(NFA.Char(digit), 2));
NFA date = NFA.Sequence(
NFA.Char(digit), NFA.Char(digit), NFA.Char(digit), NFA.Char(digit),
NFA.Char(dash),
NFA.Char(digit), NFA.Char(digit),
NFA.Char(dash),
NFA.Char(digit), NFA.Char(digit)
);
NFA time = NFA.Sequence(
NFA.Char(digit), NFA.Char(digit),
NFA.Char(colon),
NFA.Char(digit), NFA.Char(digit)
);
NFA datetime = NFA.Sequence(date, NFA.Char(seperator), time);
NFA nfa = NFA.Or(date, time, datetime);
DFA dfa = nfa.ToDfa();
Assert.IsTrue(dfa.IsMatch("00:00"));
Assert.IsTrue(dfa.IsMatch("23:15"));
Assert.IsTrue(dfa.IsMatch("23:59"));
Assert.IsTrue(dfa.IsMatch("2014-01-03"));
Assert.IsTrue(dfa.IsMatch("0000-00-00"));
Assert.IsTrue(dfa.IsMatch("2014-01-03 23:15"));
}
public void Time()
{
CharRange d09 = new CharRange('0', '9');
CharRange d05 = new CharRange('0', '5');
CharRange d03 = new CharRange('0', '3');
CharRange colon = new CharRange(':');
NFA a = NFA.Sequence(NFA.Or(NFA.Char('0'), NFA.Char('1')), NFA.Char(d09), NFA.Char(colon), NFA.Char(d05), NFA.Char(d09)); // [01][0-9]:[0-5][0-9]
NFA b = NFA.Sequence(NFA.Char('2'), NFA.Char(d03), NFA.Char(colon), NFA.Char(d05), NFA.Char(d09)); // [2][0-3]:[0-5][0-9]
NFA c = NFA.Sequence(NFA.Char('2'), NFA.Char('4'), NFA.Char(colon), NFA.Char('0'), NFA.Char('0')); // [2][4]:[0][0]
NFA nfa = NFA.Or(a, b, c);
DFA dfa = nfa.ToDfa();
Assert.IsTrue(dfa.IsMatch("00:00"));
Assert.IsTrue(dfa.IsMatch("01:50"));
Assert.IsTrue(dfa.IsMatch("23:15"));
Assert.IsTrue(dfa.IsMatch("23:59"));
Assert.IsTrue(dfa.IsMatch("24:00"));
Assert.IsFalse(dfa.IsMatch("14:78"));
Assert.IsFalse(dfa.IsMatch("24:59"));
}
// http://web.cecs.pdx.edu/~harry/compilers/slides/LexicalPart3.pdf
public DFA ToDfa()
{
// each DFA states corresponds to several NFA states
Dictionary<DFA.State, HashSet<NFA.State>> map = new Dictionary<DFA.State, HashSet<NFA.State>>();
// create a start state for DFA
DFA.State start = new DFA.State();
DFA dfa = new DFA(start);
map[start] = EmptyClosure(new[] { Start });
Stack<DFA.State> unmarked = new Stack<DFA.State>();
unmarked.Push(start);
while (unmarked.Count > 0)
{
DFA.State state = unmarked.Pop();
// todo: split unique ranges
IEnumerable<CharRange> alphabet = CharRange.Split(map[state].SelectMany(s => s.Alphabet).Distinct().ToArray()).Distinct();
foreach (CharRange c in alphabet)
{
IEnumerable<State> reachableStates = map[state].Where(s => s[c] != null).SelectMany(s => s[c]).ToArray();
HashSet<State> move = EmptyClosure(reachableStates);
if (move.Count > 0)
{
DFA.State newState = map.Where(kp => kp.Value.SetEquals(move))
.Select(kp => kp.Key)
.FirstOrDefault();
if (newState == null)
{
newState = new DFA.State();
unmarked.Push(newState);
map[newState] = move;
}
state.AddTransition(c, newState);
}
}
}
// if any NFA state is a final state, that DFA state is also a final state
foreach (DFA.State state in map.Keys)
{
if (map[state].Any(s => s.IsFinal))
{
state.IsFinal = true;
}
state.Values = map[state].Where(s => s.Values != null).SelectMany(s => s.Values).Distinct().OrderBy(v => v).ToArray();
state.Minimize();
}
return dfa;
}
