//chooses a random word with at least n
private static string RegularGetRandomWord(StringDFA dfa, string currentState, int nRest)
{
if (currentState.Equals("-1"))
{
return(null);
}
if (dfa.F.Contains(currentState) && nRest <= 0)
{
return("");
}
if (nRest < lowestNRest)
{
return(shortestAcceptingWord(dfa, currentState));
}
string[] alphArr = new string[dfa.alphabet.Count];
dfa.alphabet.CopyTo(alphArr, 0);
HashSet <string> letters = new HashSet <string>(alphArr);
while (letters.Any())
{
int i = randInt(0, letters.Count);
string letter = letters.ToArray()[i];
letters.Remove(letter);
string state = dfa.getStateFromState(letter, currentState);
string returnedWord = RegularGetRandomWord(dfa, state, nRest - 1);
if (returnedWord != null)
{
return(letter + returnedWord);
}
}
return(null);
}
// returns start and end index (both inclusive) of mid word
private static TwoTuple <int, int> detectLoopFromState(StringDFA dfa, string currentState, string word, int n)
{
List <string> statesVisited = new List <string>();
if (!dfa.Accepts(word))
{
throw new PumpingLemmaException("Automaton does not accept this word!");
}
statesVisited.Add(currentState);
int currentLetter = 0;
while (currentLetter <= n && currentLetter < word.Length)
{
string newState = dfa.delta[new TwoTuple <string, string>(currentState, word.ElementAt(currentLetter) + "")];
if (statesVisited.Contains(newState))
{
int index = statesVisited.IndexOf(newState);
return(new TwoTuple <int, int>(index, currentLetter));
}
else
{
currentLetter++;
currentState = newState;
statesVisited.Add(currentState);
}
}
return(null);
}
private static bool RegularCheckSplit(StringDFA dfa, string start, string mid, string end)
{
string fullWord = pumpMid(start, mid, end, 1);
HashSet <Tuple <string, string, string> > equivalentSplits = new HashSet <Tuple <string, string, string> >();
equivalentSplits.Add(new Tuple <string, string, string>(start, mid, end));
for (int k = 1; k <= mid.Length; k++)
{
string newEnd = String.Copy(end);
string newStart = String.Copy(start);
while (newEnd.Length >= k)
{
string pre = mid.Length > k?mid.Substring(k) : "";
if (pre + newEnd.Substring(0, k) == mid)
{
newEnd = newEnd.Substring(k);
newStart = newStart + mid.Substring(0, k);
equivalentSplits.Add(new Tuple <string, string, string>(newStart, mid, newEnd));
}
else
{
break;
}
}
newEnd = String.Copy(end);
newStart = String.Copy(start);
while (newStart.Length >= k)
{
string post = mid.Length > k?mid.Substring(0, k) : "";
if (newStart.Substring(newStart.Length - k) + post == mid)
{
newEnd = mid.Substring(mid.Length - k) + newEnd;
newStart = newStart.Substring(0, newStart.Length - k);
equivalentSplits.Add(new Tuple <string, string, string>(newStart, mid, newEnd));
}
else
{
break;
}
}
}
foreach (var split in equivalentSplits)
{
//check whether mid is a loop
string stateAfterStart = dfa.getStateFromState(split.Item1, dfa.q_0);
if (stateAfterStart.Equals(dfa.getStateFromState(split.Item2, stateAfterStart)))
{
return(true);
}
}
return(false);
}
public static Tuple <string, string, string> RegularGetSplit(StringDFA dfa, string word, int n)
{
TwoTuple <int, int> midIndex = detectLoopFromState(dfa, dfa.q_0, word, n);
if (midIndex != null)
{
string start = word.Substring(0, midIndex.first);
string mid = word.Substring(midIndex.first, midIndex.second - midIndex.first + 1);
string end = word.Substring(midIndex.second + 1);
return(Tuple.Create(start, mid, end));
}
return(null);
}
public DFA <string, HashSet <State <Set <State <string> > > > > ToDFA()
{
//check if every variable appears only once
varsSeen = new HashSet <VariableType>();
if (!checkVariableOnce(symbolic_string))
{
throw new PumpingLemmaException("Each variable must only appear once!");
}
NFA <string, string> nfa = null;
var epsilonTransitions = new HashSet <TwoTuple <State <string>, State <string> > >();
ArithmeticLanguage unaryLanguage = this;
var comparisons = unaryLanguage.getReducedUnaryConstraints();
currentId = 0;
//only epsilon
if (symbolic_string.isEpsilon())
{
var startState = new State <string>(0, "0");
var finalState = new State <string>(1, "1");
var states = new HashSet <State <string> >();
states.Add(startState);
states.Add(finalState);
var Q_0 = new HashSet <State <string> >();
Q_0.Add(startState);
var F = new HashSet <State <string> >();
F.Add(startState);
var delta = new Dictionary <TwoTuple <State <string>, string>, HashSet <State <string> > >();
foreach (var letter in alphabet)
{
delta.Add(new TwoTuple <State <string>, string>(startState, letter), new HashSet <State <string> >(new State <string>[] { finalState }));
}
nfa = new NFA <string, string>(states, new HashSet <string>(alphabet), delta, Q_0, F);
}
else
{
var tuple = epsNFA(symbolic_string, new HashSet <string>(alphabet), comparisons);
nfa = tuple.Item1;
epsilonTransitions = tuple.Item2;
}
NFA <string, string> nfaCollected = StringDFA.collectEpsilonTransitions(nfa.Q, new HashSet <string>(alphabet), nfa.delta, nfa.Q_0, nfa.F, epsilonTransitions);
var dfa = nfaCollected.NFAtoDFA();
var dfa_min = dfa.MinimizeHopcroft();
return(dfa_min);
}
public static string RegularGetWord(StringDFA dfa, int n)
{
if (dfa.states.Count <= n)
{
//choose random word
return(RegularGetRandomWord(dfa, dfa.q_0, n));
}
//choose word that doesn't contain loop
string word = RegularGetUnpumpableWord(dfa, dfa.q_0, new HashSet <string>(new string[] { dfa.q_0 }), n);
if (word == null)
{
return(RegularGetRandomWord(dfa, dfa.q_0, n));
}
return(word);
}
/*
* ----------------------------------------------------------------------------------------------------
* Decision Making
* ----------------------------------------------------------------------------------------------------
*/
public static string RegularCheckWord(StringDFA dfa, int n, string word)
{
if (word.Length < n)
{
return("<false>Word is too short.</false>");
}
foreach (char c in word)
{
if (!dfa.alphabet.Contains(c + ""))
{
return("<false>Word contains illegal letters.</false>");
}
}
if (dfa.Accepts(word))
{
return("<true></true>");
}
return("<false>Word is not in the language.</false>");
}
public static int RegularGetI(StringDFA dfa, string start, string mid, string end)
{
if (!dfa.Accepts(start + end))
{
return(0);
}
if (RegularCheckSplit(dfa, start, mid, end))
{
return(1); //AI admits defeat
}
int i = 2;
while (dfa.Accepts(pumpMid(start, mid, end, i)))
{
i++;
//for debuugging purposes:
if (i > 99)
{
return(1);
}
}
return(i);
}
public static bool RegularCheckI(StringDFA dfa, string start, string mid, string end, int i)
{
return(dfa.Accepts(pumpMid(start, mid, end, i)));
}
private static string RegularGetUnpumpableWord(StringDFA dfa, string currentState, HashSet <string> statesUsed, int nRest)
{
if (currentState.Equals("-1"))
{
return(null);
}
if (dfa.F.Contains(currentState) && nRest <= 0)
{
return("");
}
if (dfa.states.Count == statesUsed.Count)
{
return(null);
}
string[] alphArr = new string[dfa.alphabet.Count];
dfa.alphabet.CopyTo(alphArr, 0);
HashSet <string> letters = new HashSet <string>(alphArr);
while (letters.Any())
{
int i = randInt(0, letters.Count);
string letter = letters.ToArray()[i];
letters.Remove(letter);
string state = dfa.getStateFromState(letter, currentState);
if (nRest > 0)
{
if (!statesUsed.Contains(state))
{
bool contin = true;
foreach (string l in alphArr)
{
if (statesUsed.Contains(dfa.getStateFromState(l, state)))
{
contin = false;
break;
}
}
if (contin)
{
HashSet <string> newStatesUsed = new HashSet <string>(statesUsed);
newStatesUsed.Add(state);
string returnedWord = RegularGetUnpumpableWord(dfa, state, newStatesUsed, nRest - 1);
if (returnedWord != null)
{
return(letter + returnedWord);
}
}
}
}
else
{
string returnedWord = RegularGetUnpumpableWord(dfa, state, statesUsed, nRest - 1);
if (returnedWord != null)
{
return(letter + returnedWord);
}
}
}
return(null);
}
public static int RegularGetN(StringDFA dfa)
{
var newDfa = dfa.ToDFA();
return(newDfa.Q.Count);
}
private static string shortestAcceptingWord(StringDFA dfa, string state)
{
Dictionary <string, int> stateDistance = new Dictionary <string, int>();
Dictionary <string, string> statePredecessor = new Dictionary <string, string>();
HashSet <string> allStates = new HashSet <string>();
foreach (string s in dfa.states)
{
stateDistance.Add(s, Int32.MaxValue);
statePredecessor.Add(s, null);
allStates.Add(s);
}
stateDistance[state] = 0;
while (allStates.Any())
{
HashSet <KeyValuePair <string, int> > minStates = new HashSet <KeyValuePair <string, int> >();
var ordered = stateDistance.OrderBy(x => x.Value);
int i = 1;
minStates.Add(ordered.First());
int minVal = ordered.First().Value;
while (i < ordered.Count() && minVal == ordered.ElementAt(i).Value)
{
minStates.Add(ordered.ElementAt(i));
i++;
}
i = randInt(0, minStates.Count());
var nextState = minStates.ToArray()[i].Key;
allStates.Remove(nextState);
HashSet <string> neighbours = new HashSet <string>();
foreach (var letter in dfa.alphabet)
{
string value = null;
if (dfa.delta.TryGetValue(new TwoTuple <string, string>(nextState, letter), out value))
{
neighbours.Add(value);
}
}
foreach (string neighbour in neighbours)
{
if (allStates.Contains(neighbour))
{
int alt = stateDistance[nextState] + 1;
if (alt < stateDistance[neighbour])
{
stateDistance[neighbour] = alt;
statePredecessor[neighbour] = nextState;
}
}
}
}
HashSet <string> shortestWords = new HashSet <string>();
foreach (var acceptingState in dfa.F)
{
StringBuilder sb = new StringBuilder();
string lastState = acceptingState;
while (statePredecessor[lastState] != null)
{
string letter = dfa.delta.Where(x =>
x.Key.first == statePredecessor[lastState] &&
x.Value == lastState).First().Key.second;
sb.Insert(0, letter);
lastState = statePredecessor[lastState];
}
shortestWords.Add(sb.ToString());
}
HashSet <string> minWords = new HashSet <string>();
var orderedWords = shortestWords.OrderBy(x => x.Length);
int j = 1;
minWords.Add(orderedWords.First());
int minL = orderedWords.First().Length;
while (j < orderedWords.Count() && minL == orderedWords.ElementAt(j).Length)
{
minWords.Add(orderedWords.ElementAt(j));
j++;
}
j = randInt(0, minWords.Count());
return(minWords.ToArray()[j]);
}
public StringDFA(XElement automatonXML, bool deterministic)
{
AutomatonXML aXML;
var xmlSerializer = new XmlSerializer(typeof(AutomatonXML));
var doc = new XDocument();
doc.Add(automatonXML);
using (var reader = doc.CreateReader())
{
aXML = (AutomatonXML)xmlSerializer.Deserialize(reader);
}
if (deterministic)
{
this.q_0 = aXML.initState[0].sid;
this.F = new HashSet <string>();
foreach (var state in aXML.acceptingStates)
{
this.F.Add(state.sid);
}
this.delta = new Dictionary <TwoTuple <string, string>, string>();
foreach (var transition in aXML.transitions)
{
delta.Add(new TwoTuple <string, string>(transition.from + "", transition.read), transition.to + "");
}
this.states = new HashSet <string>();
foreach (var state in aXML.states)
{
this.states.Add(state.sid);
}
this.alphabet = new HashSet <string>();
foreach (string letter in aXML.alphabet)
{
alphabet.Add(letter);
}
}
else
{
//NFA
HashSet <State <string> > states = new HashSet <State <string> >();
foreach (var state in aXML.states)
{
if (Int32.TryParse(state.sid, out int parsed))
{
states.Add(new State <string>(parsed, state.sid));
}
else
{
states.Add(new State <string>(0, state.sid));
}
}
HashSet <string> alphabet = new HashSet <string>();
foreach (var letter in aXML.alphabet)
{
alphabet.Add(letter);
}
HashSet <TwoTuple <State <string>, State <string> > > epsilonTransitions = new HashSet <TwoTuple <State <string>, State <string> > >();
Dictionary <TwoTuple <State <string>, string>, HashSet <State <string> > > delta = new Dictionary <TwoTuple <State <string>, string>, HashSet <State <string> > >();
foreach (var transition in aXML.transitions)
{
if (transition.read.Equals("epsilon"))
{
epsilonTransitions.Add(new TwoTuple <State <string>, State <string> >(new State <string>(transition.from + ""), new State <string>(transition.to + "")));
}
else
{
TwoTuple <State <string>, string> twoTuple = new TwoTuple <State <string>, string>(new State <string>(transition.from + ""), transition.read);
HashSet <State <string> > set;
if (delta.TryGetValue(twoTuple, out set))
{
set.Add(new State <string>(transition.to + ""));
}
else
{
set = new HashSet <State <string> >();
set.Add(new State <string>(transition.to + ""));
delta.Add(new TwoTuple <State <string>, string>(new State <string>(transition.from + ""), transition.read), set);
}
}
}
HashSet <State <string> > Q_0 = new HashSet <State <string> >();
foreach (var state in aXML.initState)
{
Q_0.Add(new State <string>(state.sid));
}
HashSet <State <string> > F = new HashSet <State <string> >();
foreach (var state in aXML.acceptingStates)
{
F.Add(new State <string>(state.sid));
}
var nfa = collectEpsilonTransitions(states, alphabet, delta, Q_0, F, epsilonTransitions);
var dfa = nfa.NFAtoDFA();
var dfa_min = dfa.MinimizeHopcroft();
var strDFA = new StringDFA(dfa_min);
//rename error set
foreach (var state in strDFA.states)
{
if (!strDFA.F.Contains(state))
{
bool errorStateFound = true;
foreach (var letter in strDFA.alphabet)
{
if (!strDFA.delta[new TwoTuple <string, string>(state, letter)].Equals(state))
{
errorStateFound = false;
break;
}
}
if (errorStateFound)
{
strDFA.states.Remove(state);
strDFA.states.Add("-1");
if (strDFA.q_0.Equals(state))
{
strDFA.q_0 = "-1";
}
HashSet <KeyValuePair <TwoTuple <string, string>, string> > entriesToChange = new HashSet <KeyValuePair <TwoTuple <string, string>, string> >();
foreach (var entry in strDFA.delta)
{
if (entry.Value.Equals(state))
{
entriesToChange.Add(entry);
}
}
foreach (var entry in entriesToChange)
{
strDFA.delta[entry.Key] = "-1";
}
foreach (var letter in strDFA.alphabet)
{
strDFA.delta.Remove(new TwoTuple <string, string>(state, letter));
strDFA.delta.Add(new TwoTuple <string, string>("-1", letter), "-1");
}
break;
}
}
}
this.alphabet = strDFA.alphabet;
this.delta = strDFA.delta;
this.F = strDFA.F;
this.q_0 = strDFA.q_0;
this.states = strDFA.states;
}
}