private static Dictionary <Set <State <S> >, TwoTuple <bool, List <Set <State <S> > > > > BuildDependencyGraph <C, S>(DFA <C, S> D)
{
//Dependency Graph for automaton D modelled as a Dictionary
//'Value' is set of all nodes, that 'key' has an edge to
var G = new Dictionary <Set <State <S> >, TwoTuple <bool, List <Set <State <S> > > > >();
for (int i = 0; i < D.Q.Count; i++)
{
for (int j = i + 1; j < D.Q.Count; j++)
{
var p = D.Q.ElementAt(i);
var q = D.Q.ElementAt(j);
var v = new Set <State <S> >();
v.content.Add(p);
v.content.Add(q);
var l = new List <Set <State <S> > >();
G.Add(v, new TwoTuple <bool, List <Set <State <S> > > >(false, l));
}
}
for (int i = 0; i < D.Q.Count; i++)
{
for (int j = i + 1; j < D.Q.Count; j++)
{
var p_dash = D.Q.ElementAt(i);
var q_dash = D.Q.ElementAt(j);
var v_dash = new Set <State <S> >();
v_dash.content.Add(p_dash);
v_dash.content.Add(q_dash);
foreach (C a in D.Sigma)
{
var t1 = new TwoTuple <State <S>, C>(p_dash, a);
var t2 = new TwoTuple <State <S>, C>(q_dash, a);
State <S> p, q;
if (!D.delta.TryGetValue(t1, out p))
{
}
if (!D.delta.TryGetValue(t2, out q))
{
}
if (!p.Equals(q))
{
Set <State <S> > v = new Set <State <S> >();
v.content.Add(p);
v.content.Add(q);
TwoTuple <bool, List <Set <State <S> > > > t;
if (!G.TryGetValue(v, out t))
{
}
t.second.Add(v_dash);
}
}
}
}
return(G);
}
public State <S> ReadWordFrom(List <C> sequence, State <S> q)
{
State <S> current = q;
for (int i = 0; i < sequence.Count; i++)
{
TwoTuple <State <S>, C> tuple = new TwoTuple <State <S>, C>(current, sequence[i]);
if (!delta.TryGetValue(tuple, out current))
{
return(null);
}
}
return(current);
}
/* METHOD THAT RUNS THIS DFA ON A WORD
*
* Input: sequence: Word over the alphabet of characters of type C
*
* Output: true, if this DFA accepts the word 'sequence'
* false, otherwise
*/
public bool AcceptsFrom(List <C> sequence, State <S> q)
{
State <S> current = q;
for (int i = 0; i < sequence.Count; i++)
{
TwoTuple <State <S>, C> tuple = new TwoTuple <State <S>, C>(current, sequence[i]);
if (!delta.TryGetValue(tuple, out current))
{
return(false);
}
}
return(F.Contains(current));
}
public ThreeTuple <bool, string[], StringBuilder[]> ComputeTapes(string[] tapeList, int maxSteps)
{
State <S> current = q_0;
ThreeTuple <State <S>, string, string> resolutionList = new ThreeTuple <State <S>, string, string>(current, "", "");
int[] tapeHeadPosition = new int[tapeList.Length];
StringBuilder[] strB = new StringBuilder[tapeList.Length];
int i = 0;
for (i = 0; i < tapeList.Length; i++)
{
tapeHeadPosition[i] = 0;
strB[i] = new StringBuilder(tapeList[i]);
}
bool acceptState;
i = 0;
for (i = 0; i < maxSteps; i++)
{
string readingSymbols = "";// = ""; //tapeList[tapeHeadPostiotions[]] + tapeList[] + tapeList[]);
for (int j = 0; j < tapeHeadPosition.Length; j++)
{
//readingSymbols = readingSymbols + tapeList[j][tapeHeadPosition[j]];
readingSymbols = readingSymbols + strB[j][tapeHeadPosition[j]];
}
TwoTuple <State <S>, string> tuple = new TwoTuple <State <S>, string>(current, readingSymbols);
if (!delta.TryGetValue(tuple, out resolutionList))
{
break;
}
for (int k = 0; k < tapeHeadPosition.Length; k++)
{
//tapeList[k][tapeHeadPosition[k]] = resolutionList.second.ToCharArray()[k];
strB[k][tapeHeadPosition[k]] = resolutionList.second.ToCharArray()[k];
current = resolutionList.first;
switch (resolutionList.third.ToCharArray()[k])
{
case 'R':
tapeHeadPosition[k]++;
if (tapeHeadPosition[k] == strB[k].Length)
{
strB[k].Append("?");
}
break;
case 'L':
if (tapeHeadPosition[k] == 0)
{
strB[k].Insert(0, "?");
}
else
{
tapeHeadPosition[k]--;
}
break;
case 'N':
break;
}
}
}
if (i == maxSteps)
{
acceptState = false;
}
else
{
acceptState = F.Contains(current);
}
/*State<S> current = q_0;
* int[] tapeHeadPosition = new int[tapeList.Length];
*
* for (int i = 0; i < maxSteps; i++)
* {
* S[] readingSymbols = new S[tapeList.Length];// = ""; //tapeList[tapeHeadPostiotions[]] + tapeList[] + tapeList[]);
* for (int j = 0; j < tapeHeadPosition.Length; j++)
* {
* readingSymbols[j] = tapeList[tapeHeadPosition[j]];
* TwoTuple<State<S>, S> tuple = new TwoTuple<State<S>, S>(current, readingSymbols);
* if (!delta.TryGetValue(tuple, out current))
* break;// return false;
* }
*
* return F.Contains(current);*/
//TODO List generation from tapeList
//var resolutionStringList = new List<string>();
var resolutionStringList = new string[tapeHeadPosition.Length];
for (int j = 0; j < tapeHeadPosition.Length; j++)
{
string currentTapeWord = "";
while (tapeHeadPosition[j] < strB[j].Length && strB[j][tapeHeadPosition[j]] != '?')
{
currentTapeWord = currentTapeWord + strB[j][tapeHeadPosition[j]];
tapeHeadPosition[j]++;
}
resolutionStringList[j] = currentTapeWord;
}
return(new ThreeTuple <bool, string[], StringBuilder[]>(acceptState, resolutionStringList, strB));
}
/* METHOD THAT MINIMIZES THIS DFA USING HOPCROFT'S ALGORITHM
*
* Output: Minimal DFA recognizing the same language as this one.
* States are labelled as sets of states of this automaton.
*/
public DFA <C, HashSet <State <S> > > MinimizeHopcroft()
{
int no_states = Q.Count;
//Stores for state q (key) in which set (value) of the state partition it is
//(the value is the new state made out of this set).
var state_dict = new Dictionary <State <S>, State <HashSet <State <S> > > >();
var P = ComputeLanguagePartition();
var Q_new = new HashSet <State <HashSet <State <S> > > >();
var delta_new = new Dictionary <TwoTuple <State <HashSet <State <S> > >, C>, State <HashSet <State <S> > > >();
var F_new = new HashSet <State <HashSet <State <S> > > >();
State <HashSet <State <S> > > q_0_new = null;
int i = 0;
foreach (HashSet <State <S> > B in P)
{
var B_as_State = new State <HashSet <State <S> > >(i, B);
Q_new.Add(B_as_State);
if (F.Contains(B.ElementAt(0)))
{
F_new.Add(B_as_State);
}
foreach (State <S> q in B)
{
state_dict.Add(q, B_as_State);
if (q.Equals(q_0))
{
q_0_new = B_as_State;
}
}
i++;
}
foreach (var c in delta)
{
State <HashSet <State <S> > > B1, B2;
State <S> q1 = c.Key.first, q2 = c.Value;
C a = c.Key.second;
if (!state_dict.TryGetValue(q1, out B1) | !state_dict.TryGetValue(q2, out B2))
{
//TODO: Throw some exception
}
var tuple = new TwoTuple <State <HashSet <State <S> > >, C>(B1, a);
State <HashSet <State <S> > > B_out;
if (!delta_new.TryGetValue(tuple, out B_out))
{
delta_new.Add(new TwoTuple <State <HashSet <State <S> > >, C>(B1, a), B2);
}
}
if (q_0_new == null)
{
//TODO: throw some exception or another
}
return(new DFA <C, HashSet <State <S> > >(Q_new, Sigma, delta_new, q_0_new, F_new));
}
/* METHOD TO EXECUTE ARBITRARY SET OPERATIONS ON THE LANGUAGES OF AUTOMATA
*
* Input: automataList: The list of deterministic automata on which the set operation is executed
* boolOp: The boolean operation describing the set operation, that is to be executed
*
* Output: Deterministic automaton, that encodes the language obtained from applying the specified set operation on the languages of the input automata
*/
public static DFA <C, NTuple <State <S> > > ExecuteSetOperation <C, S>(List <DFA <C, S> > automataList, BooleanOperation boolOp)
{
int noAutomata = automataList.Count;
//Initialize all five components (Q, Sigma, delta, q_0, F) of the resulting automaton:
var Q = new HashSet <State <NTuple <State <S> > > >();
var Sigma = automataList[0].Sigma;
var delta = new Dictionary <TwoTuple <State <NTuple <State <S> > >, C>, State <NTuple <State <S> > > >();
var F = new HashSet <State <NTuple <State <S> > > >();
var TupleStateDict = new Dictionary <NTuple <State <S> >, State <NTuple <State <S> > > >();
var q_0_as_array = new State <S> [noAutomata];
for (int i = 0; i < noAutomata; i++)
{
q_0_as_array[i] = automataList[i].q_0;
}
var q_0_as_ntuple = new NTuple <State <S> >(q_0_as_array);
//Initialize workset with q_0. The workset contains all state (in NTuple-form) that still need to be processed
var W = new HashSet <NTuple <State <S> > >();
W.Add(q_0_as_ntuple);
int id = 0;
var q_0 = new State <NTuple <State <S> > >(id, q_0_as_ntuple); id++;
Q.Add(q_0);
TupleStateDict.Add(q_0_as_ntuple, q_0);
//Main loop:
while (W.Count > 0)
{
var q_tuple = W.ElementAt(0);
W.Remove(q_tuple);
State <NTuple <State <S> > > q;
if (!TupleStateDict.TryGetValue(q_tuple, out q))
{
//TODO: Exception ??
}
//If 'q_tuple' is final, add it to 'F_Tuples'
bool[] q_acceptance_array = new bool[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
q_acceptance_array[i] = automataList[i].F.Contains(q_tuple.content[i]);
}
if (boolOp.IsTrueForInterpretation(q_acceptance_array))
{
F.Add(q);
}
//Determine where transitions out of 'q_tuple' need to go
foreach (C a in Sigma)
{
var q_dash_array = new State <S> [noAutomata];
for (int i = 0; i < noAutomata; i++)
{
State <S> q_i_dash;
var q_i_a_tuple = new TwoTuple <State <S>, C>(q_tuple.content[i], a);
if (!automataList[i].delta.TryGetValue(q_i_a_tuple, out q_i_dash))
{
//TODO: Throw exception. Non-total transition function!
}
q_dash_array[i] = q_i_dash;
}
var q_dash_tuple = new NTuple <State <S> >(q_dash_array);
State <NTuple <State <S> > > q_dash;
if (!TupleStateDict.ContainsKey(q_dash_tuple))
{
W.Add(q_dash_tuple);
q_dash = new State <NTuple <State <S> > >(id, q_dash_tuple); id++;
Q.Add(q_dash);
TupleStateDict.Add(q_dash_tuple, q_dash);
}
else if (!TupleStateDict.TryGetValue(q_dash_tuple, out q_dash))
{
//TODO: Exception. That'd be weird.
}
delta.Add(new TwoTuple <State <NTuple <State <S> > >, C>(q, a), q_dash);
}
}
return(new DFA <C, NTuple <State <S> > >(Q, Sigma, delta, q_0, F));
}
//Old version of method 'ExecuteSetOperation':
public static DFA <C, List <State <S> > > ExecuteSetOperationOld <C, S>(List <DFA <C, S> > automataList, BooleanOperation boolOp)
{
int noAutomata = automataList.Count;
//Give every state in each automaton 'Q' in 'automataList' a unique id between '0' and 'Q.Count' (included and excluded):
foreach (DFA <C, S> D in automataList)
{
D.Enumerate();
}
//Array, thats i-th component contains the number of states of 'automataList[i]':
int[] automataSizes = new int[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
automataSizes[i] = automataList[i].Q.Count;
}
//Stores references to all states of product-automaton, that have already been created:
Array Q_reference_array = Array.CreateInstance(typeof(State <List <State <S> > >), automataSizes);
//Initialize all five components (Q,Sigma,delta,q_0,F) of the resulting automaton:
HashSet <State <List <State <S> > > > Q = new HashSet <State <List <State <S> > > >();
HashSet <C> Sigma = automataList[0].Sigma;
Dictionary <TwoTuple <State <List <State <S> > >, C>, State <List <State <S> > > > delta = new Dictionary <TwoTuple <State <List <State <S> > >, C>, State <List <State <S> > > >();
HashSet <State <List <State <S> > > > F = new HashSet <State <List <State <S> > > >();
List <State <S> > q_0_as_list = new List <State <S> >();
foreach (DFA <C, S> D in automataList)
{
q_0_as_list.Add(D.q_0);
}
//Initialize workset with the initial state [q_0_1, q_0_2, ...]:
HashSet <List <State <S> > > W = new HashSet <List <State <S> > >();
W.Add(q_0_as_list);
while (W.Count > 0)
{
//Pick 'q = [q_1,q_2,...]' from 'W' and add it to 'Q'.
//Mark in 'Q_reference_array', that 'q' has been added, by referencing it at the position determined by the id's of the states 'q_1', 'q_2', ... respectively:
List <State <S> > q_list = W.ElementAt(0);
W.Remove(q_list);
int[] indices_q = new int[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
indices_q[i] = q_list[i].id;
}
State <List <State <S> > > q;
if (Q_reference_array.GetValue(indices_q) == null)
{
q = new State <List <State <S> > >(q_list);
Q_reference_array.SetValue(q, indices_q);
}
else
{
q = (State <List <State <S> > >)Q_reference_array.GetValue(indices_q);
}
Q.Add(q);
//Add q to F if it is accepting
bool[] q_acceptance_array = new bool[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
q_acceptance_array[i] = automataList[i].F.Contains(q_list[i]);
}
if (boolOp.IsTrueForInterpretation(q_acceptance_array))
{
F.Add(q);
}
//Determine, where transitions out of 'q' need to go:
foreach (C c in Sigma)
{
//Determine 'q_new = delta(q, c)' and its id-array ('indices'):
List <State <S> > q_new_list = new List <State <S> >();
int[] indices = new int[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
State <S> q_temp;
TwoTuple <State <S>, C> tuple = new TwoTuple <State <S>, C>(q_list[i], c);
if (!automataList[i].delta.TryGetValue(tuple, out q_temp))
{
return(null); //TODO: throw proper exception rather than returning null
}
q_new_list.Add(q_temp);
indices[i] = q_temp.id;
}
//If not yet in there, add 'q_new' to 'Q':
State <List <State <S> > > q_new;
if (Q_reference_array.GetValue(indices) == null)
{
q_new = new State <List <State <S> > >(q_new_list);
Q_reference_array.SetValue(q_new, indices);
W.Add(q_new_list);
}
else
{
q_new = (State <List <State <S> > >)Q_reference_array.GetValue(indices);
}
//Add new transition to 'delta':
TwoTuple <State <List <State <S> > >, C> key = new TwoTuple <State <List <State <S> > >, C>(q, c);
delta.Add(key, q_new);
}
}
//Determine id-array of initial state:
int[] indices_q_0 = new int[noAutomata];
for (int i = 0; i < noAutomata; i++)
{
indices_q_0[i] = automataList[i].q_0.id;
}
State <List <State <S> > > q_0 = (State <List <State <S> > >)Q_reference_array.GetValue(indices_q_0);
//Return new DFA composed of calculated sets:
return(new DFA <C, List <State <S> > >(Q, Sigma, delta, q_0, F));
}
