public override IAcceptWord Join(IJoin A) {
if (!(A is DFA D2))
throw new NotSupportedException();
if (!this.SameAlphabet(D2))
throw new NotImplementedException("Different Alphabets are not implemented");
var deat = new DFATransform();
var accStates = new List<uint>(this.AcceptedStates.Length + D2.AcceptedStates.Length);
uint sc = this.StatesCount;
foreach (var t in (DFATransform)Transforms)
deat.Add(t.Key.q, t.Key.c.Value, t.Value[0]);
foreach (var t in (DFATransform)D2.Transforms)
deat.Add(t.Key.q + sc, t.Key.c.Value, t.Value[0] + sc);
accStates.AddRange(this.AcceptedStates);
for (int i = 0; i < D2.AcceptedStates.Length; i++)
accStates.Add(D2.AcceptedStates[i] + sc);
accStates.Sort();
return new DFA($"DFA_Join({Name}+{A.Name})", (D2.StatesCount + sc), this.Alphabet, deat, this.StartState, accStates.ToArray());
}
/// <summary>
/// Minimize DFA with TableFillingAlg
/// </summary>
/// <returns></returns>
public DFA Minimize() {
var tfEqClasses = TableFillingAlgEqClasses(this); // half matrix TF
var State2eqClass = new uint[this.StatesCount];
// Fill state to eqClass matching
for (uint i = 0; i < tfEqClasses.Length; i++)
for (int j = 0; j < tfEqClasses[i].Length; j++)
State2eqClass[tfEqClasses[i][j]] = i;
// generate Transform, and modify to eqclasses
var deaT = new DFATransform();
foreach (var item in Transforms) {
// q,qnext EqClass
uint tSrcEqClass = State2eqClass[item.Key.q];
uint tDstEqClass = State2eqClass[item.Value[0]];
deaT.TryAdd(tSrcEqClass, item.Key.c.Value, tDstEqClass);
}
// add eqClasses of accepted states
var acc = new List<uint>(AcceptedStates.Length);
for (uint i = 0; i < AcceptedStates.Length; i++)
acc.Add(State2eqClass[AcceptedStates[i]]);
acc.Sort();
// give each onging state its eqClass states[] as name
string[] names = new string[tfEqClasses.Length];
for (uint i = 0; i < tfEqClasses.Length; i++)
names[i] = string.Join(',', tfEqClasses[i]);
return new DFA($"DFA_Minimized({Name})", names, this.Alphabet, deaT, State2eqClass[this.StartState], acc.Distinct().ToArray());
}
public override IAutomat PurgeStates() {
(uint[] translate, string[] names, uint[] aStates) = base.RemovedStateTranslateTables();
var newT = new DFATransform();
foreach (var t2 in Transforms)
if (translate.Contains(t2.Key.q))
foreach (var v in t2.Value)
if (translate.Contains(v))
newT.Add(translate.ArrayIndex(t2.Key.q), t2.Key.c.Value, translate.ArrayIndex(v));
return new DFA($"{Name}_purged", names, Alphabet, newT, translate.ArrayIndex(StartState), aStates);
}
} // end StatesEqual
#region "Operations"
public override IAutomat HomomorphismChar(Dictionary<char, char> Translate) {
var deat = new DFATransform();
var Alp = (char[])this.Alphabet.Clone();
foreach (var dt in (DFATransform)Transforms)
if (Translate.ContainsKey(dt.Key.c.Value))
deat.Add(dt.Key.q, Translate[dt.Key.c.Value], dt.Value[0]);
else
deat.Add(dt.Key.q, dt.Key.c.Value, dt.Value[0]);
for (int i = 0; i < this.Alphabet.Length; i++)
if (Translate.ContainsKey(this.Alphabet[i]))
Alp[i] = Translate[this.Alphabet[i]];
return new DFA($"DFA_HomomorphismChar({Name})", this.StatesCount, Alp, deat, this.StartState, this.AcceptedStates);
}
public static DFA GenerateRandom() {
const byte MAX_STATES = 20;
const byte MAX_CHAR = 7;
var rnd = Uni.Utils.RND;
int stateCount = rnd.Next(1, MAX_STATES);
char[] alphabet = RandomGenerator.RandomAlphabet(1, MAX_CHAR);
uint[] accState = RandomGenerator.RandomAcceptedStates(1, stateCount / 3, stateCount);
var t = new DFATransform();
for (uint i = 0; i < stateCount; i++) {
char[] rndAlph = alphabet.Randomize();
for (int j = 0; j < rndAlph.Length; j++)
t.Add(i, alphabet[j], (uint)rnd.Next(0, stateCount));
}
var ret = new DFA("DFA_Random", (uint)stateCount, alphabet, t, (uint)rnd.Next(0, stateCount), accState);
ret.Name = $"DFA_Random_q{stateCount}_a{alphabet.Length}_{ret.GetHashCode()}";
return ret;
}
public static DFA ProductDea(DFA D1, DFA D2, eProductDeaMode mode) {
uint len = (D1.StatesCount * D2.StatesCount);
char[] newAlphabet = D1.Alphabet.Union(D2.Alphabet).ToArray();
// if (!D1.SameAlphabet(D2))
// throw new NotImplementedException("Different Alphabets are not implemented");
var accStates = new List<uint>(D1.AcceptedStates.Length + D2.AcceptedStates.Length);
string[] stateNames = new string[len];
var deat = new DFATransform();
// iterate Cross D1xD2, chars
for (uint i = 0; i < D1.StatesCount; i++) {
for (uint j = 0; j < D2.StatesCount; j++) {
// index of state in matrix
uint index = (i * D2.StatesCount + j);
stateNames[index] = $"{i},{j}";
foreach (char c in newAlphabet) {
// Transform exists, out qNext
bool exist1 = ((DFATransform)D1.Transforms).TryGetValue(i, c, out uint qNext1);
bool exist2 = ((DFATransform)D2.Transforms).TryGetValue(j, c, out uint qNext2);
// same calc logic for dstIndex in Matrix
uint dstIndex;
if (exist1 & exist2)
dstIndex = (qNext1 * D2.StatesCount + qNext2);
else if (exist1)
dstIndex = (qNext1 * D2.StatesCount + qNext1);
else if (exist2)
dstIndex = qNext2;
else
throw new ApplicationException();
// add non existing tuple
if (!deat.ContainsKey(index, c)) // & exist1 & exist2)
deat.Add(index, c, dstIndex);
else
throw new ApplicationException();
if (mode == eProductDeaMode.Intersect) {
// add to accStates if both dea state ist acc
if (D1.IsAcceptedState(i) & D2.IsAcceptedState(j))
accStates.Add(index);
} else if (mode == eProductDeaMode.Union) {
// add to accStates if one dea state ist acc
if (D1.IsAcceptedState(i) | D2.IsAcceptedState(j))
accStates.Add(index);
} else if (mode == eProductDeaMode.Diff) {
// add to accStates if first and not second accepted
if (D1.IsAcceptedState(i) & !D2.IsAcceptedState(j))
accStates.Add(index);
}
}
}
}
return new DFA($"DEA_Product{mode}({D1.Name}+{D2.Name})", stateNames, newAlphabet, deat, 0, accStates.Distinct().ToArray());
}
public DFA(string name, string[] states, char[] alphabet, DFATransform transform, uint startState, params uint[] acceptedStates)
: base(name, states, alphabet, transform, startState, acceptedStates) {
}
