P := {F, Q \ F};
W := {F};
while (W is not empty) do
choose and remove a set A from W
for each c in ∑ do
let X be the set of states for which a transition on c leads to a state in A
for each set Y in P for which X ∩ Y is nonempty do
replace Y in P by the two sets X ∩ Y and Y \ X
if Y is in W
replace Y in W by the same two sets
else
if |X ∩ Y| <= |Y \ X|
add X ∩ Y to W
else
add Y \ X to W
end;
end;
end;
I made a converting from DFA to minimal DFA by using Hopcroft algorithm. I find a pseudo code from Wikipedia by this link, http://en.wikipedia.org/wiki/DFA_minimization#Hopcroft.27s_algorithm and I made python code to converting dfa.
def minimize(self,dfa):
P = [set(dfa.finalstates),dfa.states.difference(set(dfa.finalstates))]
W = [set(dfa.finalstates)]
while len(W) != 0:
A = W[0]
W.remove(A)
X = set()
for c in dfa.alphabet:
for from_state, to_state in dfa.transitions.items():
for toNum, value in to_state.items():
if c in value and toNum in A:
X.update(set([from_state]))
for Y in P:
if not X.intersection(Y) == set():
P.append(X.intersection(Y))
P.append(Y.difference(X))
if Y in W:
W.append(X.intersection(Y))
W.append(Y.difference(X))
W.remove(Y)
else :
if len(X.intersection(Y)) <= len (Y.difference(X)):
W.append(X.intersection(Y))
#W.remove(Y)
else :
W.append(Y.difference(X))
#W.remove(Y)
P.remove(Y)
print P,W
my DFA consists of five indicators,
dfa.states = set() of states.
dfa.startstate = int number of start state number
dfa.finalstates = list structure consisting of final states
dfa.transitions = dictionary structure of dfa transitions.
ex) {from state : {to state1 : set of character to go to state1 , to state 2 : set of charac...}}
dfa.alphabet = set of dfa alphabets.
I don't know why this algorithm not work my code, is any problem in my code?
