def rename_states(self):
"""
Renames all the states in the dfa.
:return: Original DFA with states renamed.
:rtype: DFA
"""
alphabet = sorted(self.alphabet)
dfa = DFA(self.alphabet, State('0'))
queue = deque([self._start_state])
visited = {self._start_state}
cnt = 1
old_to_new = {self._start_state: State('0')}
while len(queue) > 0:
state = queue.popleft()
for a in alphabet:
if state in self._transitions and a in self._transitions[state]:
to_state = self.transition(state, a)
if to_state not in visited:
queue.append(to_state)
visited.add(to_state)
old_to_new[to_state] = State(str(cnt))
cnt += 1
for old, new in old_to_new.items():
old_transitions = self._transitions[old]
for sym, state in old_transitions.items():
dfa.add_transition(new, old_to_new[state], sym)
if old in self.accept_states:
dfa.accept_states.add(new)
return dfa
def minimize(self):
"""
Minimizes the dfa using Hopcroft's algorithm.
Please consult the following paper
https://pdfs.semanticscholar.org/e622/10eea9d53bc36af50675017a830c967fea3f.pdf
for an explanation of this algorithm.
:return: Minimized dfa
:rtype: DFA
"""
p = self._hopcroft()
start = [
state_set for state_set in p if self._start_state in state_set
]
assert len(start) == 1
minimized_dfa = DFA(self.alphabet, State(''.join(map(str, start[0]))))
for state_set in p:
for a in self.alphabet:
for state in state_set:
if self.transition_exists(state, a):
to_state = self.transition(state, a)
to = [s for s in p if to_state in s]
assert len(to) == 1
to_state_set = to[0]
minimized_dfa.add_transition(
State(''.join(map(str, state_set))),
State(''.join(map(str, to_state_set))), a)
break
if any(s in self.accept_states for s in state_set):
minimized_dfa.accept_states.add(
State(''.join(map(str, state_set))))
return minimized_dfa.rename_states()
def __init__(self, alphabet: Set[str], start_state: State = State('')):
"""
:param alphabet: The alphabet of the regular language
:type alphabet: set
:param start_state: the initial state of the dfa
:type start_state: State
"""
super().__init__(alphabet)
self._start_state = start_state
self.states = {self._start_state}
self.accept_states = set()
self.reject_states = set()
self._transitions = defaultdict(OrderedDict)