def to_dfa(self):
dfa = DFA(self.start_state)
frontier = [self.start_state]
seen = set()
while frontier:
current = frontier.pop()
inputs = self.get_inputs(current)
for input in inputs:
if input == NFA.EPSILON: continue
new_state = self.next_state(current, input)
if new_state not in seen:
frontier.append(new_state)
seen.add(new_state)
if self.is_final(new_state):
dfa.add_final_state(new_state)
if input == NFA.ANY:
dfa.set_default_transition(current, new_state)
else:
dfa.add_transition(current, input, new_state)
return dfa
class Converter:
def __init__(self, nfa, alpha):
self.nfa = nfa
self.alpha = alpha
# returns all states reachable through s by taking char c
# is c is None, does one level of spontaneaous transitions
def edge(self, s, c):
res = set()
for d in range(self.nfa.sc):
if c in self.nfa.edges(s, d):
res.add(d)
return res
# S set of states
# returns all set reachables from any sate in S, using only spontaneaous transitions
def closure(self, S):
S = set(S)
while True:
copy = set(S)
for s in copy:
for x in self.edge(s, None):
S.add(x)
if S == copy:
break
return S
# let d a set of states in NFA (equivalent to one state in the DFA)
# returns a new states of states in NFA (equivalent to one state in the DFA)
# rechable from tacking char c from any state in d, then taking spontaneaous transitions
def dfa_edge(self, d, c):
succ = set()
for s in d:
for x in self.edge(s, c):
succ.add(x)
return self.closure(succ)
def find_state(self, st):
for i, other in enumerate(self.states):
if other == st:
return i
return None
def build(self):
self.states = []
self.doc = Program.instance().add_doc(MdGfmDoc, "NFA to DFA")
self.doc.h1("DFA construction")
# First state is empty
# This is the error state
# All invalid transitions are stuck in this state
self.states.append(set())
self.dump_state(0)
# Second state is the eps-closure of the start state
self.states.append(self.closure({self.nfa.start}))
self.dump_state(1)
self.trans_list = []
j = 0
while j < len(self.states):
for c in self.alpha.larr:
# compute new state from state j, taking char c
e = self.dfa_edge(self.states[j], c)
# check if same set of states already exists
i = self.find_state(e)
if i is None:
# add new state
i = len(self.states)
self.states.append(e)
self.dump_state(i)
# record transition
self.trans_list.append((j, c, i))
j += 1
# Compute list of final states
# one state is final if any of it's NFA states is final
self.finals = [
d for (d, st) in enumerate(self.states) if self.nfa.final in st
]
self.dump_finals()
# Build DFA
self.dfa = DFA(len(self.states),
start_state=1,
final_states=self.finals,
err_state=0)
for t in self.trans_list:
self.dfa.add_transition(s0=t[0], s1=t[2], c=t[1])
self.doc.h1('DFA')
self.doc.write(self.dfa)
return self.dfa
def dump_state(self, idx):
st = self.states[idx]
self.doc.write('- Inserted state {}: `{{'.format(idx))
for s in st:
self.doc.write('{}; '.format(s))
self.doc.write('}`\n')
def dump_finals(self):
self.doc.write('- Final states: `{')
for s in self.finals:
self.doc.write('{}; '.format(s))
self.doc.write('}`\n')
