def to_dfa(self):
"""
Returns the DFA corresponding to the NFA.
It uses the powerset construction.
See: https://en.wikipedia.org/wiki/Powerset_construction
"""
symbols = set(self._symbols)
if self.has_epsilon_moves():
symbols.remove(Nfa.EPSILON)
states = set()
transitions = dict()
final_states = set()
new_states = [self.epsilon_closure(self._initial_state)]
initial_state = Nfa._set_to_state(new_states[0])
while new_states:
state = new_states.pop()
new_state = Nfa._set_to_state(state)
states.add(new_state)
if self._final_states.intersection(state):
final_states.add(new_state)
transitions[new_state] = dict()
for symbol in symbols:
t = set()
for s in state:
for i in self.delta(s, symbol):
t.update(self.epsilon_closure(i))
if t:
ns = Nfa._set_to_state(t)
transitions[new_state][symbol] = ns
if ns not in states and t not in new_states:
new_states.append(t)
return Dfa(states, symbols, transitions, initial_state, final_states)
def a1():
Q = {'S1', 'S2'}
S = {'0', '1'}
d = {'S1': {'0': 'S2', '1': 'S1'}, 'S2': {'0': 'S1', '1': 'S2'}}
q0 = 'S1'
F = {'S1'}
return Dfa(Q, S, d, q0, F)
def test_init_5():
with pytest.raises(FsmError):
Q = {'S0', 'S1', 'S2'}
S = {'0', '1'}
d = [] # d is not a dictionnary
q0 = 'S0'
F = {'S0'}
Dfa(Q, S, d, q0, F)
def test_init_1():
with pytest.raises(FsmError):
Q = {'S0', 'S1', 'S2'}
S = {'0', '1'}
d = {
'S0': {
'0': 'S0',
'1': 'S1'
},
'S1': {
'0': 'S2',
'1': 'S0'
},
'S2': {
'0': 'S1',
'1': 'S2'
}
}
q0 = 'S3' # Q does not contain q0
F = {'S0'}
Dfa(Q, S, d, q0, F)
def test_init_4():
with pytest.raises(FsmError):
Q = {'S0', 'S1'}
S = {'0', '1'}
d = {
'S0': {
'0': 'S0',
'1': 'S1'
},
'S1': {
'0': 'S2',
'1': 'S0'
},
'S2': { # S2 is not in Q
'0': 'S1',
'1': 'S2'
}
}
q0 = 'S0'
F = {'S0'}
Dfa(Q, S, d, q0, F)
def test_init_2():
with pytest.raises(FsmError):
Q = {'S0', 'S1', 'S2'}
S = {'0', '1'}
d = {
'S0': {
'0': 'S0',
'1': 'S1'
},
'S1': {
'0': 'S2',
'1': 'S0'
},
'S2': {
'0': 'S1',
'1': 'S2'
}
}
q0 = 'S0'
F = {'S0', 'S3'} # Q does not contain all states of F
Dfa(Q, S, d, q0, F)
def test_init_3():
with pytest.raises(FsmError):
Q = {0, 1, 2, 3}
S = {'a', 'b'}
d = {
0: {
'a': {0, 1},
'b': {0}
},
1: {
'a': {2}
},
2: {
'a': {3}
},
3: {
'a': {3},
'b': {3}
}
} # the state-transition function is not deterministic
q0 = 0
F = {3}
Dfa(Q, S, d, q0, F)
Graph: graph1_dfa.dot
Source: https://en.wikipedia.org/wiki/Deterministic_finite_automaton#Example
"""
from fsmdot.dfa import Dfa
Q = {'S1', 'S2'}
S = {'0', '1'}
d = {
'S1': {
'0': 'S2',
'1': 'S1'
},
'S2': {
'0': 'S1',
'1': 'S2'
}
}
q0 = 'S1'
F = {'S1'}
a = Dfa(Q, S, d, q0, F)
a.print_table()
print(a.accept('11110'))
print(a.accept('110110110101'))
G = a.dot_graph()
print(G.to_string())
G.write('graph1_dfa.dot')