def test_epsilon(self):
""" Generic tests for epsilon """
eps0 = Epsilon()
eps1 = Epsilon()
symb = Symbol(0)
self.assertEqual(eps0, eps1)
self.assertNotEqual(eps0, symb)
def test_intersection(self):
""" Tests the intersection of two enfas """
enfa0 = get_enfa_example0()
symb_a = Symbol("a")
symb_b = Symbol("b")
eps = Epsilon()
enfa1 = EpsilonNFA()
state0 = State(10)
state1 = State(11)
state2 = State(12)
state3 = State(13)
state4 = State(14)
enfa1.add_start_state(state0)
enfa1.add_final_state(state3)
enfa1.add_final_state(state4)
enfa1.add_transition(state0, eps, state1)
enfa1.add_transition(state1, symb_a, state2)
enfa1.add_transition(state2, eps, state3)
enfa1.add_transition(state3, symb_b, state4)
enfa = enfa0 & enfa1
self.assertEqual(len(enfa.start_states), 4)
self.assertEqual(len(enfa.final_states), 2)
self.assertEqual(len(enfa.symbols), 2)
self.assertTrue(enfa.accepts([symb_a, symb_b]))
self.assertFalse(enfa.accepts([symb_b]))
self.assertFalse(enfa.accepts([symb_a]))
self.assertFalse(enfa.accepts([]))
self.assertFalse(enfa.accepts([symb_a, symb_a, symb_b]))
def test_check_intersection():
# Declare NFAs
enfa0 = EpsilonNFA()
enfa1 = EpsilonNFA()
# Declare the states
states = [State("q" + str(x)) for x in range(7)]
# Declare the symbols
epsilon = Epsilon()
symb_a = Symbol("a")
symb_b = Symbol("b")
symb_c = Symbol("c")
# epsilonNFA 0
# Add a start state
enfa0.add_start_state(states[0])
# Add a final state
enfa0.add_final_state(states[1])
# Add the transitions
enfa0.add_transition(states[0], symb_a, states[1])
enfa0.add_transition(states[1], symb_a, states[1])
# epsilonNFA 1
# Add a start states
enfa1.add_start_state(states[0])
enfa1.add_final_state(states[4])
# Add a final states
enfa1.add_final_state(states[5])
enfa1.add_final_state(states[6])
# Add the transitions
enfa1.add_transition(states[0], symb_a, states[1])
enfa1.add_transition(states[0], symb_b, states[2])
enfa1.add_transition(states[0], symb_c, states[3])
enfa1.add_transition(states[1], symb_a, states[4])
enfa1.add_transition(states[2], symb_b, states[5])
enfa1.add_transition(states[3], symb_c, states[6])
# Now enfa0 accepts a* \ {epsilon}
# enfa1 accepts aa, bb, cc
# Intersection of enfa0 and enfa1
enfa_res = enfa0.get_intersection(enfa1)
# Check if a word is accepted
assert enfa_res.accepts([symb_a, symb_a]), "Should accept aa"
# Check non-correct words
assert not enfa_res.accepts([epsilon]), "Accepts empty word, but it mustn't"
assert not enfa_res.accepts([symb_a, symb_a, symb_a]), "Accepts aaa, but it mustn't"
assert not enfa_res.accepts([symb_a]), "Accepts a, but it mustn't"
assert not enfa_res.accepts([symb_b, symb_b]), "Accepts bb, but it mustn't"
assert not enfa_res.accepts([symb_c, symb_c]), "Accepts cc, but it mustn't"
def test_cyclic(self):
enfa = EpsilonNFA()
state0 = State(0)
state1 = State(1)
symb_a = Symbol('a')
enfa.add_start_state(state0)
enfa.add_transition(state0, symb_a, state1)
enfa.add_transition(state1, Epsilon(), state0)
self.assertFalse(enfa.is_acyclic())
def test_to_regex3(self):
""" Tests the transformation to regex """
enfa = EpsilonNFA()
state0 = State(0)
state1 = State(1)
symb_a = Symbol("0")
symb_b = Symbol("1")
enfa.add_start_state(state0)
enfa.add_final_state(state1)
enfa.add_transition(state0, symb_a, state0)
enfa.add_transition(state1, symb_b, state0)
enfa.add_transition(state1, symb_b, state1)
regex = enfa.to_regex()
enfa2 = regex.to_epsilon_nfa()
self.assertFalse(enfa2.accepts([symb_a]))
self.assertFalse(enfa2.accepts([symb_a, symb_a]))
self.assertFalse(enfa2.accepts([symb_a, symb_a, symb_b]))
self.assertFalse(
enfa2.accepts([symb_a, symb_a, symb_b, symb_b, symb_a]))
self.assertFalse(
enfa2.accepts([symb_a, symb_a, symb_b, symb_b, symb_a, symb_b]))
self.assertFalse(enfa2.accepts([symb_b]))
epsilon = Epsilon()
enfa.add_transition(state0, epsilon, state1)
regex = enfa.to_regex()
enfa2 = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([]))
self.assertTrue(enfa.accepts([symb_a]))
self.assertTrue(enfa2.accepts([symb_a]))
self.assertTrue(enfa2.accepts([symb_a, symb_a]))
self.assertTrue(enfa2.accepts([symb_a, symb_a, symb_b, symb_b]))
self.assertTrue(
enfa2.accepts([symb_a, symb_a, symb_b, symb_b, symb_a, symb_b]))
self.assertTrue(enfa2.accepts([symb_b]))
self.assertTrue(enfa2.accepts([]))
enfa.remove_transition(state0, symb_a, state0)
regex = enfa.to_regex()
enfa2 = regex.to_epsilon_nfa()
self.assertFalse(enfa2.accepts([symb_a]))
self.assertFalse(enfa2.accepts([symb_a, symb_a]))
self.assertFalse(enfa2.accepts([symb_a, symb_a, symb_b]))
self.assertFalse(
enfa2.accepts([symb_a, symb_a, symb_b, symb_b, symb_a]))
self.assertFalse(
enfa2.accepts([symb_a, symb_a, symb_b, symb_b, symb_a, symb_b]))
self.assertTrue(enfa2.accepts([symb_b]))
self.assertTrue(enfa2.accepts([]))
enfa.remove_transition(state1, symb_b, state1)
regex = enfa.to_regex()
enfa2 = regex.to_epsilon_nfa()
self.assertTrue(enfa2.accepts([symb_b, symb_b]))
enfa.add_transition(state0, symb_a, state0)
regex = enfa.to_regex()
enfa2 = regex.to_epsilon_nfa()
self.assertTrue(enfa2.accepts([symb_a, symb_b]))
def get_enfa_example0_bis():
""" A non minimal NFA, equivalent to example0 """
enfa0 = EpsilonNFA()
state3 = State(3)
state4 = State(4)
state0 = State(0)
state1 = State(1)
state2 = State(2)
symb_a = Symbol("a")
symb_b = Symbol("b")
enfa0.add_start_state(state0)
enfa0.add_final_state(state2)
enfa0.add_final_state(state4)
enfa0.add_transition(state0, symb_a, state0)
enfa0.add_transition(state0, Epsilon(), state1)
enfa0.add_transition(state1, symb_b, state2)
# New part
enfa0.add_transition(state0, Epsilon(), state3)
enfa0.add_transition(state3, symb_a, state3)
enfa0.add_transition(state3, symb_b, state4)
return enfa0
def graph_to_dfa(g: Graph):
nfa = EpsilonNFA()
state_count = 0
for tup in g:
sub, pred, obj = map(str, tup)
# nfa.add_transition(State(sub), Symbol(pred), State(obj))
nfa.add_start_state(State(sub))
nfa.add_start_state(State(obj))
nfa.add_final_state(State(sub))
nfa.add_final_state(State(obj))
nfa.add_transition(State(sub), Epsilon(), State(state_count))
for c in pred:
nfa.add_transition(State(state_count),
Symbol(c),
State(state_count+1))
state_count += 1
nfa.add_transition(State(state_count),
Epsilon(),
State(obj))
return nfa.to_deterministic()
def add_transitions(self, member, enter_state, exit_state):
self.prefix += 1
if member == None:
self.add_transition(enter_state, Epsilon(), exit_state)
return
if member["type"] == "BLANK":
self.add_transition(enter_state, Epsilon(), exit_state)
if member["type"] == "SYMBOL":
if member["name"][0] == "_" and member["name"] not in self.externals:
self.add_transitions(self.node_types[member["name"]], enter_state, exit_state)
else:
symbol = Symbol(member["name"])
self.add_transition(enter_state, symbol, exit_state)
if member["type"] == "STRING":
symbol = Symbol(member["value"])
self.add_transition(enter_state, symbol, exit_state)
# memb = regex_to_member(member["value"])
# self.add_transitions(memb, enter_state, exit_state)
if member["type"] == "PATTERN":
# symbol = Symbol("regex:"+member["value"])
memb = regex_to_member(member["value"])
self.add_transitions(memb, enter_state, exit_state)
# self.add_transition(enter_state, symbol, exit_state)
if member["type"] in ["FIELD", "PREC","PREC_LEFT","PREC_RIGHT","ALIAS", "TOKEN"]:
self.add_transitions(member["content"], enter_state, exit_state)
if member["type"] == "SEQ":
prev_state = enter_state
for i, SEQ_member in enumerate(member["members"]):
next_state = State(f"SEQ{self.prefix}_St_{i}")
self.add_transitions(SEQ_member, prev_state, next_state)
prev_state = next_state
self.add_transition(next_state, Epsilon(), exit_state)
if member["type"] == "CHOICE":
for i, CHOICE_member in enumerate(member["members"]):
choice_state = State(f"CH{self.prefix}_St_{i}")
self.add_transitions(CHOICE_member, enter_state, choice_state)
self.add_transition(choice_state, Epsilon(), exit_state)
if member["type"] == "REPEAT":
self.add_transition(enter_state, Epsilon(), exit_state)
self.add_transition(exit_state, Epsilon(), enter_state)
self.add_transitions(member["content"], enter_state, exit_state)
if member["type"] == "REPEAT1":
self.add_transition(exit_state, Epsilon(), enter_state)
self.add_transitions(member["content"], enter_state, exit_state)
def test_get_as_dict(self):
enfa0 = EpsilonNFA()
state0 = State("0")
state1 = State(1)
symb_a = Symbol('a')
enfa0.add_start_state(state0)
enfa0.add_final_state(state1)
enfa0.add_transition(state0, symb_a, state1)
enfa0.add_transition(state1, Epsilon(), state0)
d_enfa = enfa0.to_dict()
self.assertIn(state0, d_enfa)
self.assertIn(symb_a, d_enfa[state0])
self.assertIn(state1, d_enfa[state0][symb_a])
def test_complement(self):
""" Tests the complement operation """
enfa = EpsilonNFA()
state0 = State(0)
state1 = State(1)
state2 = State(2)
symb_a = Symbol("a")
enfa.add_start_state(state0)
enfa.add_final_state(state2)
enfa.add_transition(state0, Epsilon(), state1)
enfa.add_transition(state1, symb_a, state2)
enfa_comp = -enfa
self.assertFalse(enfa_comp.accepts([symb_a]))
def test_import_networkx(self):
enfa = EpsilonNFA()
state0 = State("0")
state1 = State(1)
symb_a = Symbol('a')
enfa.add_start_state(state0)
enfa.add_final_state(state1)
enfa.add_transition(state0, symb_a, state1)
enfa.add_transition(state1, Epsilon(), state0)
graph = enfa.to_networkx()
enfa_from_nx = EpsilonNFA.from_networkx(graph)
self.assertTrue(enfa_from_nx.accepts([symb_a]))
self.assertTrue(enfa_from_nx.accepts([symb_a, symb_a]))
self.assertFalse(enfa_from_nx.accepts([]))
def test_non_equivalent(self):
enfa0 = EpsilonNFA()
state0 = State("0")
state1 = State(1)
symb_a = Symbol('a')
enfa0.add_start_state(state0)
enfa0.add_final_state(state1)
enfa0.add_transition(state0, symb_a, state1)
enfa0.add_transition(state1, Epsilon(), state0)
enfa1 = EpsilonNFA()
enfa1.add_start_state(state0)
enfa1.add_final_state(state1)
enfa1.add_transition(state0, symb_a, state1)
enfa1.add_transition(state1, symb_a, state0)
self.assertFalse(enfa0.is_equivalent_to(enfa1))
def get_enfa_example0():
""" Gives an example ENFA
Accepts a*b
"""
enfa0 = EpsilonNFA()
state0 = State(0)
state1 = State(1)
state2 = State(2)
symb_a = Symbol("a")
symb_b = Symbol("b")
enfa0.add_start_state(state0)
enfa0.add_final_state(state2)
enfa0.add_transition(state0, symb_a, state0)
enfa0.add_transition(state0, Epsilon(), state1)
enfa0.add_transition(state1, symb_b, state2)
return enfa0
def test_iter(self):
enfa = EpsilonNFA()
state0 = State("0")
state1 = State(1)
symb_a = Symbol('a')
enfa.add_start_state(state0)
enfa.add_final_state(state1)
enfa.add_transition(state0, symb_a, state1)
enfa.add_transition(state1, Epsilon(), state0)
counter = 0
for s_from, symb, s_to in enfa:
counter += 1
self.assertIn((s_from, symb, s_to), enfa)
self.assertNotIn((state1, symb_a, state1), enfa)
self.assertIn(("0", "a", 1), enfa)
self.assertEqual(counter, 2)
def test_export_networkx(self):
enfa = EpsilonNFA()
state0 = State("0")
state1 = State(1)
symb_a = Symbol('a')
enfa.add_start_state(state0)
enfa.add_final_state(state1)
enfa.add_transition(state0, symb_a, state1)
enfa.add_transition(state1, Epsilon(), state0)
graph = enfa.to_networkx()
self.assertTrue(isinstance(graph, networkx.MultiDiGraph))
self.assertTrue("0" in graph)
self.assertTrue(("0", 1) in graph.edges)
self.assertIn("a", [x["label"] for x in graph["0"][1].values()])
self.assertTrue(graph.nodes["0"]["is_start"])
self.assertFalse(graph.nodes["0"]["is_final"])
self.assertFalse(graph.nodes[1]["is_start"])
self.assertTrue(graph.nodes[1]["is_final"])
enfa.write_as_dot("enfa.dot")
def test_eclose(self):
""" Test of the epsilon closure """
states = [State(x) for x in range(8)]
epsilon = Epsilon()
symb_a = Symbol("a")
symb_b = Symbol("b")
enfa = EpsilonNFA()
enfa.add_transition(states[1], epsilon, states[2])
enfa.add_transition(states[1], epsilon, states[4])
enfa.add_transition(states[2], epsilon, states[3])
enfa.add_transition(states[3], epsilon, states[6])
enfa.add_transition(states[5], epsilon, states[7])
enfa.add_transition(states[4], symb_a, states[5])
enfa.add_transition(states[5], symb_b, states[6])
self.assertEqual(len(enfa.eclose(states[1])), 5)
self.assertEqual(len(enfa.eclose(states[2])), 3)
self.assertEqual(len(enfa.eclose(states[5])), 2)
self.assertEqual(len(enfa.eclose(states[6])), 1)
self.assertEqual(len(list(enfa._transition_function.get_edges())), 7)
self.assertEqual(enfa.remove_transition(states[1], epsilon, states[4]),
1)
self.assertFalse(enfa.is_deterministic())
def get_digits_enfa():
""" An epsilon NFA to recognize digits """
epsilon = Epsilon()
plus = Symbol("+")
minus = Symbol("-")
point = Symbol(".")
digits = [Symbol(x) for x in range(10)]
states = [State("q" + str(x)) for x in range(6)]
enfa = EpsilonNFA()
enfa.add_start_state(states[0])
enfa.add_final_state(states[5])
enfa.add_transition(states[0], epsilon, states[1])
enfa.add_transition(states[0], plus, states[1])
enfa.add_transition(states[0], minus, states[1])
for digit in digits:
enfa.add_transitions([(states[1], digit, states[1]),
(states[1], digit, states[4]),
(states[2], digit, states[3]),
(states[3], digit, states[3])])
enfa.add_transitions([(states[1], point, states[2]),
(states[4], point, states[3]),
(states[3], epsilon, states[5])])
return enfa, digits, epsilon, plus, minus, point
def test_to_fst(self):
""" Tests to turn a ENFA into a FST """
enfa = EpsilonNFA()
fst = enfa.to_fst()
self.assertEqual(len(fst.states), 0)
self.assertEqual(len(fst.final_states), 0)
self.assertEqual(len(fst.start_states), 0)
self.assertEqual(len(fst.input_symbols), 0)
self.assertEqual(len(fst.output_symbols), 0)
self.assertEqual(fst.get_number_transitions(), 0)
state0 = State("q0")
s0bis = State("q0bis")
enfa.add_start_state(state0)
enfa.add_start_state(s0bis)
fst = enfa.to_fst()
self.assertEqual(len(fst.states), 2)
self.assertEqual(len(fst.final_states), 0)
self.assertEqual(len(fst.start_states), 2)
self.assertEqual(len(fst.input_symbols), 0)
self.assertEqual(len(fst.output_symbols), 0)
self.assertEqual(fst.get_number_transitions(), 0)
sfinal = State("qfinal")
sfinalbis = State("qfinalbis")
enfa.add_final_state(sfinal)
enfa.add_final_state(sfinalbis)
fst = enfa.to_fst()
self.assertEqual(len(fst.states), 4)
self.assertEqual(len(fst.final_states), 2)
self.assertEqual(len(fst.start_states), 2)
self.assertEqual(len(fst.input_symbols), 0)
self.assertEqual(len(fst.output_symbols), 0)
self.assertEqual(fst.get_number_transitions(), 0)
enfa.add_transition(state0, Symbol("a"), sfinal)
enfa.add_transition(sfinal, Symbol("b"), sfinal)
enfa.add_transition(state0, Symbol("c"), sfinalbis)
fst = enfa.to_fst()
self.assertEqual(len(fst.states), 4)
self.assertEqual(len(fst.final_states), 2)
self.assertEqual(len(fst.start_states), 2)
self.assertEqual(len(fst.input_symbols), 3)
self.assertEqual(len(fst.output_symbols), 3)
self.assertEqual(fst.get_number_transitions(), 3)
enfa.add_transition(state0, Epsilon(), sfinalbis)
fst = enfa.to_fst()
self.assertEqual(len(fst.states), 4)
self.assertEqual(len(fst.final_states), 2)
self.assertEqual(len(fst.start_states), 2)
self.assertEqual(len(fst.input_symbols), 3)
self.assertEqual(len(fst.output_symbols), 3)
self.assertEqual(fst.get_number_transitions(), 4)
trans0 = list(fst.translate(["a"]))
self.assertEqual(trans0, [["a"]])
trans0 = list(fst.translate(["a", "b", "b"]))
self.assertEqual(trans0, [["a", "b", "b"]])
trans0 = list(fst.translate(["b", "b"]))
self.assertEqual(trans0, [])
trans0 = list(fst.translate(["c"]))
self.assertEqual(trans0, [["c"]])
def test_invalid_epsilon(self):
""" Tests invalid transition """
transition_function = TransitionFunction()
with self.assertRaises(InvalidEpsilonTransition):
transition_function.add_transition("1", Epsilon(), "2")
def test_epsilon_refused(self):
dfa = NondeterministicFiniteAutomaton()
state0 = State(0)
state1 = State(1)
with self.assertRaises(InvalidEpsilonTransition):
dfa.add_transition(state0, Epsilon(), state1)
