def test_intersection_regex(self):
""" Tests the intersection with a regex """
# pylint: disable=too-many-locals
state_p = State("p")
state_q = State("q")
state_r = State("r")
state_i = Symbol("i")
state_e = Symbol("e")
state_z = StackSymbol("Z")
state_x0 = StackSymbol("X0")
pda = PDA(states={state_p, state_q, state_r},
input_symbols={state_i, state_e},
stack_alphabet={state_z, state_x0},
start_state=state_p,
start_stack_symbol=state_x0,
final_states={state_r})
pda.add_transition(state_p, Epsilon(), state_x0, state_q,
[state_z, state_x0])
pda.add_transition(state_q, state_i, state_z, state_q,
[state_z, state_z])
pda.add_transition(state_q, state_e, state_z, state_q, [])
pda.add_transition(state_q, Epsilon(), state_x0, state_r, [])
state_s = finite_automaton.State("s")
state_t = finite_automaton.State("t")
i_dfa = finite_automaton.Symbol("i")
e_dfa = finite_automaton.Symbol("e")
dfa = finite_automaton.DeterministicFiniteAutomaton(
states={state_s, state_t},
input_symbols={i_dfa, e_dfa},
start_state=state_s,
final_states={state_s, state_t})
dfa.add_transition(state_s, i_dfa, state_s)
dfa.add_transition(state_s, e_dfa, state_t)
dfa.add_transition(state_t, e_dfa, state_t)
new_pda = pda.intersection(dfa)
pda_es = new_pda.to_empty_stack()
cfg = pda_es.to_cfg()
self.assertEqual(new_pda.get_number_transitions(), 6)
self.assertEqual(len(new_pda.states), 5)
self.assertEqual(len(new_pda.final_states), 2)
self.assertEqual(len(new_pda.input_symbols), 2)
self.assertEqual(len(new_pda.stack_symbols), 2)
i_cfg = Terminal("i")
e_cfg = Terminal("e")
self.assertTrue(cfg.contains([i_cfg, i_cfg, e_cfg, e_cfg, e_cfg]))
new_pda = pda.intersection(
finite_automaton.DeterministicFiniteAutomaton())
self.assertEqual(new_pda.get_number_transitions(), 0)
def _process_to_enfa_when_no_son(self, s_from, s_to):
if isinstance(self.head,
pyformlang.regular_expression.regex_objects.Epsilon):
self._add_epsilon_transition_in_enfa_between(s_from, s_to)
elif not isinstance(self.head,
pyformlang.regular_expression.regex_objects.Empty):
symbol = finite_automaton.Symbol(self.head.value)
self._enfa.add_transition(s_from, symbol, s_to)
def test_to_enfa0(self):
""" Tests the transformation to a regex """
symb_a = finite_automaton.Symbol("a")
symb_b = finite_automaton.Symbol("b")
symb_c = finite_automaton.Symbol("c")
epsilon = finite_automaton.Epsilon()
regex = Regex("a|b")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a]))
self.assertTrue(enfa.accepts([symb_b]))
self.assertFalse(enfa.accepts([symb_c]))
self.assertFalse(enfa.accepts([epsilon]))
self.assertFalse(enfa.accepts([symb_a, symb_b]))
regex = Regex("a b")
enfa = regex.to_epsilon_nfa()
self.assertFalse(enfa.accepts([symb_a]))
self.assertFalse(enfa.accepts([symb_b]))
self.assertTrue(enfa.accepts([symb_a, symb_b]))
regex = Regex("a b c")
enfa = regex.to_epsilon_nfa()
self.assertFalse(enfa.accepts([symb_a, symb_b]))
self.assertTrue(enfa.accepts([symb_a, symb_b, symb_c]))
self.assertFalse(enfa.accepts([symb_a, symb_b, symb_a]))
regex = Regex("(a b)|c")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a, symb_b]))
self.assertFalse(enfa.accepts([symb_a, symb_c]))
self.assertFalse(enfa.accepts([symb_b, symb_c]))
self.assertTrue(enfa.accepts([symb_c]))
regex = Regex("")
enfa = regex.to_epsilon_nfa()
self.assertFalse(enfa.accepts([symb_a]))
self.assertFalse(enfa.accepts([symb_b]))
self.assertFalse(enfa.accepts([symb_c]))
self.assertFalse(enfa.accepts([]))
regex = Regex("a*")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a]))
self.assertTrue(enfa.accepts([]))
self.assertTrue(enfa.accepts([symb_a, symb_a]))
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_a]))
def test_to_enfa1(self):
""" Tests the transformation to a regex """
symb_a = finite_automaton.Symbol("a")
symb_b = finite_automaton.Symbol("b")
symb_c = finite_automaton.Symbol("c")
regex = Regex("a**")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a]))
self.assertTrue(enfa.accepts([]))
self.assertTrue(enfa.accepts([symb_a, symb_a]))
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_a]))
regex = Regex("a*b|c")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_b]))
self.assertTrue(enfa.accepts([symb_b]))
self.assertTrue(enfa.accepts([symb_c]))
self.assertFalse(enfa.accepts([symb_a, symb_a, symb_c]))
regex = Regex("a*(b|c)")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_b]))
self.assertTrue(enfa.accepts([symb_b]))
self.assertTrue(enfa.accepts([symb_c]))
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_c]))
regex = Regex("a*.(b|c)")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_b]))
self.assertTrue(enfa.accepts([symb_b]))
self.assertTrue(enfa.accepts([symb_c]))
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_c]))
regex = Regex("a*.(b|c)epsilon")
enfa = regex.to_epsilon_nfa()
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_b]))
self.assertTrue(enfa.accepts([symb_b]))
self.assertTrue(enfa.accepts([symb_c]))
self.assertTrue(enfa.accepts([symb_a, symb_a, symb_c]))
regex = Regex("$")
enfa = regex.to_epsilon_nfa()
self.assertFalse(enfa.accepts([symb_a]))
self.assertFalse(enfa.accepts([symb_b]))
self.assertFalse(enfa.accepts([symb_c]))
self.assertTrue(enfa.accepts([]))
def intersection(self, other: Any) -> "PDA":
""" Gets the intersection of the current PDA with something else
Equivalent to:
>> pda and regex
Parameters
----------
other : any
The other part of the intersection
Returns
----------
new_pda : :class:`~pyformlang.pda.PDA`
The pda resulting of the intersection
Raises
----------
NotImplementedError
When intersecting with something else than a regex or a finite
automaton
"""
if isinstance(other, Regex):
other = other.to_epsilon_nfa().to_deterministic()
elif isinstance(other, FiniteAutomaton):
if not other.is_deterministic():
other = other.to_deterministic()
else:
raise NotImplementedError
start_state_other = other.start_states
if len(start_state_other) == 0:
return PDA()
pda_state_converter = _PDAStateConverter(self._states, other.states)
start_state_other = list(start_state_other)[0]
final_state_other = other.final_states
start = pda_state_converter.to_pda_combined_state(
self._start_state, start_state_other)
pda = PDA(start_state=start,
start_stack_symbol=self._start_stack_symbol)
symbols = self._input_symbols.copy()
symbols.add(Epsilon())
to_process = [(self._start_state, start_state_other)]
processed = {(self._start_state, start_state_other)}
while to_process:
state_in, state_dfa = to_process.pop()
if (state_in in self._final_states
and state_dfa in final_state_other):
pda.add_final_state(
pda_state_converter.to_pda_combined_state(
state_in, state_dfa))
for symbol in symbols:
if symbol == Epsilon():
symbol_dfa = finite_automaton.Epsilon()
else:
symbol_dfa = finite_automaton.Symbol(symbol.value)
if symbol == Epsilon():
next_states_dfa = [state_dfa]
else:
next_states_dfa = other(state_dfa, symbol_dfa)
if len(next_states_dfa) == 0:
continue
for stack_symbol in self._stack_alphabet:
next_states_self = self._transition_function(
state_in, symbol, stack_symbol)
for next_state, next_stack in next_states_self:
for next_state_dfa in next_states_dfa:
pda.add_transition(
pda_state_converter.to_pda_combined_state(
state_in, state_dfa), symbol, stack_symbol,
pda_state_converter.to_pda_combined_state(
next_state, next_state_dfa), next_stack)
if (next_state, next_state_dfa) not in processed:
to_process.append((next_state, next_state_dfa))
processed.add((next_state, next_state_dfa))
return pda
def intersection(self, other: Any) -> "PDA":
""" Gets the intersection of the language L generated by the \
current PDA when accepting by final state with something else
Currently, it only works for regular languages (represented as \
regular expressions or finite automata) as the intersection \
between two PDAs is not context-free (it cannot be represented \
with a PDA).
Equivalent to:
>> pda and regex
Parameters
----------
other : any
The other part of the intersection
Returns
----------
new_pda : :class:`~pyformlang.pda.PDA`
The pda resulting of the intersection
Raises
----------
NotImplementedError
When intersecting with something else than a regex or a finite
automaton
"""
if isinstance(other, regular_expression.Regex):
enfa = other.to_epsilon_nfa()
other = enfa.to_deterministic()
elif isinstance(other, FiniteAutomaton):
is_deterministic = other.is_deterministic()
if not is_deterministic:
other = other.to_deterministic()
else:
raise NotImplementedError
start_state_other = other.start_states
if len(start_state_other) == 0:
return PDA()
pda_state_converter = _PDAStateConverter(self._states, other.states)
start_state_other = list(start_state_other)[0]
final_state_other = other.final_states
start = pda_state_converter.to_pda_combined_state(self._start_state,
start_state_other)
pda = PDA(start_state=start,
start_stack_symbol=self._start_stack_symbol)
symbols = self._input_symbols.copy()
symbols.add(Epsilon())
to_process = [(self._start_state, start_state_other)]
processed = {(self._start_state, start_state_other)}
while to_process:
state_in, state_dfa = to_process.pop()
if (state_in in self._final_states and state_dfa in
final_state_other):
pda.add_final_state(
pda_state_converter.to_pda_combined_state(state_in,
state_dfa))
for symbol in symbols:
if symbol == Epsilon():
symbol_dfa = finite_automaton.Epsilon()
else:
symbol_dfa = finite_automaton.Symbol(symbol.value)
if symbol == Epsilon():
next_states_dfa = [state_dfa]
else:
next_states_dfa = other(state_dfa, symbol_dfa)
if len(next_states_dfa) == 0:
continue
for stack_symbol in self._stack_alphabet:
next_states_self = self._transition_function(state_in,
symbol,
stack_symbol)
for next_state, next_stack in next_states_self:
for next_state_dfa in next_states_dfa:
pda.add_transition(
pda_state_converter.to_pda_combined_state(
state_in,
state_dfa),
symbol,
stack_symbol,
pda_state_converter.to_pda_combined_state(
next_state,
next_state_dfa),
next_stack)
if (next_state, next_state_dfa) not in processed:
to_process.append((next_state, next_state_dfa))
processed.add((next_state, next_state_dfa))
return pda