def _build_automata(self):
rows = self.row_symbols
atoms = [AtomicFormula(r) for r in rows]
alphabet = Alphabet(set(rows))
ldlf = LDLf_EmptyTraces(alphabet)
f = PathExpressionEventually(
PathExpressionSequence.chain([
PathExpressionStar(
And.chain([Not(atoms[0]),
Not(atoms[1]),
Not(atoms[2])])),
PathExpressionStar(
And.chain([atoms[0],
Not(atoms[1]),
Not(atoms[2])])),
# Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
PathExpressionStar(
And.chain([atoms[0], atoms[1],
Not(atoms[2])])),
# Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2]]), # Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], atoms[4], Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], atoms[4], atoms[5] ])
]),
And.chain([atoms[0], atoms[1], atoms[2]]))
nfa = ldlf.to_nfa(f)
dfa = _to_pythomata_dfa(nfa)
return dfa
def test_minimal_models(self):
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
alphabet = Alphabet({a, b, c})
pl = PL(alphabet)
atomic_a = AtomicFormula(a)
atomic_b = AtomicFormula(b)
atomic_c = AtomicFormula(c)
self.assertEqual(
pl.minimal_models(TrueFormula()),
{PLInterpretation(alphabet, {
a: False,
b: False,
c: False
})})
self.assertEqual(pl.minimal_models(FalseFormula()), set())
self.assertEqual(
pl.minimal_models(atomic_a),
{PLInterpretation(alphabet, {
a: True,
b: False,
c: False
})})
self.assertEqual(
pl.minimal_models(Not(atomic_a)),
{PLInterpretation(alphabet, {
a: False,
b: False,
c: False
})})
self.assertEqual(
pl.minimal_models(And(atomic_a, atomic_b)),
{PLInterpretation(alphabet, {
a: True,
b: True,
c: False
})})
self.assertEqual(pl.minimal_models(And(atomic_a, Not(atomic_a))),
set())
self.assertEqual(
pl.minimal_models(Or(atomic_a, atomic_b)), {
PLInterpretation(alphabet, {
a: False,
b: True,
c: False
}),
PLInterpretation(alphabet, {
a: True,
b: False,
c: False
})
})
self.assertEqual(
pl.minimal_models(And.chain([atomic_a, atomic_b, atomic_c])),
{PLInterpretation(alphabet, {
a: True,
b: True,
c: True
})})
def to_nfa(self, f: Formula):
# TODO: optimize!!!
assert self.is_formula(f)
nnf_f = self.to_nnf(f)
alphabet = powerset(self.alphabet.symbols)
initial_states = {frozenset([nnf_f])}
final_states = {frozenset()}
delta = set()
pl, I = PL._from_set_of_propositionals(set(), Alphabet(set()))
d = self.delta(nnf_f, frozenset(), epsilon=True)
if pl.truth(d, I):
final_states.add(frozenset([nnf_f]))
states = {frozenset(), frozenset([nnf_f])}
states_changed, delta_changed = True, True
while states_changed or delta_changed:
states_changed, delta_changed = False, False
for actions_set in alphabet:
states_list = list(states)
for q in states_list:
delta_formulas = [
self.delta(subf, actions_set) for subf in q
]
atomics = [
s for subf in delta_formulas
for s in PL.find_atomics(subf)
]
symbol2formula = {
Symbol(str(f)): f
for f in atomics
if f != TrueFormula() and f != FalseFormula()
}
formula2atomic_formulas = {
f: AtomicFormula.fromName(str(f))
if f != TrueFormula() and f != FalseFormula() else f
for f in atomics
}
transformed_delta_formulas = [
self._tranform_delta(f, formula2atomic_formulas)
for f in delta_formulas
]
conjunctions = And.chain(transformed_delta_formulas)
models = frozenset(
PL(Alphabet(
set(symbol2formula))).minimal_models(conjunctions))
if len(models) == 0:
continue
for min_model in models:
q_prime = frozenset({
symbol2formula[s]
for s in min_model.symbol2truth
if min_model.symbol2truth[s]
})
len_before = len(states)
states.add(q_prime)
if len(states) == len_before + 1:
states_list.append(q_prime)
states_changed = True
len_before = len(delta)
delta.add((q, actions_set, q_prime))
if len(delta) == len_before + 1:
delta_changed = True
# check if q_prime should be added as final state
if len(q_prime) == 0:
final_states.add(q_prime)
else:
q_prime_delta_conjunction = And.chain([
self.delta(subf, frozenset(), epsilon=True)
for subf in q_prime
])
pl, I = PL._from_set_of_propositionals(
set(), Alphabet(set()))
if pl.truth(q_prime_delta_conjunction, I):
final_states.add(q_prime)
return {
"alphabet": alphabet,
"states": frozenset(states),
"initial_states": frozenset(initial_states),
"transitions": delta,
"accepting_states": frozenset(final_states)
}
def test_chain(self):
a_sym, b_sym, c_sym = [Symbol(s) for s in ["a", "b", "c"]]
a, b, c = [AtomicFormula(s) for s in [a_sym,b_sym,c_sym]]
and_chain = And.chain([a, b, c])
self.assertEqual(and_chain, And(a, And(b, And(c, TrueFormula()))))