def _make_transition(Q, i: PLInterpretation):
actions_set = i.true_propositions
new_macrostate = set()
for q in Q:
# delta function applied to every formula in the macro state Q
delta_formulas = [f.delta(actions_set) for f in q]
# find the list of atoms, which are "true" atoms (i.e. propositional atoms) or LDLf formulas
atomics = [s for subf in delta_formulas for s in find_atomics(subf)]
atom2id = {v: k for k, v in enumerate(atomics)}
id2atom = {v: k for k, v in atom2id.items()}
# "freeze" the found atoms as symbols and build a mapping from symbols to formulas
symbol2formula = {atom2id[f] for f in atomics if f != PLTrue() and f != PLFalse()}
# build a map from formula to a "freezed" propositional Atomic Formula
formula2atomic_formulas = {
f: PLAtomic(atom2id[f])
if f != PLTrue() and f != PLFalse() # and not isinstance(f, PLAtomic)
else f for f in atomics
}
# the final list of Propositional Atomic Formulas, one for each formula in the original macro state Q
transformed_delta_formulas = [_transform_delta(f, formula2atomic_formulas) for f in delta_formulas]
# the empy conjunction stands for true
if len(transformed_delta_formulas) == 0:
conjunctions = PLTrue()
elif len(transformed_delta_formulas) == 1:
conjunctions = transformed_delta_formulas[0]
else:
conjunctions = PLAnd(transformed_delta_formulas)
# the model in this case is the smallest set of symbols s.t. the conjunction of "freezed" atomic formula
# is true.
models = frozenset(conjunctions.minimal_models(Alphabet(symbol2formula)))
for min_model in models:
q_prime = frozenset({id2atom[s] for s in min_model.true_propositions})
new_macrostate.add(q_prime)
return frozenset(new_macrostate)
def to_automaton_(f, labels:Set[Symbol]=None):
"""
DEPRECATED
From a LDLfFormula, build the automaton.
:param f: a LDLfFormula;
:param labels: a set of Symbol, the fluents of our domain. If None, retrieve them from the formula;
:param determinize: True if you need to determinize the NFA, obtaining a DFA;
:param minimize: True if you need to minimize the DFA (if determinize is False this flag has no effect.)
:return: a NFA or a DFA which accepts the same traces that makes the formula True.
"""
nnf = f.to_nnf()
if labels is None:
# if the labels of the formula are not specified in input,
# retrieve them from the formula
labels = nnf.find_labels()
# the alphabet is the powerset of the set of fluents
alphabet = powerset(labels)
initial_state = MacroState({nnf})
final_states = {MacroState()}
delta = set()
d = f.delta(PLFalseInterpretation(), epsilon=True)
if d.truth(d):
final_states.add(initial_state)
states = {MacroState(), initial_state}
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 function applied to every formula in the macro state Q
delta_formulas = [f.delta(actions_set) for f in q]
# find the list of atoms, which are "true" atoms (i.e. propositional atoms) or LDLf formulas
atomics = [s for subf in delta_formulas for s in find_atomics(subf)]
# "freeze" the found atoms as symbols and build a mapping from symbols to formulas
symbol2formula = {Symbol(str(f)): f for f in atomics if f != PLTrue() and f != PLFalse()}
# build a map from formula to a "freezed" propositional Atomic Formula
formula2atomic_formulas = {
f: PLAtomic(Symbol(str(f)))
if f != PLTrue() and f != PLFalse()# and not isinstance(f, PLAtomic)
else f for f in atomics
}
# the final list of Propositional Atomic Formulas, one for each formula in the original macro state Q
transformed_delta_formulas = [_transform_delta(f, formula2atomic_formulas) for f in delta_formulas]
# the empty conjunction stands for true
if len(transformed_delta_formulas) == 0:
conjunctions = PLTrue()
elif len(transformed_delta_formulas) == 1:
conjunctions = transformed_delta_formulas[0]
else:
conjunctions = PLAnd(transformed_delta_formulas)
# the model in this case is the smallest set of symbols s.t. the conjunction of "freezed" atomic formula
# is true.
models = frozenset(conjunctions.minimal_models(Alphabet(symbol2formula)))
if len(models) == 0:
continue
for min_model in models:
q_prime = MacroState(
{symbol2formula[s] for s in min_model.true_propositions})
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:
subf_deltas = [subf.delta(PLFalseInterpretation(), epsilon=True) for subf in q_prime]
if len(subf_deltas)==1:
q_prime_delta_conjunction = subf_deltas[0]
else:
q_prime_delta_conjunction = PLAnd(subf_deltas)
if q_prime_delta_conjunction.truth(PLFalseInterpretation()):
final_states.add(q_prime)
alphabet = PythomataAlphabet({PLInterpretation(set(sym)) for sym in alphabet})
delta = frozenset((i, PLInterpretation(set(a)), o) for i, a, o in delta)
nfa = NFA.fromTransitions(
alphabet=alphabet,
states=frozenset(states),
initial_state=initial_state,
accepting_states=frozenset(final_states),
transitions=delta
)
return nfa
