def test_delta():
parser = LDLfParser()
i_ = {}
i_a = {"A": True}
i_b = {"B": True}
i_ab = {"A": True, "B": True}
true = PLTrue()
false = PLFalse()
tt = PLAtomic(LDLfLogicalTrue())
ff = PLAtomic(LDLfLogicalFalse())
assert parser("<A>tt").delta(i_) == false
assert parser("<A>tt").delta(i_a) == tt
assert parser("<A>tt").delta(i_b) == false
assert parser("<A>tt").delta(i_ab) == tt
assert parser("[B]ff").delta(i_) == true
assert parser("[B]ff").delta(i_a) == true
assert parser("[B]ff").delta(i_b) == ff
assert parser("[B]ff").delta(i_ab) == ff
f = parser("!(<?(!last)>end)")
assert f.delta(i_) == f.to_nnf().delta(i_)
assert f.delta(i_ab) == f.to_nnf().delta(i_ab)
assert f.delta(i_, epsilon=True) == f.to_nnf().delta(i_, epsilon=True)
assert f.delta(i_ab, epsilon=True) == f.to_nnf().delta(i_ab, epsilon=True)
# with epsilon=True, the result is either PLTrue or PLFalse
assert f.delta(i_, epsilon=True) in [PLTrue(), PLFalse()]
def _delta(self, i: PLInterpretation, epsilon=False):
if epsilon:
return PLFalse()
else:
return PLAnd(
[PLAtomic(self.f),
PLAtomic(LTLfNot(LTLfEnd()).to_nnf())])
def test_nnf():
parser = PLParser()
sa, sb = "A", "B"
a, b = PLAtomic(sa), PLAtomic(sb)
i_ = PLInterpretation(set())
i_a = PLInterpretation({sa})
i_b = PLInterpretation({sb})
i_ab = PLInterpretation({sa, sb})
not_a_and_b = parser("!(A&B)")
nnf_not_a_and_b = parser("!A | !B")
assert not_a_and_b.to_nnf() == nnf_not_a_and_b
assert nnf_not_a_and_b == nnf_not_a_and_b.to_nnf()
dup = parser("!(A | A)")
nnf_dup = dup.to_nnf()
assert nnf_dup == PLNot(a)
material_implication = parser("!A | B <-> !(A & !B) <-> A->B")
nnf_material_implication = parser(
"((!A | B) & (!A | B) & (!A | B)) | ((A & !B) & (A & !B) & (A & !B))")
nnf_m = material_implication.to_nnf()
assert nnf_m == nnf_material_implication.to_nnf()
assert nnf_m.truth(i_) == material_implication.truth(
i_) == nnf_material_implication.truth(i_) == True
assert nnf_m.truth(i_a) == material_implication.truth(
i_a) == nnf_material_implication.truth(i_a) == True
assert nnf_m.truth(i_b) == material_implication.truth(
i_b) == nnf_material_implication.truth(i_b) == True
assert nnf_m.truth(i_ab) == material_implication.truth(
i_ab) == nnf_material_implication.truth(i_ab) == True
def test_always(self):
parser = self.parser
i_, i_a, i_b, i_ab = self.i_, self.i_a, self.i_b, self.i_ab
true = self.true
false = self.false
assert parser("G a").delta(i_a) == PLAnd([
true,
PLOr([
false,
PLOr([
PLAtomic(LTLfRelease([LTLfFalse(),
LTLfAtomic("a")])),
PLAtomic(LTLfRelease([LTLfFalse(),
LTLfFalse()])),
]),
]),
])
assert parser("G a").delta(i_a) == PLAnd([
true,
PLOr([
false,
PLOr([
PLAtomic(LTLfRelease([LTLfFalse(),
LTLfAtomic("a")])),
PLAtomic(LTLfRelease([LTLfFalse(),
LTLfFalse()])),
]),
]),
])
assert parser("G a").delta(i_a, epsilon=True) == true
assert parser("G a").delta(i_, epsilon=True) == true
def test_eventually(self):
parser = self.parser
i_, i_a, i_b, i_ab = self.i_, self.i_a, self.i_b, self.i_ab
true = self.true
false = self.false
assert parser("F a").delta(i_a) == PLOr([
true,
PLAnd([
true,
PLAnd([
PLAtomic(LTLfUntil([LTLfTrue(),
LTLfAtomic("a")])),
PLAtomic(LTLfUntil([LTLfTrue(), LTLfTrue()])),
]),
]),
])
assert parser("F a").delta(i_) == PLOr([
false,
PLAnd([
true,
PLAnd([
PLAtomic(LTLfUntil([LTLfTrue(),
LTLfAtomic("a")])),
PLAtomic(LTLfUntil([LTLfTrue(), LTLfTrue()])),
]),
]),
])
assert parser("F a").delta(i_a, epsilon=True) == false
assert parser("F a").delta(i_, epsilon=True) == false
def _delta(self, i: PropositionalInterpretation, epsilon=False):
"""Apply the delta function."""
if epsilon:
return PLFalse()
else:
return PLAnd(
[PLAtomic(self.f),
PLAtomic(LTLfNot(LTLfEnd()).to_nnf())])
def setup_class(cls):
cls.sa, cls.sb = "a", "b"
cls.i_ = PLInterpretation(set())
cls.i_a = PLInterpretation({cls.sa})
cls.i_b = PLInterpretation({cls.sb})
cls.i_ab = PLInterpretation({cls.sa, cls.sb})
cls.a, cls.b = PLAtomic(cls.sa), PLAtomic(cls.sb)
def setup_class(cls):
cls.sa, cls.sb = "a", "b"
cls.i_ = {}
cls.i_a = {cls.sa: True}
cls.i_b = {cls.sb: True}
cls.i_ab = {cls.sa: True, cls.sb: True}
cls.a, cls.b = PLAtomic(cls.sa), PLAtomic(cls.sb)
def test_nnf():
parser = PLParser()
sa, sb = "A", "B"
a, b = PLAtomic(sa), PLAtomic(sb)
i_ = {}
i_a = {sa: True}
i_b = {sb: True}
i_ab = {sa: True, sb: True}
not_a_and_b = parser("!(A&B)")
nnf_not_a_and_b = parser("!A | !B")
assert not_a_and_b.to_nnf() == nnf_not_a_and_b
assert nnf_not_a_and_b == nnf_not_a_and_b.to_nnf()
dup = parser("!(A | A)")
nnf_dup = dup.to_nnf()
assert nnf_dup == PLAnd([PLNot(a), PLNot(a)])
material_implication = parser("!A | B <-> !(A & !B) <-> A->B")
nnf_material_implication = parser(
"((!A | B) & (!A | B) & (!A | B)) | ((A & !B) & (A & !B) & (A & !B))"
)
nnf_m = material_implication.to_nnf()
assert nnf_m == nnf_material_implication.to_nnf()
assert (
nnf_m.truth(i_)
== material_implication.truth(i_)
== nnf_material_implication.truth(i_)
== True
)
assert (
nnf_m.truth(i_a)
== material_implication.truth(i_a)
== nnf_material_implication.truth(i_a)
== True
)
assert (
nnf_m.truth(i_b)
== material_implication.truth(i_b)
== nnf_material_implication.truth(i_b)
== True
)
assert (
nnf_m.truth(i_ab)
== material_implication.truth(i_ab)
== nnf_material_implication.truth(i_ab)
== True
)
def test_until(self):
parser = self.parser
i_, i_a, i_b, i_ab = self.i_, self.i_a, self.i_b, self.i_ab
true = self.true
false = self.false
assert parser("A U B").delta(i_a) == PLOr([
false,
PLAnd([
true,
PLAtomic(LTLfUntil([LTLfAtomic("A"), LTLfAtomic("B")])),
PLAtomic(LTLfEventually(LTLfTrue()).to_nnf())
])
])
assert parser("A U B").delta(i_ab, epsilon=True) == false
def test_release(self):
parser = self.parser
i_, i_a, i_b, i_ab = self.i_, self.i_a, self.i_b, self.i_ab
true = self.true
false = self.false
assert parser("A R B").delta(i_a) == PLAnd([
false,
PLOr([
true,
PLAtomic(LTLfRelease([LTLfAtomic("A"), LTLfAtomic("B")])),
PLAtomic(LTLfAlways(LTLfFalse()).to_nnf())
])
])
assert parser("A R B").delta(i_ab, epsilon=True) == true
def p_propositional(self, p):
"""propositional : propositional EQUIVALENCE propositional
| propositional IMPLIES propositional
| propositional OR propositional
| propositional AND propositional
| NOT propositional
| FALSE
| TRUE
| ATOM"""
if len(p)==4:
if p[2] == Symbols.EQUIVALENCE.value:
p[0] = PLEquivalence([p[1], p[3]])
elif p[2] == Symbols.IMPLIES.value:
p[0] = PLImplies([p[1], p[3]])
elif p[2] == Symbols.OR.value:
p[0] = PLOr([p[1], p[3]])
elif p[2] == Symbols.AND.value:
p[0] = PLAnd([p[1], p[3]])
else:
raise ValueError
# else:
# p[0] = p[2]
elif len(p)==3:
p[0] = PLNot(p[2])
elif len(p)==2:
if p[1]==Symbols.TRUE.value:
p[0] = PLTrue()
elif p[1]==Symbols.FALSE.value:
p[0] = PLFalse()
else:
p[0] = PLAtomic(p[1])
else:
raise ValueError
def delta_box(self, f: LDLfFormula, i: PLInterpretation, epsilon=False):
if epsilon:
return PLTrue()
if self.pl_formula.truth(i):
return PLAtomic(_expand(f))
else:
return PLTrue()
def to_automaton(f) -> SymbolicDFA: # noqa: C901
"""Translate to automaton."""
f = f.to_nnf()
initial_state = frozenset({frozenset({PLAtomic(f)})})
states = {initial_state}
final_states = set()
transition_function = {} # type: Dict
all_labels = f.find_labels()
alphabet = powerset(all_labels)
if f.delta({}, epsilon=True) == PLTrue():
final_states.add(initial_state)
visited = set() # type: Set
to_be_visited = {initial_state}
while len(to_be_visited) != 0:
for q in list(to_be_visited):
to_be_visited.remove(q)
for actions_set in alphabet:
new_state = _make_transition(
q, {label: True
for label in actions_set})
if new_state not in states:
states.add(new_state)
to_be_visited.add(new_state)
transition_function.setdefault(q, {})[actions_set] = new_state
if new_state not in visited:
visited.add(new_state)
if _is_true(new_state):
final_states.add(new_state)
automaton = SymbolicAutomaton()
state2idx = {}
for state in states:
state_idx = automaton.create_state()
state2idx[state] = state_idx
if state == initial_state:
automaton.set_initial_state(state_idx)
if state in final_states:
automaton.set_accepting_state(state_idx, True)
for source in transition_function:
for symbol, destination in transition_function[source].items():
source_idx = state2idx[source]
dest_idx = state2idx[destination]
pos_expr = sympy.And(*map(sympy.Symbol, symbol))
neg_expr = sympy.And(*map(lambda x: sympy.Not(sympy.Symbol(x)),
all_labels.difference(symbol)))
automaton.add_transition(
(source_idx, sympy.And(pos_expr, neg_expr), dest_idx))
determinized = automaton.determinize()
minimized = determinized.minimize()
return minimized
def find_atomics(formula: Formula) -> Set[PLAtomic]:
"""Finds all the atomic formulas"""
res = set()
if isinstance(formula, PLFormula):
res = formula.find_atomics()
else:
res.add(PLAtomic(formula))
return res
def test_1(self):
sa, sb = "A", "B"
a, b = PLAtomic(sa), PLAtomic(sb)
i_ = {}
i_a = {"A": True}
i_b = {"B": True}
i_ab = {"A": True, "B": True}
tr_false_a_b_ab = [i_, i_a, i_b, i_ab, i_]
tt = LDLfLogicalTrue()
ff = LDLfLogicalFalse()
assert tt.truth(tr_false_a_b_ab, 0)
assert not ff.truth(tr_false_a_b_ab, 0)
assert not LDLfNot(tt).truth(tr_false_a_b_ab, 0)
assert LDLfNot(ff).truth(tr_false_a_b_ab, 0)
# assert LDLfAnd([LDLfPropositional(a), LDLfPropositional(b)]).truth(
# tr_false_a_b_ab, 3
# )
assert not LDLfDiamond(RegExpPropositional(PLAnd([a, b])), tt).truth(
tr_false_a_b_ab, 0)
trace = self.trace
parser = self.parser
formula = "<true*;A&B>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 0)
formula = "[(A+!B)*]<C>tt"
parsed_formula = parser(formula)
assert not parsed_formula.truth(trace, 1)
formula = "<?(<!C>tt)><A>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 1)
formula = "<!C+A>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 1)
formula = "<!C+A>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 1)
def test_delta():
parser = LDLfParser()
sa, sb, sc = "A", "B", "C"
a, b, c = PLAtomic(sa), PLAtomic(sb), PLAtomic(sc)
i_ = PLFalseInterpretation()
i_a = PLInterpretation({sa})
i_b = PLInterpretation({sb})
i_ab = PLInterpretation({sa, sb})
true = PLTrue()
false = PLFalse()
tt = LDLfLogicalTrue()
ff = LDLfLogicalFalse()
assert parser("<A>tt").delta(i_) == false
assert parser("<A>tt").delta(i_a) == PLAtomic(tt)
assert parser("<A>tt").delta(i_b) == false
assert parser("<A>tt").delta(i_ab) == PLAtomic(tt)
assert parser("[B]ff").delta(i_) == true
assert parser("[B]ff").delta(i_a) == true
assert parser("[B]ff").delta(i_b) == PLAtomic(ff)
assert parser("[B]ff").delta(i_ab) == PLAtomic(ff)
f = parser("!(<!(A<->B)+(B;A)*+(!last)?>[(true)*]end)")
assert f.delta(i_) == f.to_nnf().delta(i_)
assert f.delta(i_ab) == f.to_nnf().delta(i_ab)
assert f.delta(i_, epsilon=True) == f.to_nnf().delta(i_, epsilon=True)
assert f.delta(i_ab, epsilon=True) == f.to_nnf().delta(i_ab, epsilon=True)
# with epsilon=True, the result is either PLTrue or PLFalse
assert f.delta(i_, epsilon=True) in [PLTrue(), PLFalse()]
def _make_transition(Q: FrozenSet[FrozenSet[PLAtomic]], 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.s.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)} # type: Dict[int, PLAtomic]
id2atom = {v: k
for k, v in atom2id.items()} # type: Dict[PLAtomic, int]
# "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 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.
alphabet = frozenset(symbol2formula)
models = frozenset(conjunctions.minimal_models(alphabet))
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 test_names():
good = [
"A",
"b",
"Hello",
"PropZero",
"Prop0",
"this_is_fine_2",
'"This is also allowed!"',
PLParser()("A -> B"),
]
bad = ["!", "&", "Invalid:", "", '"', "="]
for name in good:
PLAtomic(name)
for name in bad:
with pytest.raises(ValueError):
PLAtomic(name)
def p_formula_atom(self, p):
"""formula : ATOM
| TRUE
| FALSE"""
if p[1] == Symbols.TRUE.value:
p[0] = PLTrue()
elif p[1] == Symbols.FALSE.value:
p[0] = PLFalse()
else:
p[0] = PLAtomic(p[1])
def test_parser():
parser = PLParser()
sa, sb = "A", "B"
a, b = PLAtomic(sa), PLAtomic(sb)
a_and_b = parser("A & B")
true_a_and_b = PLAnd([a, b])
assert a_and_b == true_a_and_b
material_implication = parser("!A | B <-> !(A & !B) <-> A->B")
true_material_implication = PLEquivalence(
[PLOr([PLNot(a), b]), PLNot(PLAnd([a, PLNot(b)])), PLImplies([a, b])]
)
assert material_implication == true_material_implication
true_a_and_false_and_true = PLAnd([a, PLFalse(), PLTrue()])
a_and_false_and_true = parser("A & false & true")
assert a_and_false_and_true == true_a_and_false_and_true
def delta_box(self,
f: LDLfFormula,
i: PropositionalInterpretation,
epsilon=False):
"""Apply delta function for regular expressions in the box operator."""
if epsilon:
return PLTrue()
if self.pl_formula.truth(i):
return PLAtomic(_expand(f))
else:
return PLTrue()
def test_truth():
sa, sb = "a", "b"
a, b = PLAtomic(sa), PLAtomic(sb)
i_ = PLFalseInterpretation()
i_a = PLInterpretation({sa})
i_b = PLInterpretation({sb})
i_ab = PLInterpretation({sa, sb})
tr_false_a_b_ab = FiniteTrace([i_, i_a, i_b, i_ab, i_])
tt = LDLfLogicalTrue()
ff = LDLfLogicalFalse()
assert tt.truth(tr_false_a_b_ab, 0)
assert not ff.truth(tr_false_a_b_ab, 0)
assert not LDLfNot(tt).truth(tr_false_a_b_ab, 0)
assert LDLfNot(ff).truth(tr_false_a_b_ab, 0)
assert LDLfAnd([LDLfPropositional(a),
LDLfPropositional(b)]).truth(tr_false_a_b_ab, 3)
assert not LDLfDiamond(RegExpPropositional(PLAnd([a, b])), tt).truth(
tr_false_a_b_ab, 0)
parser = LDLfParser()
trace = FiniteTrace.from_symbol_sets([{}, {"A"}, {"A"}, {"A", "B"}, {}])
formula = "<true*;A&B>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 0)
formula = "[(A+!B)*]<C>tt"
parsed_formula = parser(formula)
assert not parsed_formula.truth(trace, 1)
formula = "<(<!C>tt)?><A>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 1)
formula = "<!C+A>tt"
parsed_formula = parser(formula)
assert parsed_formula.truth(trace, 1)
def test_next(self):
parser = self.parser
i_, i_a, i_b, i_ab = self.i_, self.i_a, self.i_b, self.i_ab
true = self.true
false = self.false
assert parser("X A").delta(i_) == PLAnd(
[PLAtomic(LTLfAtomic("A")), PLAtomic(LTLfEventually(LTLfTrue()).to_nnf())])
assert parser("X A").delta(i_a) == PLAnd(
[PLAtomic(LTLfAtomic("A")), PLAtomic(LTLfEventually(LTLfTrue()).to_nnf())])
assert parser("X A").delta(i_b) == PLAnd(
[PLAtomic(LTLfAtomic("A")), PLAtomic(LTLfEventually(LTLfTrue()).to_nnf())])
assert parser("X A").delta(i_ab) == PLAnd(
[PLAtomic(LTLfAtomic("A")), PLAtomic(LTLfEventually(LTLfTrue()).to_nnf())])
assert parser("X A").delta(i_, epsilon=True) == false
def to_automaton(f, labels: Optional[Set[Symbol]] = None):
initial_state = frozenset({frozenset({PLAtomic(f)})})
states = {initial_state}
final_states = set()
transition_function = {}
# the alphabet is the powerset of the set of fluents
alphabet = powerset(labels if labels is not None else f.find_labels())
if f.delta(PLFalseInterpretation(), epsilon=True) == PLTrue():
final_states.add(initial_state)
visited = set()
to_be_visited = {initial_state}
while len(to_be_visited) != 0:
for q in list(to_be_visited):
to_be_visited.remove(q)
for actions_set in alphabet:
new_state = _make_transition(q, PLInterpretation(actions_set))
if new_state not in states:
states.add(new_state)
to_be_visited.add(new_state)
transition_function.setdefault(
q, {})[PLInterpretation(actions_set)] = new_state
if new_state not in visited:
visited.add(new_state)
if _is_true(new_state):
final_states.add(new_state)
new_alphabet = {PLInterpretation(set(sym)) for sym in alphabet}
dfa = DFA(states, new_alphabet, initial_state, final_states,
transition_function)
dfa = dfa.minimize()
dfa = dfa.trim()
return dfa
def _make_transition(marco_q: FrozenSet[FrozenSet[PLAtomic]],
i: PropositionalInterpretation):
new_macrostate = set()
for q in marco_q:
# delta function applied to every formula in the macro state Q
delta_formulas = [cast(Delta, f.s).delta(i) for f in q]
# find atomics -> so also ldlf formulas
# replace atomic with custom object
# convert to sympy
# 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: str(k)
for k, v in enumerate(atomics)} # type: Dict[PLAtomic, str]
id2atom = {v: k
for k, v in atom2id.items()} # type: Dict[str, PLAtomic]
# 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 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) # type: ignore
# the model in this case is the smallest set of symbols
# s.t. the conjunction of "freezed" atomic formula is true.
# alphabet = frozenset(symbol2formula)
# models = frozenset(conjunctions.minimal_models(alphabet))
formula = to_sympy(conjunctions, replace=atom2id) # type: ignore
all_models = list(sympy.satisfiable(formula, all_models=True))
if len(all_models) == 1 and all_models[0] == BooleanFalse():
models = [] # type: List[Set[str]]
elif len(all_models) == 1 and all_models[0] == {True: True}:
models = [set()]
else:
models = list(
map(lambda x: {k
for k, v in x.items()
if v is True}, all_models))
for min_model in models:
q_prime = frozenset({id2atom[s] for s in map(str, min_model)})
new_macrostate.add(q_prime)
return frozenset(new_macrostate)
def to_LDLf(self):
return LDLfPropositional(PLAtomic(self.s)).convert()
def find_labels(self):
return PLAtomic(self.s).find_labels()
def truth(self, i: FiniteTrace, pos: int = 0):
return PLAtomic(self.s).truth(i.get(pos))
def _delta(self, i: PLInterpretation, epsilon: bool = False):
if epsilon:
return PLFalse()
return PLTrue() if PLAtomic(self.s).truth(i) else PLFalse()