def setUp(self):
"""Set up test fixtures, if any."""
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
self.not_a = Not(self.a)
self.not_a_and_b = And(self.not_a, self.b)
self.not_a_or_c = Or(self.not_a, self.c)
self.true = TrueFormula()
self.false = FalseFormula()
self.symbol2truth = {
self.a_sym: True,
self.b_sym: False,
self.c_sym: True
}
self.I = PLInterpretation(self.alphabet, self.symbol2truth)
self.PL = PL(self.alphabet)
def test_to_nnf_allowed_formulas_not_normalized(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.to_nnf(Not(Not(b))), b)
self.assertEqual(pl.to_nnf(Not(And(a, Not(b)))), Or(Not(a), b))
def test_to_nnf_derived_formula(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.to_nnf(Not(Or(b, Not(a)))), And(Not(b), a))
self.assertEqual(pl.to_nnf(Not(Implies(b, Not(a)))), And(b, a))
def test_expand_formula_allowed_formulas(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(a), a)
self.assertEqual(pl.expand_formula(Not(b)), Not(b))
self.assertEqual(pl.expand_formula(And(a, b)), And(a, b))
def test_find_atomics(self):
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
atomic_a = AtomicFormula(a)
atomic_b = AtomicFormula(b)
atomic_c = AtomicFormula(c)
self.assertEqual(
PL.find_atomics(And(atomic_a, And(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
self.assertEqual(PL.find_atomics(Or(atomic_a, Or(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
self.assertEqual(
PL.find_atomics(Equivalence(atomic_a, Or(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
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_expand_formula_error(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = Next(AtomicFormula(a_sym))
pl = PL(alphabet)
with self.assertRaises(ValueError) as ve:
pl.expand_formula(a)
def test_is_formula_composed(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
pl = PL(alphabet)
self.assertTrue(
pl.is_formula(
Implies(Not(a), And(TrueFormula(), Not(FalseFormula())))))
self.assertFalse(
pl.is_formula(
Implies(Not(a), And(TrueFormula(), Next(FalseFormula())))))
def setUp(self):
# Symbols
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
self.ref = REf(self.alphabet)
self.trace_1_list = [
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.b_sym, self.c_sym},
]
self.trace_1 = FiniteTrace(self.trace_1_list, self.alphabet)
def test_expand_formula_derived_formulas(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
# T = Not(And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC))
# F = And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC)
T = TrueFormula()
F = FalseFormula()
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(TrueFormula()), T)
self.assertEqual(pl.expand_formula(FalseFormula()), F)
self.assertEqual(pl.expand_formula(Or(a, b)), Not(And(Not(a), Not(b))))
self.assertEqual(pl.expand_formula(Implies(a, b)),
Not(And(Not(Not(a)), Not(b))))
self.assertEqual(pl.expand_formula(Implies(b, a)),
Not(And(Not(Not(b)), Not(a))))
# A === B = (A AND B) OR (NOT A AND NOT B) = NOT( NOT(A AND B) AND NOT(NOT A AND NOT B) )
self.assertEqual(pl.expand_formula(Equivalence(a, b)),
Not(And(Not(And(a, b)), Not(And(Not(a), Not(b))))))
def _is_formula(self, f: Formula):
"""Check if a formula is legal in the current formal system"""
if isinstance(f, AtomicFormula):
return f.symbol in self.alphabet.symbols or f == AtomicFormula(
DUMMY_SYMBOL)
elif isinstance(f, UnaryOperator):
return self.is_formula(f.f)
elif isinstance(f, BinaryOperator):
return self.is_formula(f.f1) and self.is_formula(f.f2)
elif isinstance(f, TrueFormula) or isinstance(f, FalseFormula):
return True
else:
raise ValueError("Argument not a valid Formula")
def test_expand_formula_composed(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
# T = Not(And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC))
# F = And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC)
T = TrueFormula()
F = FalseFormula()
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(And(TrueFormula(), FalseFormula())),
And(T, F))
self.assertEqual(pl.expand_formula(Or(TrueFormula(), FalseFormula())),
Not(And(Not(T), Not(F))))
self.assertEqual(
pl.expand_formula(Implies(TrueFormula(), FalseFormula())),
Not(And(Not(Not(T)), Not(F))))
self.assertEqual(
pl.expand_formula(Equivalence(TrueFormula(), FalseFormula())),
Not(And(Not(And(T, F)), Not(And(Not(T), Not(F))))))
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()))))
def test_sequence(self):
alphabet = Alphabet.fromStrings({"a", "b"})
a = AtomicFormula.fromName("a")
b = AtomicFormula.fromName("b")
ref = REf(alphabet)
self.assertTrue(ref.is_formula(PathExpressionSequence(a, b)))
def test_is_formula_error(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = Next(AtomicFormula(a_sym))
pl = PL(alphabet)
self.assertFalse(pl.is_formula(a))
def test_star(self):
alphabet = Alphabet.fromStrings({"a"})
a = AtomicFormula.fromName("a")
ref = REf(alphabet)
self.assertTrue(ref.is_formula(PathExpressionStar(a)))
def test_is_formula_atomic(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
pl = PL(alphabet)
self.assertTrue(pl.is_formula(a))
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 setUp(self):
"""Set up test fixtures, if any."""
# Symbols
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
# Propositionals
self.not_a = Not(self.a)
self.not_b = Not(self.b)
self.not_c = Not(self.c)
self.a_and_b = And(self.a, self.b)
self.a_and_c = And(self.a, self.c)
self.b_and_c = And(self.b, self.c)
self.abc = And(self.a, And(self.b, self.c))
self.b_or_c = Or(self.b, self.c)
self.a_or_b = Or(self.a, self.b)
self.not_abc = Not(And(self.a, And(self.b, self.c)))
### Path expression
# Tests
self.test_a = PathExpressionTest(self.a)
self.test_b = PathExpressionTest(self.b)
self.test_not_a = PathExpressionTest(self.not_a)
self.test_not_b = PathExpressionTest(self.not_b)
# Union
self.path_a_or_b = PathExpressionUnion(self.a, self.b)
self.path_b_or_c = PathExpressionUnion(self.b, self.c)
# Sequence
self.path_seq_a_and_b__a_and_c = PathExpressionSequence(
self.a_and_b, self.a_and_c)
self.path_a_or_b__b_or_c = PathExpressionSequence(
self.path_a_or_b, self.path_b_or_c)
# Stars
self.path_b_or_c_star = PathExpressionStar(self.path_b_or_c)
self.path_not_abc = PathExpressionStar(self.not_abc)
# Modal connective
self.eventually_propositional_a_and_b__a_and_c = PathExpressionEventually(
self.a_and_b, self.a_and_c)
self.eventually_test_a__c = PathExpressionEventually(
self.test_a, self.c)
self.eventually_test_a__b = PathExpressionEventually(
self.test_a, self.b)
self.eventually_seq_a_and_b__a_and_c__not_c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.not_c)
self.eventually_seq_a_and_b__a_and_c__c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.c)
self.eventually_b_or_c_star__b_and_c = PathExpressionEventually(
self.path_b_or_c_star, self.b_and_c)
self.next_a_and_c = PathExpressionEventually(TrueFormula(),
self.a_and_c)
self.liveness_b_and_c = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.b_and_c)
self.liveness_abc = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.abc)
self.always_true__a = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.a)
self.always_true__b_or_c = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.b_or_c)
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
# Traces
self.ldlf = LDLf(self.alphabet)
self.trace_1_list = [
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.b_sym, self.c_sym},
]
self.trace_1 = FiniteTrace(self.trace_1_list, self.alphabet)
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_propositional_is_formula(self):
alphabet = Alphabet.fromStrings({"a"})
a = AtomicFormula.fromName("a")
ref = REf(alphabet)
self.assertTrue(ref.is_formula(a))