def test_releases(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x V y)", str(x_.releases(y_)))
def test_magicmethod_or(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x | y)", str(x_ | y_))
def test_triggered(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x T y)", str(x_.triggered(y_)))
def test_iff(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x <-> y)", str(x_.iff(y_)))
def test_depth(self):
# raw symbol has no depth
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
# propositional connectives do not increase the depth
self.assertEqual(0, (x_ & y_).depth)
self.assertEqual(0, (x_ | y_).depth)
self.assertEqual(0, (- x_).depth)
self.assertEqual(0, (x_.implies(y_)).to_negation_normal_form().depth)
self.assertEqual(0, (x_.iff(y_)).to_negation_normal_form().depth)
# temporal operators do increase the depth
self.assertEqual(42, x_.next_times(42).depth) # 42 times X ( .. X(x))
self.assertEqual( 1, x_.opnext().depth) # X x
self.assertEqual( 1, x_.opprec().depth) # Y x
self.assertEqual( 1, x_.opnotprecnot().depth) # Z x
self.assertEqual( 1, x_.globally().depth) # G x
self.assertEqual( 1, x_.historically().depth) # H x
self.assertEqual( 1, x_.eventually().depth) # F x
self.assertEqual( 1, x_.once().depth) # O x
self.assertEqual( 1, x_.until(y_).depth) # x U y
self.assertEqual( 1, x_.since(y_).depth) # x S y
self.assertEqual( 1, x_.releases(y_).depth) # x V y
self.assertEqual( 1, x_.triggered(y_).depth) # x T y
def test_and_(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x & y)", str(x_.and_(y_)))
def test_until_with_loop(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("(a U b)")
# bound 1
offset = 0
bound = 1
loop = 0
# remember: the NuSMV std apis incorporate the loop condition !
ref_expr= ltlspec.bounded_semantics_single_loop(fsm, formula, bound, loop)
expr = ltlspec.bounded_semantics_with_loop_at_offset(fsm, formula, 0, bound, loop, offset) \
& bmcutils.loop_condition(self.enc, bound, loop)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# ---- other offset ----
# bound 2
offset = 1
bound = 2
loop = 0
car = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
cdr = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
# because of the way the loop condition is encoded !
ref_expr= self.enc.shift_to_time(cdr, offset) | (self.enc.shift_to_time(car, offset) \
& self.enc.shift_to_time(cdr, offset+1))
expr = ltlspec.bounded_semantics_with_loop_at_offset(fsm, formula, 0, bound, loop, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# because loop < i, the condition must be the same as before
expr = ltlspec.bounded_semantics_with_loop_at_offset(fsm, formula, 1, bound, loop, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
def test_constraint_context_sigma(self):
fsm = master_be_fsm()
_true = Node.from_ptr(parse_ltl_spec("TRUE"))
_true = bmcutils.make_nnf_boolean_wff(_true)
_truen= _true.to_node()
cond = Wff(parse_ltl_spec("G !(mouse = hover)"))\
.to_boolean_wff()\
.to_negation_normal_form()
off_1 = 0
off_2 = 2
length= 1
# sigma1
problem = diagnosability.generate_sat_problem([], (_truen, _truen), length, _true, cond.to_node(), _truen)
tm_cond = ltlspec.bounded_semantics_at_offset(fsm, cond.to_node(), length, off_1)
canonical_p = tests.canonical_cnf(problem)
canonical_f = tests.canonical_cnf(tm_cond)
self.assertTrue(all(clause in canonical_p for clause in canonical_f))
# sigma2
problem = diagnosability.generate_sat_problem([], (_truen, _truen), length, _true, _truen, cond.to_node())
tm_cond = ltlspec.bounded_semantics_at_offset(fsm, cond.to_node(), length, off_2)
canonical_p = tests.canonical_cnf(problem)
canonical_f = tests.canonical_cnf(tm_cond)
self.assertTrue(all(clause in canonical_p for clause in canonical_f))
def test_since(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x S y)", str(x_.since(y_)))
def test_until(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x U y)", str(x_.until(y_)))
def test_constraint_context_theta(self):
enc = master_be_fsm().encoding
cond = Wff(parse_simple_expression("mouse = down")).to_boolean_wff()
theta = diagnosability.constraint_context_theta_initial(cond, 0, 1)
manual= enc.shift_to_time(cond.to_be(enc), 0) \
& enc.shift_to_time(cond.to_be(enc), 1) \
self.assertEqual(theta, manual)
def test_constraint_context_theta(self):
enc = master_be_fsm().encoding
cond = Wff(parse_simple_expression("mouse = down")).to_boolean_wff()
theta = diagnosability.constraint_context_theta_initial(cond, 0, 1)
manual= enc.shift_to_time(cond.to_be(enc), 0) \
& enc.shift_to_time(cond.to_be(enc), 1) \
self.assertEqual(theta, manual)
def test_to_negation_normal_form(self):
x = self.enc.by_name["x"]
y = self.enc.by_name["y"]
x_ = Wff.decorate(x.name)
y_ = Wff.decorate(y.name)
self.assertEqual("(x -> y)", str(x_.implies(y_)))
self.assertEqual("(!x | y)", str(x_.implies(y_).to_negation_normal_form()))
self.assertEqual("(x <-> y)", str(x_.iff(y_)))
self.assertEqual("((!x | y) & (x | !y))", str(x_.iff(y_).to_negation_normal_form()))
def test_decorate(self):
for prop in glob.prop_database():
# can decorate a property
dec = Wff.decorate(prop.exprcore)
self.assertEqual(str(dec), str(prop.exprcore))
# can decorate a plain node
x = self.enc.by_name["x"]
_x = Wff.decorate(x.name)
self.assertEqual("x", str(_x))
# combination possible between plain nodes and specs
self.assertEqual(str(dec | _x), '('+str(prop.exprcore)+" | x)")
def test_next_no_loop(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("X (a <-> !b)")
# bound 0
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 0)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 0, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 1)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 1, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# ---- other offset ----
# bound 0
offset = 1
ref_expr= Be.false(fsm.encoding.manager)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 0, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 1
ref_expr= Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
ref_expr= fsm.encoding.shift_to_time(ref_expr, offset+1)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 1, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
def test_bounded_semantics_with_loop_optimized_depth1(self):
spec = Node.from_ptr(parse_ltl_spec("G ( y <= 7 )")) # depth == 1
# it must raise exception when the bound is not feasible
with self.assertRaises(ValueError):
ltlspec.bounded_semantics_all_loops_optimisation_depth1(
self.fsm, spec, -1)
# should yield the same result (w/ opt) as regular all loops when depth is one
optimized = ltlspec.bounded_semantics_all_loops_optimisation_depth1(
self.fsm, spec, 5)
regular = ltlspec.bounded_semantics_all_loops(self.fsm,
spec,
bound=5,
loop=0)
self.assertEqual(regular, optimized)
# but not when the optim is turned off on 'all loops'
regular = ltlspec.bounded_semantics_all_loops(self.fsm,
spec,
bound=5,
loop=0,
optimized=False)
self.assertNotEqual(regular, optimized)
# and it should only be applied when the depth is equal to one
spec = Node.from_ptr(parse_ltl_spec("F G ( y <= 7 )")) # depth == 2
self.assertEqual(2, Wff.decorate(spec).depth)
optimized = ltlspec.bounded_semantics_all_loops_optimisation_depth1(
self.fsm, spec, 5)
regular = ltlspec.bounded_semantics_all_loops(self.fsm,
spec,
bound=5,
loop=0)
self.assertNotEqual(regular, optimized)
def make_nnf_boolean_wff(prop_node):
"""
Decorates the property identified by `prop_node` to become a boolean WFF,
and converts the resulting formula to negation normal form. (negation sign
on literals only).
"""
return Wff.decorate(prop_node).\
to_boolean_wff().\
to_negation_normal_form()
def nnf(self, text):
"""
Utility function to convert text into an equivalent Node form in NNF
:return: an NNF node version of the text
"""
return Wff(parse_ltl_spec(text)).to_boolean_wff()\
.to_negation_normal_form()\
.to_node()
def test_until(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("(a U !b)")
# bound 0
offset = 0
bound = 0
ref_expr= ltlspec.bounded_semantics(fsm, formula, bound)
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 0
bound = 1
ref_expr= ltlspec.bounded_semantics(fsm, formula, bound)
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# ---- other offset ----
# bound 0
offset = 2
bound = 0
cdr = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
ref_expr= self.enc.shift_to_time(cdr, 0+offset)
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 2
bound = 1
car = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
cdr = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
ref_expr= self.enc.shift_to_time(cdr, 0+offset) \
| (self.enc.shift_to_time(car, 0+offset) & self.enc.shift_to_time(cdr, 1+offset))
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
def test_releases_no_loop(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("(a V b)")
# bound 0
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 0)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 0, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 1)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 1, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 2 -- verification must be done by hand because the different
# cnf literals mess the comparison
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 2)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 2, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# ---- other offset ----
# bound 0
offset = 1
bound = 0
left = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
right = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
ref_expr= self.enc.shift_to_time(right, offset) & self.enc.shift_to_time(left, offset)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 1
bound = 1
left = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
right = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
ref_expr= self.enc.shift_to_time(right, offset) & ( self.enc.shift_to_time(left, offset) \
| (self.enc.shift_to_time(right, 1+offset) & self.enc.shift_to_time(left, 1+offset)))
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
def test_until_no_loop(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("(a U b)")
# bound 0
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 0)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 0, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 1)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 1, 0)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 2 -- verification must be done by hand because the different
# cnf literals mess the comparison
# ref_expr= ltlspec.bounded_semantics_without_loop(fsm, formula, 2)
# expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 2, 0)
# self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# ---- other offset ----
# bound 0
offset = 1
ref_expr= Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
ref_expr= fsm.encoding.shift_to_time(ref_expr, offset)
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 0, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 1
cdr = Wff.decorate(ltlspec.cdr(formula)).to_be(fsm.encoding)
car = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
ref_expr= fsm.encoding.shift_to_time(cdr, offset) \
| ( fsm.encoding.shift_to_time(car, offset) \
& fsm.encoding.shift_to_time(cdr, offset+1))
expr = ltlspec.bounded_semantics_without_loop_at_offset(fsm, formula, 0, 1, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
def test_bounded_semantics_with_loop_optimized_depth1(self):
spec = Node.from_ptr(parse_ltl_spec("G ( y <= 7 )")) # depth == 1
# it must raise exception when the bound is not feasible
with self.assertRaises(ValueError):
ltlspec.bounded_semantics_all_loops_optimisation_depth1(self.fsm, spec, -1)
# should yield the same result (w/ opt) as regular all loops when depth is one
optimized = ltlspec.bounded_semantics_all_loops_optimisation_depth1(self.fsm, spec, 5)
regular = ltlspec.bounded_semantics_all_loops(self.fsm, spec, bound=5, loop=0)
self.assertEqual(regular, optimized)
# but not when the optim is turned off on 'all loops'
regular = ltlspec.bounded_semantics_all_loops(self.fsm, spec, bound=5, loop=0, optimized=False)
self.assertNotEqual(regular, optimized)
# and it should only be applied when the depth is equal to one
spec = Node.from_ptr(parse_ltl_spec("F G ( y <= 7 )")) # depth == 2
self.assertEqual(2, Wff.decorate(spec).depth)
optimized = ltlspec.bounded_semantics_all_loops_optimisation_depth1(self.fsm, spec, 5)
regular = ltlspec.bounded_semantics_all_loops(self.fsm, spec, bound=5, loop=0)
self.assertNotEqual(regular, optimized)
def _booleanize(self):
"""
Returns a boolean expression (Be) corresponding to this simple
boolean expression (text).
.. note::
Albeit feasible, working directly with variables as offered by the
encoding is a little bit limiting as it de facto rejects any symbol
which is not a variable. As a consequence, the DEFINES, or
arithmetic expressions are not usable.
The use of this function palliates that limitation and makes the
use of any simple boolean expression possible.
:return: a be expression (Be) corresponding to `self`
"""
if not self._booleanized:
befsm = master_be_fsm()
node = parse_simple_expression(self.id)
self._booleanized = Wff(node).to_boolean_wff().to_be(
befsm.encoding)
return self._booleanized
def test_next(self):
with Configure(self, __file__, "/models/flipflops.smv"):
fsm = self.befsm
formula = self.nnf("X (a <-> !b)")
# bound 0
offset = 0
bound = 0
ref_expr= ltlspec.bounded_semantics(fsm, formula, bound)
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
self.assertEqual(canonical_cnf(expr), canonical_cnf(ref_expr))
# bound 1
offset = 0
bound = 1
# done this way to avoid the depth 1 optimisation
car = Wff.decorate(ltlspec.car(formula)).to_be(fsm.encoding)
ref_expr= self.enc.shift_to_time(car, offset+1) \
| (self.enc.shift_to_time(car, offset) & bmcutils.loop_condition(self.enc, bound, 0))
expr = ltlspec.bounded_semantics_at_offset(fsm, formula, bound, offset)
def test_bounded_semantics_without_loop(self):
# parse the ltl property
spec = Node.from_ptr(parse_ltl_spec("G ( y <= 7 )"))
# it must raise exception when the bound is not feasible
with self.assertRaises(ValueError):
ltlspec.bounded_semantics_without_loop(self.fsm, spec, bound=-1)
# verify that the generated expression corresponds to what is announced
no_loop = ltlspec.bounded_semantics_without_loop(self.fsm, spec, 10)
# globally w/o loop is false (this is just a test)
self.assertEqual(no_loop, Be.false(self.fsm.encoding.manager))
# an other more complex generation
spec = Node.from_ptr(parse_ltl_spec("F (y <= 7)"))
no_loop = ltlspec.bounded_semantics_without_loop(self.fsm, spec, 10)
#
# The generated expression is [[f]]^{0}_{k} so (! L_{k}) is not taken
# care of. And actually, NuSMV does not generate that part of the
# formula: it only enforce the loop condition when the semantics with
# loop is used
#
handcrafted = Be.false(self.fsm.encoding.manager)
y_le_seven = Wff(parse_ltl_spec("y <= 7")).to_boolean_wff().to_be(
self.fsm.encoding)
for time_x in reversed(
range(11)): # 11 because range 'eats' up the last step
handcrafted |= self.fsm.encoding.shift_to_time(y_le_seven, time_x)
#### debuging info #####
#print("noloop = {}".format(no_loop.to_cnf()))
#print("hancraft= {}".format(handcrafted.to_cnf()))
#print(self.fsm.encoding)
self.assertEqual(no_loop, handcrafted)
def test_constraint_context_sigma(self):
fsm = master_be_fsm()
_true = Node.from_ptr(parse_ltl_spec("TRUE"))
_true = bmcutils.make_nnf_boolean_wff(_true)
_truen = _true.to_node()
cond = Wff(parse_ltl_spec("G !(mouse = hover)"))\
.to_boolean_wff()\
.to_negation_normal_form()
off_1 = 0
off_2 = 2
length = 1
# sigma1
problem = diagnosability.generate_sat_problem([], (_truen, _truen),
length, _true,
cond.to_node(), _truen)
tm_cond = ltlspec.bounded_semantics_at_offset(fsm, cond.to_node(),
length, off_1)
canonical_p = tests.canonical_cnf(problem)
canonical_f = tests.canonical_cnf(tm_cond)
self.assertTrue(all(clause in canonical_p for clause in canonical_f))
# sigma2
problem = diagnosability.generate_sat_problem([], (_truen, _truen),
length, _true, _truen,
cond.to_node())
tm_cond = ltlspec.bounded_semantics_at_offset(fsm, cond.to_node(),
length, off_2)
canonical_p = tests.canonical_cnf(problem)
canonical_f = tests.canonical_cnf(tm_cond)
self.assertTrue(all(clause in canonical_p for clause in canonical_f))
def test_once(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(" O x", str(x_.once()))
def test_eventually(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(" F x", str(x_.eventually()))
def test_to_node(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(x.name, x_.to_node())
def test_to_boolean_wff(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name).to_boolean_wff(glob.bdd_encoding())
# TODO: find something better to validate this
self.assertIsNotNone(x_)
def test_globally(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(" G x", str(x_.globally()))
def test_historically(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(" H x", str(x_.historically()))
def test_next_times(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual("x", str(x_.next_times(0)))
self.assertEqual(" X x", str(x_.next_times(1)))
self.assertEqual(" X ( X ( X x))", str(x_.next_times(3)))
def test_false(self):
self.assertEqual("FALSE", str(Wff.false()))
self.assertEqual(0, Wff.false().depth)
def test_true(self):
self.assertEqual("TRUE", str(Wff.true()))
self.assertEqual(0, Wff.true().depth)
def test_magicmethod_invert(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual("!x", str(~x_))
def test_opnotprecnot(self):
x = self.enc.by_name["x"]
x_ = Wff.decorate(x.name)
self.assertEqual(" Z x", str(x_.opnotprecnot()))