def test_incremental(self):
a = Symbol('a', BOOL)
b = Symbol('b', BOOL)
c = Symbol('c', BOOL)
for name in get_env().factory.all_solvers(logic=QF_BOOL):
with Solver(name) as solver:
solver.add_assertion(Or(a, b))
solver.add_assertion(Or(Not(b), c))
self.assertTrue(solver.solve())
try:
solver.push(1)
except NotImplementedError:
# if push not implemented, pop shouldn't be either
self.assertRaises(NotImplementedError, solver.pop)
continue
solver.add_assertion(And(Not(a), Not(c)))
self.assertFalse(solver.solve())
solver.pop(1)
self.assertTrue(solver.solve())
solver.add_assertion(FALSE())
self.assertFalse(solver.solve())
solver.reset_assertions()
solver.add_assertion(a)
self.assertTrue(solver.solve())
def construct_spread_formula_from_graph(spread_graph, limit, target):
initial_infection_ints = [
Symbol('init_int_' + str(i), INT) for i in spread_graph.nodes
]
final_infection_ints = [
Symbol('final_int_' + str(i), INT) for i in spread_graph.nodes
]
spreading_clauses = []
origin_clauses = []
all_bounds = []
# Here, we ensure that, if node i is selected as an initial infector, all of its neighbors are also infected:
for starting_node in spread_graph.nodes:
initial_infection_bounds = And(
LE(initial_infection_ints[int(starting_node)], Int(1)),
GE(initial_infection_ints[int(starting_node)], Int(0)))
infected_neighbors = And([
Equals(final_infection_ints[int(i)], Int(1))
for i in spread_graph.successors(starting_node)
])
infected_nodes = And(
infected_neighbors,
Equals(final_infection_ints[int(starting_node)], Int(1)))
spreading_forumla = Implies(
Equals(initial_infection_ints[int(starting_node)], Int(1)),
infected_nodes)
spreading_clauses.append(spreading_forumla)
all_bounds.append(initial_infection_bounds)
# Here, we ensure that, if node i becomes infected, either it was infected by an initial infectors with an edge to node i
# of node i itself was an initial infector.
for infected_node in spread_graph.nodes:
final_infection_bounds = And(
LE(final_infection_ints[int(infected_node)], Int(1)),
GE(final_infection_ints[int(infected_node)], Int(0)))
origin_neighbors = Or([
Equals(initial_infection_ints[int(i)], Int(1))
for i in spread_graph.predecessors(infected_node)
])
origin_nodes = Or(
origin_neighbors,
Equals(initial_infection_ints[int(infected_node)], Int(1)))
origin_formula = Implies(
Equals(final_infection_ints[int(infected_node)], Int(1)),
origin_nodes)
origin_clauses.append(origin_formula)
all_bounds.append(final_infection_bounds)
initial_infection_limit = LE(Plus(initial_infection_ints), Int(limit))
final_infection_target = GE(Plus(final_infection_ints), Int(target))
return And(
And(spreading_clauses), And(origin_clauses), And(all_bounds),
initial_infection_limit,
final_infection_target), initial_infection_ints, final_infection_ints
def encode_node(self, node):
"""
Encode a node of a tree.
"""
if '_' not in node.name:
# continuous features => expecting an upper bound
# feature and its upper bound (value)
f, v = node.name, node.threshold
existing = True if tuple([f, v]) in self.idmgr.obj2id else False
vid = self.idmgr.id(tuple([f, v]))
bv = Symbol('bvar{0}'.format(vid), typename=BOOL)
if not existing:
if self.intvs:
d = self.imaps[f][v] + 1
pos, neg = self.ivars[f][:d], self.ivars[f][d:]
self.enc.append(Iff(bv, Or(pos)))
self.enc.append(Iff(Not(bv), Or(neg)))
else:
fvar, fval = Symbol(f, typename=REAL), Real(v)
self.enc.append(Iff(bv, LT(fvar, fval)))
return bv, Not(bv)
else:
# all features are expected to be categorical and
# encoded with one-hot encoding into Booleans
# each node is expected to be of the form: f_i < 0.5
bv = Symbol(node.name, typename=BOOL)
# left branch is positive, i.e. bv is true
# right branch is negative, i.e. bv is false
return Not(bv), bv
def all_loopbacks(self, vars, k, heqvar=None):
lvars = list(vars)
vars_k = [TS.get_timed(v, k) for v in lvars]
loopback = FALSE()
eqvar = None
heqvars = None
if heqvar is not None:
eqvar = Symbol(EQVAR, BOOL)
heqvars = []
peqvars = FALSE()
for i in range(k):
vars_i = [TS.get_timed(v, i) for v in lvars]
eq_k_i = And(
[EqualsOrIff(vars_k[j], vars_i[j]) for j in range(len(lvars))])
if heqvar is not None:
eqvar_i = TS.get_timed(eqvar, i)
peqvars = Or(peqvars, eqvar_i)
eq_k_i = And(eqvar_i, Iff(eqvar_i, eq_k_i))
heqvars.append(Iff(TS.get_timed(heqvar, i), peqvars))
loopback = Or(loopback, eq_k_i)
if heqvar is not None:
loopback = And(loopback, And(heqvars))
return loopback
def break_dfa_symmetry_bfs(x, y, sigma, prefixes_r, h):
epsilon_i = prefixes_r[()]
assert epsilon_i == 0
constraints = []
constraints.append(Equals(x[epsilon_i], Int(1)))
t = [[Symbol(f"t_{i}_{j}", BOOL) for j in range(h)] for i in range(h)]
p = [[Symbol(f"p_{i}_{j}", BOOL) for j in range(h)] for i in range(h)]
for i, j in it.combinations(range(h), 2):
constraints.append(Iff(
t[i][j],
Or(*(Equals(Select(y[l], Int(i+1)), Int(j+1)) for l in range(len(sigma))))
))
constraints.append(Iff(
p[j][i],
And(
t[i][j],
*(Not(t[k][j]) for k in range(i))
)
))
for j in range(1, h):
constraints.append(Or(*(p[j][k] for k in range(j))))
for k, i, j in it.combinations(range(h-1), 3):
constraints.append(Implies(p[j][i], Not(p[j+1][k])))
assert len(sigma) == 2
for i, j in it.combinations(range(h-1), 2):
constraints.append(Implies(And(p[j][i], p[j+1][i]), Equals(Select(y[0], Int(i+1)), Int(j+1))))
return constraints
def get_wire_formulas(w, lst):
r = None
if w.type == Wire.INPUT:
r = Symbol(w.name)
elif w.type == 'not':
r = Not(lst[0])
elif w.type == 'buf':
r = lst[0]
elif w.type == 'buff':
r = lst[0]
elif w.type == 'and':
r = And(lst)
elif w.type == 'nand':
r = And(lst)
r = Not(r)
elif w.type == 'or':
r = Or(lst)
elif w.type == 'nor':
r = Or(lst)
r = Not(r)
elif w.type == 'xor':
assert (len(lst) == 2)
r = Xor(lst[0], lst[1])
elif w.type == 'xnor':
assert (len(lst) == 2)
r = Xor(lst[0], lst[1])
r = Not(r)
elif w.type == 'mux':
assert (len(lst) == 3)
r = Or(And(Not(lst[0]), lst[1]), And(lst[0], lst[2]))
else:
logging.critical('unspecified gate type')
exit()
return r
def __init__(self, oracle_cir, obf_cir):
self.oracle_cir = oracle_cir
self.obf_cir = obf_cir
# generate solver formulas
for w in self.oracle_cir.wire_objs:
lst = []
for op in w.operands:
lst.append(Symbol(op.name))
r = self.get_wire_formulas(w, lst)
w.formula = Iff(Symbol(w.name), r)
# generate formulas for two copies of obfuscated circuit
ckt1 = self.gen_dip_chk('dc1', '_0', None)
ckt2 = self.gen_dip_chk('dc2', '_1', None)
output_xors = []
for w in self.obf_cir.output_wires:
output_xors.append(
Xor(Symbol(w.name + '@dc1'), Symbol(w.name + '@dc2')))
self.dip_gen_ckt = And(Or(output_xors), ckt1, ckt2)
# key inequality circuit
key_symbols1 = []
key_symbols2 = []
for w in self.obf_cir.wire_objs:
if 'keyinput' in w.name:
key_symbols1.append(Symbol(w.name + '_0'))
key_symbols2.append(Symbol(w.name + '_1'))
output_xors = []
for i in range(self.obf_cir.k_inputs):
output_xors.append(Xor(key_symbols1[i], key_symbols2[i]))
self.key_inequality_ckt = Or(output_xors)
def k_sequence_WH(m, K, K_seq_len=100, count=100):
k_seq = [Symbol('x_%i' % i, INT) for i in range(K_seq_len)]
domain = And([Or(Equals(x, Int(0)), Equals(x, Int(1))) for x in k_seq])
K_window = And([
LE(Plus(k_seq[t:min(K_seq_len, t + K)]), Int(m))
for t in range(max(1, K_seq_len - K + 1))
])
formula = And(domain, K_window)
solver = Solver(name='yices',
incremental=True,
random_seed=randint(2 << 30))
solver.add_assertion(formula)
for _ in range(count):
result = solver.solve()
if not result:
solver = Solver(name='z3',
incremental=True,
random_seed=randint(2 << 30))
solver.add_assertion(formula)
solver.solve()
model = solver.get_model()
model = array(list(map(lambda x: model.get_py_value(x), k_seq)),
dtype=bool)
yield model
solver.add_assertion(
Or([NotEquals(k_seq[i], Int(model[i])) for i in range(K_seq_len)]))
def solve_inc(self, hts, prop, k, all_vars=True):
if all_vars:
relevant_vars = hts.vars
else:
relevant_vars = hts.state_vars | hts.input_vars | hts.output_vars
init = hts.single_init()
trans = hts.single_trans()
invar = hts.single_invar()
init = And(init, invar)
init_0 = self.at_time(init, 0)
nprop = self.enc.to_nnf(Not(prop))
self._reset_assertions(self.solver)
self._add_assertion(self.solver, init_0)
for t in range(1, k + 1, 1):
trans_t = self.unroll(trans, invar, t)
self._add_assertion(self.solver, trans_t)
lb = self.all_simple_loopbacks(relevant_vars, t)
self._push(self.solver)
self._push(self.solver)
nprop_k = self.enc.encode(nprop, 0, t)
self._add_assertion(self.solver, And(nprop_k, Not(Or(lb))))
if self._solve(self.solver):
Logger.log("Counterexample (no-loop) found with k=%s" % (t), 1)
model = self._get_model(self.solver)
return (t, model)
nltlprop = []
self._pop(self.solver)
for l in range(t + 1):
nprop_l = self.enc.encode_l(nprop, 0, t, l)
nltlprop.append(And(lb[l], nprop_l))
self._add_assertion(self.solver, Or(nltlprop))
if self._solve(self.solver):
Logger.log("Counterexample (with-loop) found with k=%s" % (t),
1)
model = self._get_model(self.solver)
return (t, model)
else:
Logger.log("No counterexample found with k=%s" % (t), 1)
Logger.msg(".", 0, not (Logger.level(1)))
self._pop(self.solver)
return (k - 1, None)
def test_boolean(self):
x, y, z = Symbol("x"), Symbol("y"), Symbol("z")
f = Or(And(Not(x), Iff(x, y)), Implies(x, z))
self.assertEqual(f.to_smtlib(daggify=False),
"(or (and (not x) (= x y)) (=> x z))")
self.assertEqual(f.to_smtlib(daggify=True),
"(let ((.def_0 (=> x z))) (let ((.def_1 (= x y))) (let ((.def_2 (not x))) (let ((.def_3 (and .def_2 .def_1))) (let ((.def_4 (or .def_3 .def_0))) .def_4)))))")
def two_comparator(input1, input2):
if SortingNetwork.simplify:
return [
simplify(Or(input1, input2)),
simplify(And(input1, input2))
]
else:
return [Or(input1, input2), And(input1, input2)]
def test_int(self):
p, q = Symbol("p", INT), Symbol("q", INT)
f = Or(Equals(Times(p, Int(5)), Minus(p,q)),
LT(p,q), LE(Int(6), Int(1)))
self.assertEqual(f.to_smtlib(daggify=False),
"(or (= (* p 5) (- p q)) (< p q) (<= 6 1))")
self.assertEqual(f.to_smtlib(daggify=True),
"(let ((.def_0 (<= 6 1))) (let ((.def_1 (< p q))) (let ((.def_2 (- p q))) (let ((.def_3 (* p 5))) (let ((.def_4 (= .def_3 .def_2))) (let ((.def_5 (or .def_4 .def_1 .def_0))) .def_5))))))")
def test_boolean(self):
x, y, z = Symbol("x"), Symbol("y"), Symbol("z")
f = Or(And(Not(x), Iff(x, y)), Implies(x, z))
self.assertEqual(f.to_smtlib(daggify=False),
"(or (and (not x) (= x y)) (=> x z))")
self.assertEqual(
f.to_smtlib(daggify=True),
"(let ((.def_0 (=> x z))) (let ((.def_1 (= x y))) (let ((.def_2 (not x))) (let ((.def_3 (and .def_2 .def_1))) (let ((.def_4 (or .def_3 .def_0))) .def_4)))))"
)
def test_prenex_basic(self):
a, b, c = (Symbol(x) for x in "abc")
f = Not(And(a, Exists([b], And(a, b)), ForAll([c], Or(a, c))))
prenex = prenex_normal_form(f)
# Two prenex normal forms are possible
my_prenex_1 = Exists([c], ForAll([b], Not(And(a, And(a, b), Or(a,
c)))))
my_prenex_2 = ForAll([b], Exists([c], Not(And(a, And(a, b), Or(a,
c)))))
self.assertTrue(prenex == my_prenex_1 or prenex == my_prenex_2)
def triangle(nvars, rand_gen):
# alpha = rand_gen.uniform(0.05, 0.25)
alpha = rand_gen.uniform(0.2, 0.25)
remain = nvars % 3
n_tris = int(nvars / 3)
variables = [Symbol(f"x{i}", REAL) for i in range(1, nvars + 1)]
lbounds = [LE(Real(0), x) for x in variables]
ubounds = [LE(x, Real(1)) for x in variables]
clauses = []
potentials = []
for i in range(n_tris):
x, y, z = variables[3 * i], variables[3 * i + 1], variables[3 * i + 2]
xc = None if 3 * i + 3 >= nvars else variables[3 * i + 3]
# x_i
clauses.append(Or(LE(x, Real(alpha)), LE(Real(1 - alpha), x)))
# x_i -- y_i
clauses.append(
Or(LE(y, Plus(x, Real(-alpha))), LE(Plus(x, Real(alpha)), y)))
# x_i -- z_i
clauses.append(Or(LE(Real(1 - alpha), x), LE(Real(1 - alpha), z)))
clauses.append(Or(LE(x, Real(alpha)), LE(z, Real(alpha))))
# z_i -- y_i
clauses.append(LE(z, y))
# x_i -- x_i+1
if xc:
clauses.append(Or(LE(x, Real(alpha)), LE(Real(1 - alpha), xc)))
clauses.append(Or(LE(Real(1 - alpha), x), LE(xc, Real(alpha))))
pot_yz = Ite(LE(z, y), Times([z, y, Real(100)]), Real(1))
pot_xy = Ite(LE(y, Plus(x, Real(-alpha))),
Times(Real(100), Plus(x, y)), Real(1))
potentials.append(pot_xy)
potentials.append(pot_yz)
if remain == 1:
x = variables[3 * n_tris]
clauses.append(Or(LE(x, Real(alpha)), LE(Real(1 - alpha), x)))
if remain == 2:
x, y = variables[3 * n_tris], variables[nvars - 1]
# x_n
clauses.append(Or(LE(x, Real(alpha)), LE(Real(1 - alpha), x)))
# x -- y
clauses.append(
Or(LE(y, Plus(x, Real(-alpha))), LE(Plus(x, Real(alpha)), y)))
potentials.append(
Ite(LE(y, Plus(x, Real(-alpha))), Times(Real(100), Plus(x, y)),
Real(1)))
domain = Domain.make(
[], # no booleans
[x.symbol_name() for x in variables],
[(0, 1) for _ in range(len(variables))])
support = And(lbounds + ubounds + clauses)
weight = Times(potentials) if len(potentials) > 1 else potentials[0]
return Density(domain, support, weight, []), alpha
def test_int(self):
p, q = Symbol("p", INT), Symbol("q", INT)
f = Or(Equals(Times(p, Int(5)), Minus(p, q)), LT(p, q),
LE(Int(6), Int(1)))
self.assertEqual(f.to_smtlib(daggify=False),
"(or (= (* p 5) (- p q)) (< p q) (<= 6 1))")
self.assertEqual(
f.to_smtlib(daggify=True),
"(let ((.def_0 (<= 6 1))) (let ((.def_1 (< p q))) (let ((.def_2 (- p q))) (let ((.def_3 (* p 5))) (let ((.def_4 (= .def_3 .def_2))) (let ((.def_5 (or .def_4 .def_1 .def_0))) .def_5))))))"
)
def k_sequence_WH_worst_case(m, K, K_seq_len=100, count=100):
k_seq = [Symbol('x_%i' % i, INT) for i in range(K_seq_len)]
domain = And([Or(Equals(x, Int(0)), Equals(x, Int(1))) for x in k_seq])
K_window = And([
LE(Plus(k_seq[t:min(K_seq_len, t + K)]), Int(m))
for t in range(max(1, K_seq_len - K + 1))
])
violate_up = And([
GT(Plus(k_seq[t:min(K_seq_len, t + K)]), Int(m - 1))
for t in range(max(1, K_seq_len - K + 1))
])
def violate_right_generator(n):
return And([
GT(Plus(k_seq[t:min(K_seq_len, t + K + n)]), Int(m))
for t in range(max(1, K_seq_len - (K + n) + 1))
])
right_shift = 1
formula = And(domain, K_window, violate_up,
violate_right_generator(right_shift))
solver = Solver(name='z3', incremental=True, random_seed=randint(2 << 30))
solver.add_assertion(formula)
solver.z3.set('timeout', 5 * 60 * 1000)
solutions = And()
for _ in range(count):
while right_shift + K < K_seq_len:
try:
result = solver.solve()
except BaseException:
result = None
if not result:
solver = Solver(name='z3',
incremental=True,
random_seed=randint(2 << 30))
right_shift += 1
solver.z3.set('timeout', 5 * 60 * 1000)
solver.add_assertion(
And(solutions, domain, K_window, violate_up,
violate_right_generator(right_shift)))
else:
break
try:
model = solver.get_model()
except BaseException:
break
model = array(list(map(lambda x: model.get_py_value(x), k_seq)),
dtype=bool)
yield model
solution = Or(
[NotEquals(k_seq[i], Int(model[i])) for i in range(K_seq_len)])
solutions = And(solutions, solution)
solver.add_assertion(solution)
def generate_false_constraint(path_constraint):
false_constraint = None
if path_constraint.is_and() or path_constraint.is_or():
prefix = None
while path_constraint.is_and() or path_constraint.is_or():
constraint = path_constraint.arg(1)
constraint_str = str(constraint.serialize())
if "angelic!bool" in constraint_str:
model = generate_model(constraint)
for var_name, byte_list in model:
if "angelic!bool" in var_name:
value = utilities.get_signed_value(byte_list)
if value != 0:
constraint = Not(constraint)
if false_constraint:
if path_constraint.is_and():
false_constraint = And(false_constraint, constraint)
elif path_constraint.is_or():
false_constraint = Or(false_constraint, constraint)
else:
false_constraint = constraint
prefix = path_constraint.arg(0)
if prefix.is_and() or prefix.is_or():
path_constraint = prefix
else:
prefix_str = str(prefix.serialize())
if "angelic!bool" in prefix_str:
model = generate_model(prefix)
for var_name, byte_list in model:
if "angelic!bool" in var_name:
value = utilities.get_signed_value(byte_list)
if value != 0:
prefix = Not(prefix)
if path_constraint.is_and():
false_constraint = And(false_constraint, prefix)
elif path_constraint.is_or():
false_constraint = Or(false_constraint, prefix)
else:
model = generate_model(path_constraint)
for var_name in model:
byte_list = model[var_name]
if "angelic!bool" in var_name:
value = utilities.get_signed_value(byte_list)
if value != 0:
false_constraint = Not(path_constraint)
else:
false_constraint = path_constraint
return false_constraint
def IsAttack(attack, plan, gridsize, obstacles, safes):
obstacles = IntifyCoords(obstacles)
safes = IntifyCoords(safes)
# (1) All attack moves are in Z_gridsize x Z_gridsize.
bounds = And([IsOnGrid(step, gridsize) for step in attack])
# (2) The attacker never moves more than 1 grid-square at a time.
adjacency = IsConnected(attack)
# (3) The attack begins in the same place as some path in the plan.
init = Or([SamePosition(path[0], attack[0]) for path in plan])
# (4) The attack enters a "safe" zone at some point.
reach = Or(
[SamePosition(coord, safe) for coord in attack for safe in safes])
# (5) The attack does not cross paths with any plans other than the one it
# replaces.
avoid = And([
Implies(SamePosition(path[i], attack[i]),
SamePosition(path[0], attack[0])) for i in range(len(attack))
for path in plan
])
# (6) The attack never runs into any obstacle.
obstacles = And([
Not(SamePosition(coord, obstacle)) for coord in attack
for obstacle in obstacles
])
# (7) Any time the attack is adjacent to some plan p, it is in the same
# place as another plan p' and therefore could be mistaken for the
# innocent plan p'.
# i is the attacker, j the observer, k the time-step.
undetected = And([
Implies(
SamePosition(plan[i][0], attack[0]),
And([
And(
Implies(Adj(plan[j][k], plan[i][k]),
SamePosition(coord, plan[i][k])),
Implies(Adj(coord, plan[j][k]),
SamePosition(coord, plan[i][k])))
for k, coord in enumerate(attack) for j in range(len(plan))
if j != i
])) for i in range(len(plan))
])
return And(bounds, adjacency, init, reach, avoid, obstacles, undetected)
def test_named_unsat_core_with_assumptions(self):
i0 = Int(0)
a = GT(Symbol("a", INT), i0)
b = GT(Symbol("b", INT), i0)
c = GT(Symbol("c", INT), i0)
n_a = Not(a)
n_b = Not(b)
n_c = Not(c)
formulae = [Or(b, n_a), Or(c, n_a), Or(n_a, n_b, n_c)]
with UnsatCoreSolver(logic=QF_LIA, unsat_cores_mode="named") as solver:
for i, f in enumerate(formulae):
solver.add_assertion(f, named=f"f{i}")
sat = solver.solve([a])
self.assertFalse(sat)
def belongs_and_unique(idx):
disequal = [Or(Not(Equals(v,
output_amt[idx])),
Equals(output_party[k],
Int(party)))\
for (k, v) in filter(lambda x: x[0] != idx, output_amt.items())]
return And(Equals(output_party[idx], Int(party)), And(disequal))
def _do_cld_check(cld):
self.cldid += 1
sel = Symbol('{0}_{1}'.format(self.selv.symbol_name(), self.cldid))
cld.append(Not(sel))
# adding clause D
self.oracle.add_assertion(Or(cld))
self.ss_assumps.append(sel)
self.setd = []
st = self.oracle.solve([self.selv] + self.ss_assumps +
self.bb_assumps)
self.ss_assumps.pop() # removing clause D assumption
if st == True:
model = self.oracle.get_model()
for l in cld[:-1]:
# filtering all satisfied literals
if int(model.get_py_value(l)) > 0:
self.ss_assumps.append(l)
else:
self.setd.append(l)
else:
# clause D is unsatisfiable => all literals are backbones
self.bb_assumps.extend([Not(l) for l in cld[:-1]])
# deactivating clause D
self.oracle.add_assertion(Not(sel))
def simple_checker_problem():
theory = Or(
And(LE(Symbol("x", REAL), Real(0.5)), LE(Symbol("y", REAL), Real(0.5))),
And(GT(Symbol("x", REAL), Real(0.5)), GT(Symbol("y", REAL), Real(0.5)))
)
return xy_domain(), theory, "simple_checker"
def generate_program_specification(binary_path):
dir_list = [f for f in os.listdir(binary_path) if not os.path.isfile(os.path.join(binary_path, f))]
expected_output_list = values.LIST_TEST_OUTPUT
test_count = len(expected_output_list)
max_skip_index = (test_count * 2) - 1
program_specification = None
for dir_name in dir_list:
if "klee-out-" not in dir_name:
continue
dir_path = os.path.join(binary_path, dir_name)
klee_index = int(dir_name.split("-")[-1])
# if klee_index <= max_skip_index:
# continue
file_list = [f for f in os.listdir(dir_path) if os.path.isfile(os.path.join(dir_path, f))]
for file_name in file_list:
if ".smt2" in file_name:
file_path = os.path.join(dir_path, file_name)
path_condition = extractor.extract_formula_from_file(file_path)
model_path = generate_model(path_condition)
var_list = list(model_path.keys())
count = 0
for var in var_list:
if "obs!" in var:
count = count + 1
if count == 0:
continue
if program_specification is None:
program_specification = path_condition
else:
program_specification = Or(program_specification, path_condition)
return program_specification
def graph_to_tree(graph: Graph,
constant: float = 1.0,
return_map=False,
n_bbox=1):
edges, nodes = list(graph.edges), list(graph.nodes)
n = len(nodes)
node_map = {}
for label in range(n):
symbol = Symbol("x_{}".format(label), REAL)
if n_bbox:
node_map[label] = TNode(label=label, symbol=symbol, n_bbox=n_bbox)
else:
node_map[label] = TNode(label=label, symbol=symbol)
for u, v in edges:
u, v = min(u, v), max(u, v) # u -> v
parent = node_map[u]
child = node_map[v]
formula = Or(parent.symbol + Real(constant) <= child.symbol,
parent.symbol + Real(-constant) >= child.symbol)
edge = TEdge(parent=parent, child=child, formula=formula)
parent.add_edge(edge)
if return_map:
return node_map[0], node_map
return node_map[0]
def get_mask(self, var_name):
""" Returns the bitmask needed to ignore the additional unused
bits used to encode the counter var_name.
"""
# minimum number of bits to represent max_value
assert var_name in self.vars2bound
max_value = self.vars2bound[var_name]
bitsize = CounterEnc._get_bitsize(max_value)
# construct the bitmask: we do NOT want all the models
i = max_value + 1
mask = FALSE()
max_value_with_bit = int(math.pow(2, bitsize)) - 1
# print "Maximum value %d" % max_value
# print "Number of bits %d" % bitsize
# print "max_repr_value %d" % max_value_with_bit
while i <= max_value_with_bit:
single_val = self.eq_val(var_name, i, True)
mask = Or(mask, single_val)
i = i + 1
assert (mask != None)
mask = Not(mask)
# TODO: get a compact representation using BDDs
if (self.use_bdds):
bdd_mask = self.bdd_converter.convert(mask)
mask = self.bdd_converter.back(bdd_mask)
return mask
def smart_walk_not(self, formula):
if formula in self.subs:
# Smarties contains a string.
# In the future, we could allow for arbitrary function calls
self.write(self.subs[formula])
else:
arg = formula.arg(0)
if arg.is_iff():
arg = self.get_iff(arg)
if arg.is_exists():
argn = ForAll(arg.quantifier_vars(), Not(arg.arg(0)))
return self.walk(argn)
elif arg.is_forall():
argn = Exists(arg.quantifier_vars(), Not(arg.arg(0)))
return self.walk(argn)
elif arg.is_and():
args = [Not(a) for a in arg.args()]
argn = Or(args)
return self.walk(argn)
elif arg.is_or():
args = [Not(a) for a in arg.args()]
argn = And(args)
return self.walk(argn)
elif arg.is_not():
return self.walk(arg.arg(0))
else:
if (arg.is_not()):
assert (0)
return HRPrinter.super(self, formula)
def get_prepared_solver(self, logic, solver_name=None):
"""Returns a solver initialized with the sudoku constraints and a
matrix of SMT variables, each representing a cell of the game.
"""
sq_size = self.size**2
ty = self.get_type()
var_table = [[FreshSymbol(ty) for _ in range(sq_size)]
for _ in range(sq_size)]
solver = Solver(logic=logic, name=solver_name)
# Sudoku constraints
# all variables are positive and lower or equal to than sq_size
for row in var_table:
for var in row:
solver.add_assertion(Or([Equals(var, self.const(i))
for i in range(1, sq_size + 1)]))
# each row and each column contains all different numbers
for i in range(sq_size):
solver.add_assertion(AllDifferent(var_table[i]))
solver.add_assertion(AllDifferent([x[i] for x in var_table]))
# each square contains all different numbers
for sx in range(self.size):
for sy in range(self.size):
square = [var_table[i + sx * self.size][j + sy * self.size]
for i in range(self.size) for j in range(self.size)]
solver.add_assertion(AllDifferent(square))
return solver, var_table
def flip_negated_literals_cnf(f):
"""
Removes the negated LRA/NRA literals in 'f' by pushing the negation into the
relation, while leaving the negated boolean atoms unaltered.
Returns a pysmt.FNode instance that is equivalent to 'f'.
Raises ValueError if the 'f' is not in CNF.
Parameters
----------
f : pysmt.FNode instance
"""
if is_literal(f):
if is_ra_literal(f) and f.is_not():
return flip_ra_atom(f.args()[0])
else:
return f
elif f.is_or():
return Or([flip_negated_literals_cnf(l) for l in f.args()])
elif f.is_and():
return And([flip_negated_literals_cnf(c) for c in f.args()])
else:
raise ValueError("Formula not in CNF {}".format(f))
def test_int(self):
p, q = Symbol("p", INT), Symbol("q", INT)
f = Or(Equals(Times(p, Int(5)), Minus(p, q)), LT(p, q),
LE(Int(6), Int(1)))
f_string = self.print_to_string(f)
self.assertEqual(f_string, "(or (= (* p 5) (- p q)) (< p q) (<= 6 1))")
def test_from_formula(self):
x, y = Symbol("x"), Symbol("y")
f = And(x, Or(y, x))
script = smtlibscript_from_formula(f)
self.assertIsNotNone(script)
outstream = cStringIO()
script.serialize(outstream)
output = outstream.getvalue()
self.assertIn("(set-logic ", output)
self.assertIn("(declare-fun x () Bool)", output)
self.assertIn("(declare-fun y () Bool)", output)
self.assertIn("(check-sat)", output)
# Use custom logic (as str)
script2 = smtlibscript_from_formula(f, logic="BOOL")
outstream = cStringIO()
script2.serialize(outstream)
output = outstream.getvalue()
self.assertIn("(set-logic BOOL)", output)
# Use custom logic (as Logic obj)
script3 = smtlibscript_from_formula(f, logic=QF_UFLIRA)
outstream = cStringIO()
script3.serialize(outstream)
output = outstream.getvalue()
self.assertIn("(set-logic QF_UFLIRA)", output)
# Custom logic must be a Logic or Str
with self.assertRaises(UndefinedLogicError):
smtlibscript_from_formula(f, logic=4)
def test_solving_under_assumption_theory(self):
x = Symbol("x", REAL)
y = Symbol("y", REAL)
v1 = GT(x, Real(10))
v2 = LE(y, Real(2))
xor = Or(And(v1, Not(v2)), And(Not(v1), v2))
for name in get_env().factory.all_solvers(logic=QF_LRA):
with Solver(name=name) as solver:
solver.add_assertion(xor)
res1 = solver.solve(assumptions=[v1, Not(v2)])
model1 = solver.get_model()
res2 = solver.solve(assumptions=[Not(v1), v2])
model2 = solver.get_model()
res3 = solver.solve(assumptions=[v1, v2])
self.assertTrue(res1)
self.assertTrue(res2)
self.assertFalse(res3)
self.assertEqual(model1.get_value(v1), TRUE())
self.assertEqual(model1.get_value(v2), FALSE())
self.assertEqual(model2.get_value(v1), FALSE())
self.assertEqual(model2.get_value(v2), TRUE())
def test_or_flattening(self):
x,y,z = (Symbol(name) for name in "xyz")
f1 = Or(x, y, z)
f2 = Or(x, Or(y, z))
self.assertEqual(f2.simplify(), f1)
def test_trivial_true_or(self):
x,y,z = (Symbol(name) for name in "xyz")
f = Or(x, y, z, Not(x))
self.assertEqual(f.simplify(), TRUE())
def test_bool_dag(self):
p = Symbol("p", INT)
x = Symbol("x")
f = Or(x, GT(p, Int(0)), And(x, x))
bool_dag = f.size(SizeOracle.MEASURE_BOOL_DAG)
self.assertEqual(bool_dag, 4)
