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 test_plus_negatives(self):
r0 = Symbol("r0", REAL)
r1 = Symbol("r1", REAL)
p_1 = Real(1)
m_1 = Real(-1)
p_2 = Real(2)
m_4 = Real(-4)
# 4 * r0 + (-1) * r1 + 2 - 4
neg_r1 = Times(m_1, r1)
m_4_r0 = Times(Real(4), r0)
expr = Plus(m_4_r0, neg_r1, p_2, m_4)
res = expr.simplify()
self.assertValid(Equals(expr, res))
stack = [res]
while stack:
curr = stack.pop()
if curr.is_plus():
stack.extend(curr.args())
elif curr.is_minus():
stack.extend(curr.args())
elif curr.is_times():
stack.extend(curr.args())
elif curr.is_constant():
self.assertNotEqual(curr, m_1)
self.assertNotEqual(curr, p_1)
elif not curr.is_symbol():
# unexpected expression type.
self.assertTrue(False)
def test_constant(self):
b1 = Bool(True)
b2 = Bool(False)
r1 = Real(5.5)
r2 = Real(5)
r3 = Real(-5.5)
i1 = Int(4)
i2 = Int(-4)
b1_string = self.print_to_string(b1)
b2_string = self.print_to_string(b2)
self.assertEqual(b1_string, "true")
self.assertEqual(b2_string, "false")
r1_string = self.print_to_string(r1)
r2_string = self.print_to_string(r2)
r3_string = self.print_to_string(r3)
self.assertEqual(r1_string, "(/ 11 2)")
self.assertEqual(r2_string, "5.0")
self.assertEqual(r3_string, "(- (/ 11 2))")
i1_string = self.print_to_string(i1)
i2_string = self.print_to_string(i2)
self.assertEqual(i1_string, "4")
self.assertEqual(i2_string, "(- 4)")
def test_get_strict_formula(self):
smtlib_single = """
(set-logic UF_LIRA)
(declare-fun x () Bool)
(declare-fun y () Bool)
(declare-fun r () Real)
(assert (> r 0.0))
(assert x)
(check-sat)
"""
smtlib_double = smtlib_single + """
(assert (not y))
(check-sat)
"""
r = Symbol("r", REAL)
x, y = Symbol("x"), Symbol("y")
target_one = And(GT(r, Real(0)), x)
target_two = And(GT(r, Real(0)), x, Not(y))
stream_in = cStringIO(smtlib_single)
f = get_formula(stream_in)
self.assertEqual(f, target_one)
stream_in = cStringIO(smtlib_double)
f = get_formula(stream_in)
self.assertEqual(f, target_two)
stream_in = cStringIO(smtlib_double)
with self.assertRaises(PysmtValueError):
f = get_formula_strict(stream_in)
def sanity_b1_r0():
domain = Domain.make(["a"])
a, = domain.get_symbols()
support = TRUE()
weight = Ite(a, Real(0.3), Real(0.7))
queries = [a, ~a]
return Density(domain, support, weight, queries)
def create_smt_formula(data, labels, dim, n_weights):
weights = []
biases = []
weight_symbols = [Symbol('weight_{}'.format(i), REAL) for i in range(n_weights[0])]
weight_symbols2 = Symbol('weight_out', REAL)
weights.append(weight_symbols)
weights.append([weight_symbols2])
bias_symbol1 = Symbol('bias_{}'.format(1), REAL)
bias_symbol2 = Symbol('bias_{}'.format(2), REAL)
biases.append([bias_symbol1])
biases.append([bias_symbol2])
layer_domains = []
layer_input = data
for i in range(len(layer_input)): # loop over data
# \sum <w_ji, x_i> + b_i
g = len(weight_symbols)//2
# Layer 1
weight_input1_i = Plus([Times(w_i, Real(int(x_j)))
for w_i, x_j in zip(weight_symbols, layer_input[i])])
prod_bias1_i = Plus(weight_input1_i, bias_symbol1)
# Layer 2
weight_input2_i = Plus(Times(prod_bias1_i, weight_symbols2))
prod_bias2_i = Plus(weight_input2_i, bias_symbol2)
# output
weight_output = prod_bias2_i
layer_domain = Equals(weight_output, Real(labels[i]))
layer_domains.append(layer_domain)
network_domain = And(x for x in layer_domains)
dnn_problem = network_domain
return dnn_problem, weights, biases
def get_coefficients(atom: FNode):
"""
obtain coefficient of variable x in atom of form a * x + b * y + const
note that when there is a * x + b * x, simplify() doesn't do multiplication
but still here we return (a + b)
:param atom: FNode, formula
:param x: FNode, symbol of variable
:return: dict with keys as variable symbol and values as coefficient in atom
"""
variables = list(get_real_variables(atom))
coefficients = defaultdict(int)
if len(variables) == 0:
return coefficients
const = get_constants(atom)
atom = simplify(Plus(atom, -const))
sub_dict = dict().fromkeys(variables, Real(0))
for i in range(len(variables)):
sub_dict[variables[i]] = Real(1)
coefficient = simplify(atom.substitute(sub_dict))
coefficients[variables[i]] = coefficient
sub_dict[variables[i]] = Real(0)
return coefficients
def operator_to_bound(self, inequality: LinearInequality, var_name: str):
result = Real(inequality.b())
for other in inequality.variables:
if other != var_name:
result += Symbol(other,
REAL) * Real(-inequality.coefficient(other))
return simplify(result * Real(1 / inequality.coefficient(var_name)))
def __init__(self, expression, aliases={}):
"""Default constructor.
Takes as input a pysmt formula representing a linear inequality and
a dictionary of aliases to be substituted before the parsing.
Args:
expression (FNode): The pysmt formula representing the inequality.
aliases (dict {FNode : FNode}): The dictionary containing the aliases definitions.
Raises:
WMIParsingException: If the expression is not an inequality or the polynomial has degree more than 1.
"""
if not (expression.is_le() or expression.is_lt()):
raise WMIParsingException(WMIParsingException.NOT_AN_INEQUALITY, expression)
left, right = expression.args()
if right.is_real_constant():
# Polynomial OP Constant
self._parse_expression(left, right, False, aliases)
elif left.is_real_constant():
# Constant OP Polynomial
self._parse_expression(right, left, True, aliases)
else:
# Polynomial1 OP Polynomial2 converted into Polynomial1 - Polynomial2 OP 0
self._parse_expression(Plus(left,Times(Real(-1),right)),Real(0),
False, aliases)
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 test_reals(self):
f = And(LT(Symbol("x", REAL), Real(2)), LE(Symbol("x", REAL), Real(3)))
for n in self.all_solvers:
with Solver(name=n, logic=QF_UFLRA) as s:
s.add_assertion(f)
res = s.solve()
self.assertTrue(res)
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_div_by_0(self):
varA = Symbol('A', REAL)
varB = Symbol('B', REAL)
f = And(Equals(varA, varB),
Not(Equals(Div(varA, Real(0)), Div(varB, Real(0)))))
self.assertUnsat(f)
def to_smt(self):
keys = {
key: Times(Symbol(n, REAL)
for n in key) if key != CONST_KEY else Real(1.0)
for key in self.poly_dict.keys()
}
return Plus(keys[key] * Real(value) if value != 1 else keys[key]
for key, value in self.poly_dict.items())
def _real_example(self, qe):
# Real Example
r, s = Symbol("r", REAL), Symbol("s", REAL)
f = ForAll([r], Implies(LT(Real(0), r), LT(s, r)))
qf = qe.eliminate_quantifiers(f).simplify()
self.assertEqual(qf, LE(s, Real(0)))
def dot(self, num_list, pysmt_list):
assert (len(num_list) == len(pysmt_list))
res = Real(0)
for n in range(len(num_list)):
nreal = Real(float(num_list[n]))
prod = Times(pysmt_list[n], nreal)
res = Plus(res, prod)
return res
def regularize(self, l=0.5):
w_reg_list = []
for i, (weight, _) in self.net_formula.items():
# print(i)
w_reg_list.append(Plus([Pow(w, Real(2)) for w_r in weight for w in w_r]))
# print(w_reg_list[-1])
regularize = And([And(GE(w, Real(-l)), LT(w, Real(l))) for w in w_reg_list])
return regularize
def run_rcwmi(density,
n_bins,
complits,
maxiters,
rand_gen,
log_path,
cache=True,
nproc=None):
if nproc is None:
nproc = 1
#log_path = join(output_folder, "comp_log.json")
if not isfile(log_path):
print("Running RCWMI")
print(f"N. compensating literals: {complits}")
print(f"Max. iterations: {maxiters}")
print(f"N. processes: {nproc}")
# create bin queries
debug_queries = []
xvals = {}
for xvar in density.domain.get_real_symbols():
x = xvar.symbol_name()
low, up = density.domain.var_domains[x]
slices = [(i / n_bins) * (up - low) + low
for i in range(0, n_bins + 1)]
xvals[x] = slices[:-1]
for i in range(len(slices) - 1):
l, u = slices[i], slices[i + 1]
debug_queries.append(LE(Real(l), xvar))
debug_queries.append(LE(xvar, Real(u)))
t0 = time.perf_counter()
rcwmi = RCWMI(density.support,
density.weight,
n_comp_lits=complits,
rand_gen=rand_gen,
max_compensate_iters=maxiters,
log_path=log_path,
debug_queries=debug_queries,
n_processes=nproc)
t1 = time.perf_counter()
# adding xvals and runtime to the log
with open(log_path, 'r') as f:
log = json.load(f)
log['runtime'] = t1 - t0
log['xvals'] = xvals
with open(log_path, 'w') as f:
json.dump(log, f)
else:
print(f"Found {log_path}")
def test_msat_back_not_identical(self):
msat = Solver(name="msat", logic=QF_UFLIRA)
r, s = FreshSymbol(REAL), FreshSymbol(REAL)
# r + 1 > s + 1
f = GT(Plus(r, Real(1)), Plus(s, Real(1)))
term = msat.converter.convert(f)
res = msat.converter.back(term)
self.assertFalse(f == res)
def ex1_b2_r2():
domain = Domain.make(["a", "b"], ["x", "y"], [(0, 1), (0, 1)])
a, b, x, y = domain.get_symbols(domain.variables)
support = (a | b) & (~a | ~b) & (x >= 0.0) & (x <= y) & (y <= 1.0)
weight = Ite(a, Real(0.6), Real(0.4)) * Ite(b, Real(0.8), Real(0.2))\
* (Ite(x >= Real(0.5), Real(0.5) * x + Real(0.1) * y, Real(0.1) * x + Real(0.7) * y))
return Density(domain, support, weight, [x <= y / 2])
def test_constant(self):
b1 = Bool(True)
b2 = Bool(False)
r1 = Real(5.5)
r2 = Real(5)
r3 = Real(-5.5)
i1 = Int(4)
i2 = Int(-4)
self.assertEqual(b1.to_smtlib(daggify=True), "true")
self.assertEqual(b2.to_smtlib(daggify=True), "false")
self.assertEqual(r1.to_smtlib(daggify=True), "(/ 11 2)")
self.assertEqual(r2.to_smtlib(daggify=True), "5.0")
self.assertEqual(r3.to_smtlib(daggify=True), "(- (/ 11 2))")
self.assertEqual(i1.to_smtlib(daggify=True), "4")
self.assertEqual(i2.to_smtlib(daggify=True), "(- 4)")
self.assertEqual(b1.to_smtlib(daggify=False), "true")
self.assertEqual(b2.to_smtlib(daggify=False), "false")
self.assertEqual(r1.to_smtlib(daggify=False), "(/ 11 2)")
self.assertEqual(r2.to_smtlib(daggify=False), "5.0")
self.assertEqual(r3.to_smtlib(daggify=False), "(- (/ 11 2))")
self.assertEqual(i1.to_smtlib(daggify=False), "4")
self.assertEqual(i2.to_smtlib(daggify=False), "(- 4)")
def test_substitution_term(self):
x, y = FreshSymbol(REAL), FreshSymbol(REAL)
# y = 0 /\ Forall x. x > 3
f = And(Equals(y, Real(0)), ForAll([x], GT(x, Real(3))))
subs = {GT(x, Real(3)): TRUE()}
f_subs = substitute(f, subs)
# Since 'x' is quantified, we cannot replace the term
# therefore the substitution does not yield any result.
self.assertEqual(f_subs, f)
def to_weight_function(self):
if self.is_leaf():
return Real(self.weight)
else:
if self.split_variable.symbol_type() == BOOL:
condition = self.split_variable
else:
condition = LE(self.split_variable, Real(self.split_value))
return Ite(condition, self.pos.to_weight_function(),
self.neg.to_weight_function())
def constructRewardMatrix(intents, tuples, matches): rewardMatrix = dict() for intent in intents: rewardMatrix[intent] = dict() for tup in tuples: if (intent, tup) in matches: rewardMatrix[intent][tup] = Real(1) else: rewardMatrix[intent][tup] = Real(0) return rewardMatrix
def test_plot_xor():
domain = Domain.make(["a", "b"], ["x", "y"], [(0, 1), (0, 1)])
a, b, x, y = domain.get_symbols()
formula = ((x * -2.539851974031258e-15 + y * 3.539312736703863e-15 <= Real(0.0)) | ~a | ~b) \
& (a | b) \
& (Real(0.0) < x * -2.539851974031258e-15 + y * 3.539312736703863e-15)
with TemporaryFile(suffix=".png") as filename:
plot_formula(filename, domain, formula)
image = Image.open(filename)
assert image.getpixel((900, 900)) == image.getpixel((300, 300))
def test_sum_all_negatives(self):
r0 = Symbol("r0", REAL)
r1 = Symbol("r1", REAL)
m_1 = Real(-1)
# -4 * r0 + (-1) * r1
neg_r1 = Times(m_1, r1)
m_4_r0 = Times(Real(-4), r0)
expr = Plus(m_4_r0, neg_r1)
res = expr.simplify()
self.assertValid(Equals(expr, res))
def ex_jonathan():
domain = Domain.make(["f0", "d0"], ["r0"], [(10, 45)])
f0, d0 = domain.get_bool_symbols()
r0, = domain.get_real_symbols()
support = ((f0 & (((d0 | ~d0) & ~(r0 <= 35)) | ((r0 <= 35) & (~d0))))
| (~f0 & (d0 & (r0 <= 35)))) & domain.get_bounds()
weight_function = Ite(f0, Real(0.0001), Real(0.00001)) * \
Ite(d0, (r0/10)-1, 8-(r0/10)) * \
Ite(r0 <= 35, -0.001*(r0-27)*(r0-27)+0.3, -0.001*(r0-27)*(r0-27)+0.3)
return Density(domain, support, weight_function, queries=[d0])
def bounds_to_SMT(self):
formula = []
for var in self.bounds:
if var.symbol_type() == REAL:
lower, upper = self.bounds[var]
formula.append(And(LE(Real(lower), var), LE(var, Real(upper))))
elif self.bounds[var] is not None:
bool_bound = var if self.bounds[var] else Not(var)
formula.append(bool_bound)
return And(formula)
def hist_to_piecewise_constant(var, breaks, ys):
assert (len(breaks) == len(ys)), "dimensions mismatch"
assert(all(breaks[i-1] < breaks[i] for i in range(1,len(breaks)))),\
"bin bounds should be sorted"
else_branch = Real(0)
for i in range(1, len(breaks)):
assert (breaks[i - 1] < breaks[i])
interval = And(LE(Real(breaks[i - 1]), var), LE(var, Real(breaks[i])))
else_branch = Ite(interval, Real(ys[i], else_branch))
return else_branch
def test_clear_pop_smtlibsolver(self):
for n in self.all_solvers:
with Solver(name=n, logic=QF_LRA) as s:
x1, x2 = [Symbol(var, REAL) for var in ["x1", "x2"]]
init = LT(Plus(x1, Real(-1), x2), Real(Fraction(1, 4)))
invar = TRUE()
safe = LT(Plus(x1, x2), Real(8))
invar_init = And(invar, init)
iv_imp = Implies(invar, safe)
self.assertFalse(s.is_unsat(invar_init))
self.assertFalse(s.is_valid(iv_imp))
def setUp(self) -> None:
parent_symbol = Symbol("x", REAL)
child_symbol = Symbol("y", REAL)
# y < 2x+1 or y > x - 1 or x > 2 or y > 0.1
atom0 = LE(child_symbol, Real(2) * parent_symbol + Real(1))
atom1 = LE(parent_symbol - 1, child_symbol)
atom2 = LE(Real(2), parent_symbol)
atom3 = LE(Real(0.1), child_symbol)
atom4 = LE(child_symbol, Real(0.4))
self.parent_symbol = parent_symbol
self.child_symbol = child_symbol
self.atoms = [atom0, atom1, atom2, atom3, atom4]
self.formula = Or(self.atoms[:4])