def _cap_top(self, idx, cap_max):
if cap_max is None:
return
# x_out = min(x, cap_max) or equivalently x_out = -max(-x, -cap_max)
# x_out = -xs1, xs1 = max(-x, -cap_max) or equivalently
# x_out = -xs1, xs1 = max(xs2, xs3), xs2 = -x, xs3 = -cap_max
x = self.model_output_vars[idx]
xs1 = getNewVariable("xs")
xs2 = getNewVariable("xs")
xs3 = getNewVariable("xs")
x_out = getNewVariable("xs")
constraint1 = Constraint(
"EQUALITY",
monomials=[Monomial(1.0, x_out),
Monomial(1.0, xs1)],
scalar=0) # x_out = -xs1
constraint2 = MaxConstraint(varsin=[xs2, xs3],
varout=xs1) # xs1 = max(xs2, xs3)
constraint3 = Constraint(
"EQUALITY",
monomials=[Monomial(1.0, xs2),
Monomial(1.0, x)],
scalar=0) # set xs2 = -x
constraint4 = Constraint("EQUALITY",
monomials=[Monomial(1.0, xs3)],
scalar=-cap_max) # set xs1 = -cap_max
self.constraints += [
constraint1, constraint2, constraint3, constraint4
]
self.model_output_vars[idx] = x_out
def constraint_variable_to_interval(variable, LB, UB):
p1 = Constraint(ConstraintType('GREATER'))
p1.monomials = [Monomial(1, variable)]
p1.scalar = LB # 0 #
#
p2 = Constraint(ConstraintType('LESS'))
p2.monomials = [Monomial(1, variable)]
p2.scalar = UB
return [p1, p2]
def setup_euler_constraint(self, dx_vec, dt):
for x, dx, next_x in zip(self.states.reshape(-1), dx_vec,
self.next_states.reshape(-1)):
c = Constraint(ConstraintType('EQUALITY'))
c.monomials = [
Monomial(1, x),
Monomial(dt, dx),
Monomial(-1, next_x)
]
self.euler_constraints.append(c)
def setup_euler_constraints(self):
for x, dx, next_x in zip(self.states.reshape(-1), self.dx,
self.next_states.reshape(-1)):
# next_x = x + dx*dt
c = Constraint(ConstraintType('EQUALITY'))
c.monomials = [
Monomial(1, x),
Monomial(self.dt, dx),
Monomial(-1, next_x)
]
self.constraints.append(c)
def ex1():
print("~~~~~ test 1 ~~~~~")
m = [Monomial(5, 'x'), Monomial(6, 'y')]
c = Constraint('LESS', monomials=m, scalar=5)
# 5x 6y < 5
print(c)
print(c.complement())
#
p = ConstraintProperty([c])
print(p)
print(p.complement())
def ex3():
print("~~~~~ test 3 ~~~~~")
m = [Monomial(-5, 'x'), Monomial(-6, 'y')]
c = Constraint('GREATER', monomials=m, scalar=-5)
# -5x -6y < -5
print(c)
print(c.complement())
#
p = ConstraintProperty([c])
print(p)
print(p.complement())
def assert_init(self, init_set):
"""
assert that states are in init set
"""
for k in init_set.keys():
self.input_vars.append(k)
LB = init_set[k][0]
UB = init_set[k][1]
cLB = Constraint('GREATER_EQ',
monomials=[Monomial(1., k)],
scalar=LB)
cUB = Constraint('LESS_EQ', monomials=[Monomial(1., k)], scalar=UB)
self.constraints += [cLB, cUB]
def ex4():
print("~~~~~ test 4 ~~~~~")
m1 = [Monomial(-5, 'x'), Monomial(-6, 'y')]
c1 = Constraint('GREATER', monomials=m1, scalar=-5)
# -5x -6y < -5
#
m2 = [Monomial(-4, 'x'), Monomial(-5, 'y')]
c2 = Constraint('GREATER', monomials=m2, scalar=-4)
# -4x -5y < -4
#
p = ConstraintProperty([c1, c2])
print(p)
print(p.complement())
def equality_constraint(varsin, varsout):
"""
If you need a list of scalar constraints instead of a single matrix constraint.
"""
assert (len(varsin) == len(varsout))
if len(varsin) > 1:
mc = matrix_equality_constraint(varsin, varsout)
return matrix_to_scalar(mc)
else:
mono1 = Monomial(1, varsin[0][0])
mono2 = Monomial(-1, varsout[0][0])
return Constraint(ConstraintType('EQUALITY'),
monomials=[mono1, mono2],
scalar=0)
def read_inequalities(self):
for i in range(self.n_ineq):
left_var = self.f['/ineq/varleft%d' % (i + 1)][()][0]
rite_var = self.f['/ineq/varright%d' % (i + 1)][()][0]
for v in [left_var, rite_var]:
if v not in self.var_dict.keys():
self.var_dict[v] = getNewVariable('xd')
# add lvar <= rvar
monomial_list = [
Monomial(1, self.var_dict[left_var]),
Monomial(-1, self.var_dict[rite_var])
]
self.ineq_list.append(
Constraint(ConstraintType('LESS_EQ'), monomial_list, 0))
def infeasible_problem_relu():
c1 = ReluConstraint(varin="x", varout="y")
c2 = Constraint("LESS_EQ", monomials=[Monomial(1., "y")], scalar=-5)
solver = GurobiPyWrapper()
solver.assert_constraints([c1, c2])
result, vals, stats = solver.check_sat()
print("result is:", result)
def ex2():
print("~~~~~ test 2 ~~~~~")
m1 = [Monomial(5, 'x'), Monomial(6, 'y')]
c1 = Constraint('LESS', monomials=m1, scalar=5)
# 5x 6y < 5
print(c1)
print(c1.complement())
#
m2 = [Monomial(4, 'x'), Monomial(5, 'y')]
c2 = Constraint('LESS', monomials=m2, scalar=4)
# 4x 5y < 4
print(c2)
print(c2.complement())
#
p = ConstraintProperty([c1, c2])
print(p)
print(p.complement())
def __init__(self):
self.control_inputs = ['T']
self.states = np.array(['theta', 'theta_dot'], dtype=object)
self.dx = ['theta_dot', 'theta_double_dot']
# the constraints that define the dx variables.
# "theta_double_dot = T + sin(theta) - 0.2*theta_dot"
self.dx_constraints = [
NLConstraint('EQUALITY', out='v1', fun="sin", indep_var="theta"),
Constraint('EQUALITY',
monomials=[
Monomial(1.0, "T"),
Monomial(1.0, "v1"),
Monomial(-0.2, "theta_dot"),
Monomial(-1.0, "theta_double_dot")
],
scalar=0)
]
def popluate_graph_mateq(self, G, eq):
A = eq.A
x = eq.x
for i in range(A.shape[0]):
new_eq = Constraint("EQUALITY", monomials=[])
for j in range(A.shape[1]):
Aij = A[i][j]
if Aij != 0.:
new_eq.monomials.append(Monomial(coeff=Aij, var=x[j]))
G = self.populate_graph_eq(G, new_eq)
return G
def feasible_problem():
c1 = Constraint('EQUALITY',
monomials=[Monomial(1., "theta@0"),
Monomial(-2., "x@1")],
scalar=1.3)
c2 = MatrixConstraint('LESS_EQ',
A=np.random.rand(3, 3),
x=["x", "theta", "x2"],
b=np.random.rand(3, ))
# NOTE: FOR GUROBI INTERFACE, variable stringnames in x must be in a list NOT a numpy array, inside MatrixConstraint
c3 = MaxConstraint(varsin=['t', 'b'], varout="theta")
c4 = ReluConstraint(varin="bob", varout="alice")
solver = GurobiPyWrapper()
solver.assert_init({'theta': [7, 9], 'bob': [-10, 1]})
solver.assert_constraints([c1, c2, c3, c4])
result, vals, stats = solver.check_sat()
def _turn_max_to_relu(self):
new_constraints = []
for c in self.constraints:
if isinstance(c, MaxConstraint):
# varnew1 - varin1 + varin2 = 0
# varnew2 = relu(varnew1)
# varout - varnew2 - varin2 = 0
var1in = c.var1in
var2in = c.var2in
varout = c.varout
varnew1 = getNewVariable("max2relu")
varnew2 = getNewVariable("max2relu")
cnew1 = Constraint("EQUALITY")
cnew1.monomials = [
Monomial(1.0, varnew1),
Monomial(-1.0, var1in),
Monomial(1.0, var2in)
]
cnew2 = ReluConstraint(varin=varnew1, varout=varnew2)
cnew3 = Constraint("EQUALITY")
cnew3.monomials = [
Monomial(1.0, varout),
Monomial(-1.0, var2in),
Monomial(-1.0, varnew2)
]
new_constraints.extend([cnew1, cnew2, cnew3])
else:
new_constraints.append(c)
self.constraints = new_constraints
def read_equations(self):
for i in range(self.n_eq):
vars = self.f['/eq/vars%d' % (i + 1)][()]
for v in vars:
if v not in self.var_dict.keys():
self.var_dict[v] = getNewVariable('xd')
coeffs = self.f['/eq/coeffs%d' % (i + 1)][()].astype(np.float)
b = self.f['/eq/scalar%d' % (i + 1)][()].astype(np.float)[0]
monomial_list = [
Monomial(c, self.var_dict[v]) for (c, v) in zip(coeffs, vars)
]
self.eq_list.append(
Constraint(ConstraintType('EQUALITY'), monomial_list, b))
def _cap_bottom(self, idx, cap_min):
if cap_min is None:
return
# x_out = max(x, cap_min)
x = self.model_output_vars[idx]
xs1 = getNewVariable("xs")
x_out = getNewVariable("xs")
constraint1 = Constraint("EQUALITY",
monomials=[Monomial(1.0, xs1)],
scalar=cap_min) # set xs1 = cap_min
constraint2 = MaxConstraint(varsin=[x, xs1],
varout=x_out) # x_out = max(x, xs1)
self.constraints += [constraint1, constraint2]
self.model_output_vars[idx] = x_out
def cnf_conversion_helper(self, constraint):
"""
Take a constraint of the form
5x + 6y -5 R 0 and turns it into
Y == 5x + 6y - 5
(for later to assert: Y >=0 or max(Y, somethingelse) >= 0)
"""
# turn into >= inequality: -5x -6y <= -5 --> 5x + 6y >= 5
geq_comp = constraint.get_geq()
# define new var: Y = 5x + 6y - 5
new_var_constraint = copy.deepcopy(geq_comp)
new_var_constraint.type = ConstraintType('EQUALITY')
Y = self.get_new_var()
new_var_constraint.monomials += [Monomial(
-1, Y)] # -a + 5x + 6y == 5 -> 5x + 6y -5 == a
return [new_var_constraint, Y]
def ex5():
print("~~~~~ test 5 ~~~~~")
m1 = [Monomial(-5, 'x'), Monomial(-6, 'y')]
c1 = Constraint('GREATER', monomials=m1, scalar=-5)
# -5x -6y < -5
#
m2 = [Monomial(-4, 'x'), Monomial(-5, 'y')]
c2 = Constraint('GREATER', monomials=m2, scalar=-4)
# -4x -5y < -4
m3 = [Monomial(-3, 'x'), Monomial(-4, 'y')]
c3 = Constraint('GREATER', monomials=m3, scalar=-3)
# -3x -4y < -3
#
p = ConstraintProperty([c1, c2, c3])
print(p)
print(p.complement())
def linear_plant_test():
"""
linear plant test
# phi
y = x
# phi hat
OA: x - 1 <= y <= x + 1
"""
print("~~~~~~~~~~~lin plant test~~~~~~~~~~~~~~~\n")
# phi
x = 'x'
y = 'y'
phi = [Constraint("EQUALITY",
[Monomial(1, x), Monomial(-1, y)], 0)] # x - y == 0
# phi hat
c1 = Constraint("LESS_EQ",
[Monomial(1, x), Monomial(-1, y)], 1) # x - y <= 1
c2 = Constraint("LESS_EQ",
[Monomial(-1, x), Monomial(1, y)], 1) # y - x <= 1
phi_hat = [c1, c2]
# check!
oav = OverapproxVerifier(phi, phi_hat)
oav.create_smtlib_script(
) # should write to file that can be checked with: https://cvc4.github.io/app/
def infeasible_problem():
c1 = Constraint('LESS_EQ', monomials=[Monomial(1., "x")], scalar=5)
c2 = Constraint('GREATER_EQ', monomials=[Monomial(1., "x")], scalar=10)
solver = GurobiPyWrapper()
solver.assert_constraints([c1, c2])
result, vals, stats = solver.check_sat()
def test_marabou_interface(alpha,
prop_desc,
n_invar,
with_relu=False,
with_max=False):
# create controller object, this is just a place holder. I will modify the object later.
model = load_model(
"../OverApprox/models/single_pend_nn_controller_lqr_data.h5")
controller = KerasController(keras_model=model)
# rewrite to make a simple controller that is always equal to alpha*x
controller.control_outputs = [['c']]
controller.state_inputs = [['xc']]
fake_constraint = []
if with_relu:
alpha_times_x = 'var1'
monomial_list = [
Monomial(alpha, controller.state_inputs[0][0]),
Monomial(-1, alpha_times_x)
]
fake_constraint.append(
Constraint(ConstraintType('EQUALITY'), monomial_list, 0.0))
relu_constraint = [
ReluConstraint(varin=alpha_times_x,
varout=controller.control_outputs[0][0])
]
controller.constraints = relu_constraint + fake_constraint
controller.relus = relu_constraint
elif with_max:
alpha_times_x = 'var1'
monomial_list = [
Monomial(alpha, controller.state_inputs[0][0]),
Monomial(-1, alpha_times_x)
]
fake_constraint.append(
Constraint(ConstraintType('EQUALITY'), monomial_list, 0.0))
max_second_arg = 'var2'
fake_constraint.append(
Constraint(ConstraintType('EQUALITY'),
[Monomial(1, max_second_arg)], -1 / 2))
max_constraint = [
MaxConstraint(varsin=[alpha_times_x, max_second_arg],
varout=controller.control_outputs[0][0])
]
controller.constraints = max_constraint + fake_constraint
controller.relus = []
else:
monomial_list = [
Monomial(-1, controller.control_outputs[0][0]),
Monomial(alpha, controller.state_inputs[0][0])
]
fake_constraint = [
Constraint(ConstraintType('EQUALITY'), monomial_list, 0.0)
]
controller.constraints = fake_constraint
controller.relus = []
# create overt dynamics objects. this is just a place holder. I will modify the object later.
overt_obj = OvertConstraint(
"../OverApprox/models/single_pend_acceleration_overt.h5")
# rewrite to make a simple controller that is always equal to x
overt_obj.control_vars = [['cd']]
overt_obj.state_vars = [['x']]
overt_obj.output_vars = [['dx']]
monomial_list2 = [
Monomial(1, overt_obj.control_vars[0][0]),
Monomial(-1, overt_obj.output_vars[0][0])
]
fake_constraint2 = [
Constraint(ConstraintType('EQUALITY'), monomial_list2, 0.5)
]
overt_obj.constraints = fake_constraint2
simple_dynamics = Dynamics(np.array(['x']), np.array(['cd']))
next_states = simple_dynamics.next_states.reshape(1, )
# x_next = x + dt*dx
dt = 1
c1 = Constraint(ConstraintType('EQUALITY'))
c1.monomials = [
Monomial(1, overt_obj.state_vars[0][0]),
Monomial(dt, overt_obj.output_vars[0][0]),
Monomial(-1, next_states[0])
]
simple_dynamics.constraints = [c1] + overt_obj.constraints
print(len(simple_dynamics.constraints))
print(len(controller.constraints))
# create transition relation using controller and dynamics
tr = TFControlledTransitionRelation(dynamics_obj=simple_dynamics,
controller_obj=controller)
# initial set
init_set = {overt_obj.state_vars[0][0]: (0., 1.)}
# build the transition system as an (S, I(S), TR) tuple
ts = TransitionSystem(states=tr.states,
initial_set=init_set,
transition_relation=tr)
# property x< 0.105, x' < 0.2
p = Constraint(ConstraintType(prop_desc["type"]))
p.monomials = [Monomial(1, overt_obj.state_vars[0][0])]
p.scalar = prop_desc["scalar"] #
prop = ConstraintProperty([p], [overt_obj.state_vars[0][0]])
# solver
solver = MarabouWrapper()
algo = BMC(ts=ts, prop=prop, solver=solver)
result, vals, stats = algo.check_invariant_until(n_invar)
return result.name
output = tf.nn.relu(tf.matmul(W1,x) + b1)
W2 = np.random.rand(1,2)
b2 = np.random.rand(1,1)
output = tf.nn.relu(tf.matmul(W2,output) + b2)
sess.run(tf.global_variables_initializer()) # actually sets Variable values to values specified
# smoosh all tf.Variables to tf.Constants, put into new graph
new_graph = smoosh_to_const(sess, output.op.name)
# create controller object with network
controller = TFController(tf_sess=tf.Session(graph=new_graph), inputNames=[x.op.name], outputName=output.op.name)
# create a super simple plant directly using constraint objects
dynamics = Dynamics(states=np.array([["x"], ["y"]]), controls=["u"], fun=np.sin)
# x' = relu(x + u) -> x + u - z = 0 , x' = relu(z)
c1 = Constraint(ConstraintType('EQUALITY'))
c1.monomials = [Monomial(1, "x"), Monomial(1,"u"), Monomial(-1,"z")]
c3 = ReluConstraint(varin="z", varout="x'")
# y' = y -> y - y' = 0
c2 = Constraint(ConstraintType('EQUALITY'))
c2.monomials = [Monomial(1,"y"), Monomial(-1, "y'")]
dynamics.constraints = [c1,c2,c3]
# create transition relation using controller and dynamics
tr = TFControlledTransitionRelation(dynamics_obj=dynamics,
controller_obj=controller)
# initial set
init_set = {"x": (1.1,2), "y": (-1,1)}
# build the transition system as an (S, I(S), TR) tuple
ts = TransitionSystem(states=tr.states, initial_set=init_set, transition_relation=tr)
import numpy as np
from dreal_interface import FormulaConverter, OverapproxVerifier
from MC_constraints import Constraint, Monomial, MaxConstraint, ReluConstraint, MatrixConstraint, NLConstraint
f = FormulaConverter()
print(f.prefix_notate("+", ["A", "B"]))
print(f.declare_const("A", "Bool"))
print(f.define_atom("A", "(< y 5)"))
print(f.negate("(< y 5)"))
c1 = Constraint('LESS_EQ', [Monomial(-6, "x"), Monomial(5, "y")], -2)
print(f.convert_Constraint(c1))
c2 = MaxConstraint(['v1', 'v2'], 'v3')
print(f.convert_MaxConstraint(c2))
c3 = ReluConstraint('p', 'q')
print(f.convert_ReluConstraint(c3))
c4 = MatrixConstraint('EQUALITY',
A=np.random.rand(2, 2),
x=np.array([['x'], ['y']], dtype='object'),
b=np.zeros((2, 1)))
print(f.convert_MatrixConstraint(c4))
c5 = NLConstraint('EQUALITY', "v1", "sin", "x")
print(f.convert_NLConstraint(c5))
# initial set
x1_init_set = (0.5, 1)
x2_init_set = (-0.5, 0.5)
init_set = {states[0]: x1_init_set, states[1]: x2_init_set}
# build the transition system as an (S, I(S), TR) tuple
ts = TransitionSystem(states=tr.states,
initial_set=init_set,
transition_relation=tr)
# solver
solver = GurobiPyWrapper() #MarabouWrapper()
prop_list = []
p1 = Constraint(ConstraintType('GREATER'))
p1.monomials = [Monomial(1, states[0])]
p1.scalar = 0.3
prop_list.append(p1)
p2 = Constraint(ConstraintType('LESS'))
p2.monomials = [Monomial(1, states[0])]
p2.scalar = 1.15
prop_list.append(p2)
# p3 = Constraint(ConstraintType('GREATER'))
# p3.monomials = [Monomial(1, states[1])]
# p3.scalar = -1.1
# prop_list.append(p3)
# #
# p4 = Constraint(ConstraintType('LESS'))
# p4.monomials = [Monomial(1, states[1])]
def convert_to_CNF(self, DNF_complements):
"""
Converts complements of constraints in DNF to CNF
using Max.
Populates self.constraint_complements.
"""
CNF_complements = []
n_clauses = len(DNF_complements)
if n_clauses == 0:
pass
elif n_clauses == 1:
# define new var: Y = 5x + 6y - 5
Y_definition, Y = self.cnf_conversion_helper(DNF_complements[0])
# we want Y >= 0
Y_ineq = Constraint(ConstraintType('GREATER_EQ'),
monomials=[Monomial(1, Y)],
scalar=0)
CNF_complements.extend([Y_definition, Y_ineq])
else: # nclauses > 1
# handle first ineq
Y_def, Y = self.cnf_conversion_helper(DNF_complements[0])
CNF_complements.append(Y_def)
# then disjunct all the complements using MaxConstraint
for c in DNF_complements[1:]:
# take complement, and turn into >= inequality
Z_def, Z = self.cnf_conversion_helper(c)
# begin disjunct train max(Z,Y) >= 0 ...
Q = self.get_new_var()
###########################################################
# changing max to be represented with Relu
YmZ = self.get_new_var()
YmZdef = Constraint('EQUALITY',
monomials=[
Monomial(1, Y),
Monomial(-1, Z),
Monomial(-1, YmZ)
],
scalar=0)
RYmZ = self.get_new_var()
RYmZdef = ReluConstraint(varin=YmZ, varout=RYmZ)
# Q = relu(Y-Z) + Z
max_constraint = Constraint('EQUALITY',
monomials=[
Monomial(1, RYmZ),
Monomial(1, Z),
Monomial(-1, Q)
],
scalar=0)
###########################################################
# max_constraint = MaxConstraint((Y,Z), Q) # version with max
# CNF_complements.extend([Z_def, max_constraint]) # version with max
############################################################
CNF_complements.extend(
[Z_def, YmZdef, RYmZdef, max_constraint])
Y = Q
# Q >= 0
geq0 = Constraint(ConstraintType('GREATER_EQ'),
monomials=[Monomial(1, Q)],
scalar=0)
CNF_complements.append(geq0)
self.constraint_complements = CNF_complements
return CNF_complements
controls = overt_obj_1.control_vars
acceleration_1 = overt_obj_1.output_vars[0]
acceleration_2 = overt_obj_2.output_vars[0]
double_pendulum_dynamics = Dynamics(np.array(states).reshape(-1, 1), np.array(controls).reshape(-1, 1))
next_states = double_pendulum_dynamics.next_states.reshape(4,)
print(states, controls, acceleration_1, acceleration_2, next_states)
dt = 0.01
# x1_next = x1 + dt*u1
c1 = Constraint(ConstraintType('EQUALITY'))
c1.monomials = [Monomial(1, theta1), Monomial(dt, theta1d), Monomial(-1, next_states[0])]
print(c1.monomials)
# x2_next = x2 + dt*u2
c2 = Constraint(ConstraintType('EQUALITY'))
c2.monomials = [Monomial(1, theta2), Monomial(dt, theta2d), Monomial(-1, next_states[1])]
print(c2.monomials)
# u1_next = u1 + dt*a1
c3 = Constraint(ConstraintType('EQUALITY'))
c3.monomials = [Monomial(1, theta1d), Monomial(dt, acceleration_1), Monomial(-1, next_states[2])]
print(c3.monomials)
# u2_next = u2 + dt*a2
c4 = Constraint(ConstraintType('EQUALITY'))
