def is_monotonic(alpha, mgr, num_features, constraint_sdd):
counterexample = [[None, None] for _ in xrange(num_features)]
for i in xrange(num_features):
beta1 = sdd.sdd_condition(i + 1, alpha, mgr)
beta2 = sdd.sdd_condition(-(i + 1), alpha, mgr)
beta3 = sdd.sdd_conjoin(beta1, beta2, mgr)
# check if f|x does not entail f|!x
gamma = sdd.sdd_conjoin(
sdd.sdd_conjoin(sdd.sdd_negate(beta2, mgr), beta1, mgr),
constraint_sdd, mgr)
model = next(models.models(gamma, sdd.sdd_manager_vtree(mgr)))
counterexample[i][0] = [v for _, v in model.items()]
if counterexample[i][0]:
counterexample[i][0][i] = 1
# check if f|!x does not entail f|x
gamma = sdd.sdd_conjoin(
sdd.sdd_conjoin(sdd.sdd_negate(beta1, mgr), beta2, mgr),
constraint_sdd, mgr)
model = next(models.models(gamma, sdd.sdd_manager_vtree(mgr)))
counterexample[i][1] = [v for _, v in model.items()]
if counterexample[i][1]:
counterexample[i][1][i] = 0
for c in counterexample:
if c[0] and c[1]:
return False, counterexample
return True, counterexample
def _primes_two(alpha, variables, cache1, cache2, pmgr, mgr):
if len(variables) == 0:
if sdd.sdd_node_is_false(alpha): return sdd.sdd_manager_false(pmgr)
if sdd.sdd_node_is_true(alpha): return sdd.sdd_manager_true(pmgr)
key = (len(variables), sdd.sdd_id(alpha))
if key in cache1:
global cache_hits
cache_hits += 1
if cache_hits % 1000 == 0: print "cache-hits-update:", cache_hits
return cache1[key]
var, remaining = variables[0], variables[1:]
alpha0 = sdd.sdd_condition(-var, alpha, mgr)
alpha1 = sdd.sdd_condition(var, alpha, mgr)
primes0 = _primes_two(alpha0, remaining, cache1, cache2, pmgr, mgr)
primes1 = _primes_two(alpha1, remaining, cache1, cache2, pmgr, mgr)
qrimes0 = _keep_imp(primes0, alpha1, remaining, cache1, cache2, pmgr, mgr)
qrimes1 = _keep_imp(primes1, alpha0, remaining, cache1, cache2, pmgr, mgr)
gamma = sdd.sdd_disjoin(qrimes0, qrimes1, pmgr)
gamma = sdd.sdd_conjoin(_sdd_unused(var, pmgr), gamma, pmgr)
kappa = sdd.sdd_conjoin(primes0, sdd.sdd_negate(qrimes0, pmgr), pmgr)
kappa = sdd.sdd_conjoin(kappa, _sdd_used_neg(var, pmgr), pmgr)
gamma = sdd.sdd_disjoin(gamma, kappa, pmgr)
kappa = sdd.sdd_conjoin(primes1, sdd.sdd_negate(qrimes1, pmgr), pmgr)
kappa = sdd.sdd_conjoin(kappa, _sdd_used_pos(var, pmgr), pmgr)
gamma = sdd.sdd_disjoin(gamma, kappa, pmgr)
cache1[key] = gamma
return gamma
def _primes_one_given_term(alpha, variables, inst, cache, cache_dummy, pmgr,
mgr):
if len(variables) == 0:
if sdd.sdd_node_is_true(alpha): return sdd.sdd_manager_true(pmgr)
if sdd.sdd_node_is_false(alpha): return sdd.sdd_manager_false(pmgr)
#add cases for true/false
key = (len(variables), sdd.sdd_id(alpha))
if key in cache:
return cache[key]
var, remaining = variables[0], variables[1:]
val, remaining_val = inst[0], inst[1:]
beta2 = sdd.sdd_forall(var, alpha, mgr)
gamma2 = _primes_one_given_term(beta2, remaining, remaining_val, cache,
cache_dummy, pmgr, mgr)
gamma9 = gamma2
pvar = 3 * (var - 1) + 1
kappa2 = sdd.sdd_manager_literal(-pvar, pmgr)
gamma2 = sdd.sdd_conjoin(gamma2, kappa2, pmgr)
if val == 0:
beta0 = sdd.sdd_condition(-var, alpha, mgr)
gamma0 = _primes_one_given_term(beta0, remaining, remaining_val, cache,
cache_dummy, pmgr, mgr)
gamma0 = sdd.sdd_conjoin(gamma0, sdd.sdd_negate(gamma9, pmgr), pmgr)
kappa0 = sdd.sdd_conjoin(sdd.sdd_manager_literal(-(pvar + 1), pmgr),
sdd.sdd_manager_literal((pvar + 2), pmgr),
pmgr)
kappa0 = sdd.sdd_conjoin(kappa0, sdd.sdd_manager_literal(pvar, pmgr),
pmgr)
gamma0 = sdd.sdd_conjoin(gamma0, kappa0, pmgr)
#gamma0 = sdd.sdd_conjoin(gamma0,sdd.sdd_negate(gamma9,pmgr),pmgr)
if val == 1:
beta1 = sdd.sdd_condition(var, alpha, mgr)
gamma1 = _primes_one_given_term(beta1, remaining, remaining_val, cache,
cache_dummy, pmgr, mgr)
gamma1 = sdd.sdd_conjoin(gamma1, sdd.sdd_negate(gamma9, pmgr), pmgr)
kappa1 = sdd.sdd_conjoin(sdd.sdd_manager_literal((pvar + 1), pmgr),
sdd.sdd_manager_literal(-(pvar + 2), pmgr),
pmgr)
kappa1 = sdd.sdd_conjoin(kappa1, sdd.sdd_manager_literal(pvar, pmgr),
pmgr)
gamma1 = sdd.sdd_conjoin(gamma1, kappa1, pmgr)
#gamma1 = sdd.sdd_conjoin(gamma1,sdd.sdd_negate(gamma9,pmgr),pmgr)
if val == 0:
gamma = sdd.sdd_disjoin(gamma0, gamma2, pmgr)
if val == 1:
gamma = sdd.sdd_disjoin(gamma1, gamma2, pmgr)
#gamma = sdd.sdd_disjoin(sdd.sdd_disjoin(gamma0, gamma1, pmgr), gamma2, pmgr)
#if len(variables) > 60:
# print len(variables), sdd.sdd_manager_count(mgr)
cache[key] = gamma
return gamma
def condition_and_minimize(alpha, mgr, num_features, inst):
for i in xrange(num_features):
if not inst[i]:
alpha = sdd.sdd_condition(-1 * (i + 1), alpha, mgr)
# After conditioning, the literals can be T or F.
# After we do global_minimize_cardinality that forces the conditioned
# literals to be F.
return sdd.sdd_global_minimize_cardinality(alpha, mgr)
def _primes_one(alpha, variables, cache, cache_dummy, pmgr, mgr):
if len(variables) == 0:
if sdd.sdd_node_is_true(alpha): return sdd.sdd_manager_true(pmgr)
if sdd.sdd_node_is_false(alpha): return sdd.sdd_manager_false(pmgr)
#add cases for true/false
key = (len(variables), sdd.sdd_id(alpha))
if key in cache:
global cache_hits
cache_hits += 1
#if cache_hits % 1000 == 0: print "cache-hits-update:", cache_hits
return cache[key]
var, remaining = variables[0], variables[1:]
beta2 = sdd.sdd_forall(var, alpha, mgr)
gamma2 = _primes_one(beta2, remaining, cache, cache_dummy, pmgr, mgr)
gamma9 = gamma2
pvar = 3 * (var - 1) + 1
kappa2 = sdd.sdd_manager_literal(-pvar, pmgr)
gamma2 = sdd.sdd_conjoin(gamma2, kappa2, pmgr)
beta0 = sdd.sdd_condition(-var, alpha, mgr)
gamma0 = _primes_one(beta0, remaining, cache, cache_dummy, pmgr, mgr)
gamma0 = sdd.sdd_conjoin(gamma0, sdd.sdd_negate(gamma9, pmgr), pmgr)
kappa0 = sdd.sdd_conjoin(sdd.sdd_manager_literal(-(pvar + 1), pmgr),
sdd.sdd_manager_literal((pvar + 2), pmgr), pmgr)
kappa0 = sdd.sdd_conjoin(kappa0, sdd.sdd_manager_literal(pvar, pmgr), pmgr)
gamma0 = sdd.sdd_conjoin(gamma0, kappa0, pmgr)
#gamma0 = sdd.sdd_conjoin(gamma0,sdd.sdd_negate(gamma9,pmgr),pmgr)
beta1 = sdd.sdd_condition(var, alpha, mgr)
gamma1 = _primes_one(beta1, remaining, cache, cache_dummy, pmgr, mgr)
gamma1 = sdd.sdd_conjoin(gamma1, sdd.sdd_negate(gamma9, pmgr), pmgr)
kappa1 = sdd.sdd_conjoin(sdd.sdd_manager_literal((pvar + 1), pmgr),
sdd.sdd_manager_literal(-(pvar + 2), pmgr), pmgr)
kappa1 = sdd.sdd_conjoin(kappa1, sdd.sdd_manager_literal(pvar, pmgr), pmgr)
gamma1 = sdd.sdd_conjoin(gamma1, kappa1, pmgr)
#gamma1 = sdd.sdd_conjoin(gamma1,sdd.sdd_negate(gamma9,pmgr),pmgr)
gamma = sdd.sdd_disjoin(gamma0, gamma1, pmgr)
gamma = sdd.sdd_disjoin(gamma, gamma2, pmgr)
cache[key] = gamma
return gamma
def least_flips(alpha, mgr, inst):
beta = alpha
for (i, element) in enumerate(inst):
literal = i + 1
if element == 0:
literal *= -1
beta = sdd.sdd_condition(literal, beta, mgr)
is_model = sdd.sdd_node_is_true(beta)
leastFlipsDict = {}
return least_flips_helper(is_model, inst, alpha, mgr, leastFlipsDict)
def is_monotone(alpha, manager):
""" A function alpha is monotone iff f|~x |= f|x for all X.
"""
result = True
var_count = sdd.sdd_manager_var_count(manager)
sdd.sdd_ref(alpha, manager)
for x in xrange(1, var_count + 1):
f_x = sdd.sdd_condition(x, alpha, manager)
sdd.sdd_ref(f_x, manager)
f_nx = sdd.sdd_condition(-x, alpha, manager)
sdd.sdd_ref(f_nx, manager)
# f|~x |= f|x iff f|~x ^ f|x == f|~x
f_both = sdd.sdd_conjoin(f_x, f_nx, manager)
if f_both != f_x:
result = False
sdd.sdd_deref(f_x, manager), sdd.sdd_deref(f_nx, manager)
if result is False: break
sdd.sdd_deref(alpha, manager)
return result
def _is_prime(prime, f, mgr):
var_count = sdd.sdd_manager_var_count(mgr)
term = prime_to_dict(prime, var_count)
for var in term:
alpha = f
for varp in term:
if varp == var: continue
lit = varp if term[varp] == 1 else -varp
alpha = sdd.sdd_condition(lit, alpha, mgr)
if sdd.sdd_node_is_true(alpha):
return False
return True
def _keep_imp(beta, alpha, variables, cache1, cache2, pmgr, mgr):
#if len(variables) == 0:
if sdd.sdd_node_is_false(beta): return sdd.sdd_manager_false(pmgr)
if sdd.sdd_node_is_false(alpha): return sdd.sdd_manager_false(pmgr)
if sdd.sdd_node_is_true(alpha): return beta
key = (len(variables), sdd.sdd_id(alpha), sdd.sdd_id(beta))
if key in cache2:
global cache_hits
cache_hits += 1
#if cache_hits % 1000 == 0: print "cache-hits-update:", cache_hits
return cache2[key]
var, remaining = variables[0], variables[1:]
pvar = 3 * (var - 1) + 1
alpha0 = sdd.sdd_condition(-var, alpha, mgr)
alpha1 = sdd.sdd_condition(var, alpha, mgr)
beta0 = sdd.sdd_condition(pvar, beta, pmgr)
beta0 = sdd.sdd_condition(-(pvar + 1), beta0, pmgr)
#beta0 = sdd.sdd_condition( (pvar+2),beta0,pmgr)
beta1 = sdd.sdd_condition(pvar, beta, pmgr)
beta1 = sdd.sdd_condition((pvar + 1), beta1, pmgr)
#beta1 = sdd.sdd_condition(-(pvar+2),beta1,pmgr)
betad = sdd.sdd_condition(-pvar, beta, pmgr)
P = _keep_imp(betad, alpha0, remaining, cache1, cache2, pmgr, mgr)
Q = _keep_imp(betad, alpha1, remaining, cache1, cache2, pmgr, mgr)
R0 = _keep_imp(beta0, alpha0, remaining, cache1, cache2, pmgr, mgr)
R1 = _keep_imp(beta1, alpha1, remaining, cache1, cache2, pmgr, mgr)
gamma = sdd.sdd_conjoin(P, Q, pmgr)
gamma = sdd.sdd_conjoin(_sdd_unused(var, pmgr), gamma, pmgr)
kappa = sdd.sdd_conjoin(_sdd_used_neg(var, pmgr), R0, pmgr)
gamma = sdd.sdd_disjoin(gamma, kappa, pmgr)
kappa = sdd.sdd_conjoin(_sdd_used_pos(var, pmgr), R1, pmgr)
gamma = sdd.sdd_disjoin(gamma, kappa, pmgr)
cache2[key] = gamma
return gamma