def test_orthotope_subseteq():
fol, prm = setup_aut()
varmap = prm._varmap
r = lat.subseteq(varmap, fol)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=1, v_x=1, u_y=2, v_y=3)
r = fol.let(d, r)
assert r == fol.false
r = lat.subseteq(varmap, fol)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=0, v_x=6, u_y=0, v_y=10)
r = fol.let(d, r)
assert r == fol.true
def setup_orthotope_vars():
fol = _fol.Context()
fol.declare(
x=(0, 5),
y=(2, 14),
px=(0, 5),
qx=(0, 5),
py=(2, 14),
qy=(2, 14),
ax=(0, 5),
bx=(0, 5),
ay=(2, 14),
by=(2, 14),
)
xvars = ['x', 'y']
px = dict(x=dict(a='px', b='qx'), y=dict(a='py', b='qy'))
qx = dict(x=dict(a='ax', b='bx'), y=dict(a='ay', b='by'))
prm = lat.Parameters()
prm.x_vars = xvars
prm._px = px
prm._qx = qx
prm.p_to_q = dict(px='ax', py='ay', qx='bx', qy='by')
prm.p_vars = set(prm.p_to_q)
prm.q_vars = set(prm.p_to_q.values())
varmap = lat.parameter_varmap(px, qx)
prm.p_leq_q = lat.subseteq(varmap, fol)
prm.p_eq_q = lat.eq(varmap, fol)
return fol, prm
def test_orthotope_contains_x():
aut, prm = setup_aut(15, 15)
u = lat.x_in_implicant(prm, aut)
values = dict(x=2, y=2, a_x=0, b_x=10, a_y=1, b_y=2)
r = aut.let(values, u)
assert r == aut.true, r
d = prm._varmap
u = lat.subseteq(d, aut)
values = dict(a_x=0, b_x=3, a_y=1, b_y=2, u_x=0, v_x=5, u_y=0, v_y=2)
r = aut.let(values, u)
assert r == aut.true, r
values = dict(a_x=0, b_x=3, a_y=1, b_y=2, u_x=0, v_x=2, u_y=0, v_y=2)
r = aut.let(values, u)
assert r == aut.false, r
def test_covers():
fol, prm = setup_aut()
# set it here to avoid calling `subseteq` from
# `setup_aut` because it will violate unit testing
p_leq_q = lat.subseteq(prm._varmap, fol)
prm.p_leq_q = p_leq_q
cover = fol.add_expr('a_x = 0 /\ b_x = 5')
# not covered
f = fol.add_expr('1 <= x /\ x <= 6')
r = cov._covers(cover, f, prm, fol)
assert r is False, r
r_ = cov._covers_naive(cover, f, prm, fol)
assert r == r_, (r, r_)
# covered
f = fol.add_expr('0 <= x /\ x <= 4')
r = cov._covers(cover, f, prm, fol)
assert r is True, r
r_ = cov._covers_naive(cover, f, prm, fol)
assert r == r_, (r, r_)
def test_orthotopes_using_robots_example():
aut, prm = setup_aut(15, 15)
p_vars = prm.p_vars
# this predicate is constructed by `contract_maker`
# for the robots example in ACC 2016
f = robots_example(aut)
prm.p_leq_q = lat.subseteq(prm._varmap, aut)
prm.p_eq_q = lat.eq(prm._varmap, aut)
u = lat.prime_implicants(f, prm, aut)
support = aut.support(u)
assert support == set(p_vars), (support, p_vars)
n_primes = aut.count(u)
k = aut.count(u)
assert n_primes == k, (n_primes, k)
log.info('{n} prime implicants'.format(n=n_primes))
u = lat.essential_orthotopes(f, prm, aut)
support = aut.support(u)
assert support == set(p_vars), (support, p_vars)
n_essential = aut.count(u)
k = aut.count(u)
assert n_essential == k, (n_essential, k)
log.info('{n} essential prime implicants'.format(n=n_essential))
assert n_essential == 7, n_essential
# result: all primes are essential in this example
#
care = aut.true
s = cov.dumps_cover(u, f, care, aut)
log.info(s)
log.info('BDD has {n} nodes'.format(n=len(aut.bdd)))
# confirm that essential orthotopes cover exactly `f`
c = lat.list_expr(u, prm, aut, simple=True)
s = stx.disj(c)
log.info(s)
z = aut.add_expr(s)
z = aut.exist(['a_x', 'b_x', 'a_y', 'b_y'], z)
assert aut.support(z) == aut.support(f)
assert z == f
if plt is not None:
_plot_orthotopes_for_robots_example(u, f, prm._px, xvars, aut)
# pprint.pprint(aut.bdd.statistics())
# pprint.pprint(aut.bdd.vars)
log.info('{n} nodes in manager'.format(n=len(aut.bdd)))
def test_orthotope_contains_x():
aut, prm = setup_aut(15, 15)
u = lat.x_in_implicant(prm, aut)
values = dict(x=2, y=2,
a_x=0, b_x=10,
a_y=1, b_y=2)
r = aut.let(values, u)
assert r == aut.true, r
d = prm._varmap
u = lat.subseteq(d, aut)
values = dict(
a_x=0, b_x=3, a_y=1, b_y=2,
u_x=0, v_x=5, u_y=0, v_y=2)
r = aut.let(values, u)
assert r == aut.true, r
values = dict(
a_x=0, b_x=3, a_y=1, b_y=2,
u_x=0, v_x=2, u_y=0, v_y=2)
r = aut.let(values, u)
assert r == aut.false, r
def test_scaling_equality():
aut = _fol.Context()
x_vars = dict(x=(0, 10), y=(0, 15), z=(0, 15))
aut.declare(**x_vars)
params = dict(pa='a', pb='b', qa='u', qb='v')
p_dom = lat._parameter_table(x_vars,
aut.vars,
a_name=params['pa'],
b_name=params['pb'])
q_dom = lat._parameter_table(x_vars,
aut.vars,
a_name=params['qa'],
b_name=params['qb'])
aut.declare(**p_dom)
aut.declare(**q_dom)
px = lat._map_vars_to_parameters(x_vars,
a_name=params['pa'],
b_name=params['pb'])
qx = lat._map_vars_to_parameters(x_vars,
a_name=params['qa'],
b_name=params['qb'])
p_to_q = lat._renaming_between_parameters(px, qx)
x_as_x = {xj: dict(a=xj, b=xj) for xj in px}
varmap = lat.parameter_varmap(px, x_as_x)
log.info('Number of variables: {n}'.format(n=len(varmap)))
u = lat.subseteq(varmap, aut)
#
s = ('( '
'(z = 1 /\ y <= 0) \/ '
'(x = 0 /\ z = 1) \/ '
'(y >= 1 /\ x <= 0) \/ '
'(y >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ y <= 0) '
') ')
f = aut.add_expr(s)
prm = lat.Parameters()
prm._px = px
lat.embed_as_implicants(f, prm, aut)
def setup_orthotope_vars():
fol = _fol.Context()
fol.declare(
x=(0, 5), y=(2, 14),
px=(0, 5), qx=(0, 5),
py=(2, 14), qy=(2, 14),
ax=(0, 5), bx=(0, 5),
ay=(2, 14), by=(2, 14),)
xvars = ['x', 'y']
px = dict(x=dict(a='px', b='qx'),
y=dict(a='py', b='qy'))
qx = dict(x=dict(a='ax', b='bx'),
y=dict(a='ay', b='by'))
prm = lat.Parameters()
prm.x_vars = xvars
prm._px = px
prm._qx = qx
prm.p_to_q = dict(px='ax', py='ay', qx='bx', qy='by')
prm.p_vars = set(prm.p_to_q)
prm.q_vars = set(prm.p_to_q.values())
varmap = lat.parameter_varmap(px, qx)
prm.p_leq_q = lat.subseteq(varmap, fol)
prm.p_eq_q = lat.eq(varmap, fol)
return fol, prm
def test_scaling_equality():
aut = _fol.Context()
x_vars = dict(x=(0, 10), y=(0, 15), z=(0, 15))
aut.declare(**x_vars)
params = dict(pa='a', pb='b', qa='u', qb='v')
p_dom = lat._parameter_table(
x_vars, aut.vars,
a_name=params['pa'], b_name=params['pb'])
q_dom = lat._parameter_table(
x_vars, aut.vars,
a_name=params['qa'], b_name=params['qb'])
aut.declare(**p_dom)
aut.declare(**q_dom)
px = lat._map_vars_to_parameters(
x_vars, a_name=params['pa'], b_name=params['pb'])
qx = lat._map_vars_to_parameters(
x_vars, a_name=params['qa'], b_name=params['qb'])
p_to_q = lat._renaming_between_parameters(px, qx)
x_as_x = {xj: dict(a=xj, b=xj) for xj in px}
varmap = lat.parameter_varmap(px, x_as_x)
log.info('Number of variables: {n}'.format(n=len(varmap)))
u = lat.subseteq(varmap, aut)
#
s = (
'( '
'(z = 1 /\ y <= 0) \/ '
'(x = 0 /\ z = 1) \/ '
'(y >= 1 /\ x <= 0) \/ '
'(y >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ y <= 0) '
') ')
f = aut.add_expr(s)
prm = lat.Parameters()
prm._px = px
lat.embed_as_implicants(f, prm, aut)