def test_copy_bdd_same_indices():
# each va has same index in each `BDD`
bdd = cudd.BDD()
other = cudd.BDD()
assert bdd != other
dvars = ['x', 'y', 'z']
for var in dvars:
bdd.add_var(var)
other.add_var(var)
s = '(x & y) | !z'
u0 = bdd.add_expr(s)
u1 = cudd.copy_bdd(u0, bdd, other)
u2 = cudd.copy_bdd(u1, other, bdd)
# involution
assert u0 == u2, (u0, u2)
# confirm
w = other.add_expr(s)
assert w == u1, (w, u1)
# different nodes
u3 = cudd.copy_bdd(other. True, other, bdd)
assert u3 != u2, (u3, u2)
# same bdd
with assert_raises(AssertionError):
cudd.copy_bdd(u0, bdd, bdd)
del u0, u1, u2, u3, w
def test_reorder():
bdd = cudd.BDD()
dvars = ['x', 'y', 'z']
for var in dvars:
bdd.add_var(var)
_confirm_var_order(dvars, bdd)
order = dict(y=0, z=1, x=2)
bdd.reorder(order)
for var in order:
level_ = order[var]
level = bdd.level_of_var(var)
assert level == level_, (var, level, level_)
# without args
bdd = cudd.BDD()
# Figs. 6.24, 6.25 Baier 2008
vrs = ['z1', 'z2', 'z3', 'y1', 'y2', 'y3']
bdd.declare(*vrs)
_confirm_var_order(vrs, bdd)
expr = '(z1 /\ y1) \/ (z2 /\ y2) \/ (z3 /\ y3)'
u = bdd.add_expr(expr)
bdd.reorder()
levels = {var: bdd.level_of_var(var) for var in vrs}
for i in range(1, 4):
a = levels['z{i}'.format(i=i)]
b = levels['y{i}'.format(i=i)]
assert abs(a - b) == 1, levels
def test_contains():
bdd = cudd.BDD()
true = bdd.true
assert true in bdd
bdd.add_var('x')
x = bdd.var('x')
assert x in bdd
# undefined `__contains__`
other_bdd = cudd.BDD()
other_true = other_bdd.true
with assert_raises(AssertionError):
other_true in bdd
def test_copy_bdd_different_indices():
# each var has different index in each `BDD`
bdd = cudd.BDD()
other = cudd.BDD()
assert bdd != other
dvars = ['x', 'y', 'z']
for var in dvars:
bdd.add_var(var)
for var in reversed(dvars):
other.add_var(var)
u0 = bdd.add_expr('(x | !y) & !z')
with assert_raises(AssertionError):
cudd.copy_bdd(u0, bdd, other)
def test_dump_load():
b = cudd.BDD()
b.declare('x', 'y', 'z')
u = b.add_expr('x /\ ~ y')
# dump
fname = 'hoho.json'
nodes = [u]
_copy.dump_json(nodes, fname)
# load
target = cudd.BDD()
roots = _copy.load_json(fname, target)
# assert
v, = roots
u_ = target.copy(v, b)
assert u == u_, (u, u_)
def test_add_expr():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# ((FALSE \/ TRUE) /\ x) \equiv x
s = '(True \/ FALSE) /\ x'
u = bdd.add_expr(s)
x = bdd.var('x')
assert u == x, (u, x)
# ((x \/ ~ y) /\ x) \equiv x
s = '(x \/ ~ y) /\ x'
u = bdd.add_expr(s)
assert u == x, (u, x)
# x /\ y /\ z
bdd.add_var('z')
z = bdd.var('z')
u = bdd.add_expr('x /\ y /\ z')
u_ = bdd.cube(dict(x=True, y=True, z=True))
assert u == u_, (u, u_)
# x /\ ~ y /\ z
u = bdd.add_expr('x /\ ~ y /\ z')
u_ = bdd.cube(dict(x=True, y=False, z=True))
assert u == u_, (u, u_)
# (\E x: x /\ y) \equiv y
y = bdd.var('y')
u = bdd.add_expr('\E x: x /\ y')
assert u == y, (str(u), str(y))
# (\A x: x \/ ~ x) \equiv TRUE
u = bdd.add_expr('\A x: ~ x \/ x')
assert u == bdd.true, u
def test_add_expr():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# (0 | 1) & x = x
s = '(True | False) & x'
u = bdd.add_expr(s)
x = bdd.var('x')
assert u == x, (u, x)
# (x | !y) & x = x
s = '(x | !y) & x'
u = bdd.add_expr(s)
assert u == x, (u, x)
# x & y & z
bdd.add_var('z')
z = bdd.var('z')
u = bdd.add_expr('x & y & z')
u_ = bdd.cube({'x', 'y', 'z'})
assert u == u_, (u, u_)
# x & !y & z
u = bdd.add_expr('x & !y & z')
u_ = bdd.cube(dict(x=True, y=False, z=True))
assert u == u_, (u, u_)
# ? x. x & y = y
y = bdd.var('y')
u = bdd.add_expr('? x. x & y')
assert u == y, (str(u), str(y))
# ! x. x | !x = 1
u = bdd.add_expr('! x. !x | x')
assert u == bdd. True, u
del x, y, z, u, u_
def test_quantify():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
x = bdd.var('x')
# ? x. x = 1
r = bdd.quantify(x, ['x'], forall=False)
assert r == bdd. True, r
# ! x. x = 0
r = bdd.quantify(x, ['x'], forall=True)
assert r == bdd. False, r
# ? y. x = x
r = bdd.quantify(x, ['y'], forall=False)
assert r == x, (r, x)
# ! y. x = x
r = bdd.quantify(x, ['y'], forall=True)
assert r == x, (r, x)
# ? x. x & y = y
y = bdd.var('y')
u = bdd.apply('and', x, y)
r = bdd.quantify(u, ['x'], forall=False)
assert r == y, (r, y)
assert r != x, (r, x)
# ! x. x & y = 0
r = bdd.quantify(u, ['x'], forall=True)
assert r == bdd. False, r
# ! x. !x | y = y
not_x = bdd.apply('not', x)
u = bdd.apply('or', not_x, y)
r = bdd.quantify(u, ['x'], forall=True)
assert r == y, (r, y)
del x, not_x, y, r, u
def solve_gpg_bdd_partial_multiple_calls(gpg_path, timeout_value):
"""
Load and solve the generalized parity game whose path is provided in parameter using the bdd implementation of the
combination of the recursive algorithm and a partial solver. This implementation performs a call to the partial
sover in each recursive call.
"""
player0_won = "TIMEOUT"
winning_0, winning_1 = None, None
start_time = time.time()
with timeout(timeout_value):
manager = _bdd.BDD()
arena, all_vertices = bdd_gpg_loader.gpg2bdd(gpg_path, manager)
winning_0, winning_1 = bdd_gpg_recursive.generalized_recursive_with_psolver_multiple_calls(
arena, manager)
vertex_0_dict_rep = next(manager.pick_iter(all_vertices[0]))
player0_won = manager.let(vertex_0_dict_rep, winning_0) == manager.true
end_time = "%.5f" % (time.time() - start_time)
if player0_won == "TIMEOUT":
end_time = "TIMEOUT"
return player0_won, end_time, winning_0, winning_1
def test_add_expr():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# (0 | 1) & x = x
s = '(True | False) & x'
u = bdd.add_expr(s)
x = bdd.var('x')
assert u == x, (u, x)
# (x | !y) & x = x
s = '(x | !y) & x'
u = bdd.add_expr(s)
assert u == x, (u, x)
# x & y & z
bdd.add_var('z')
z = bdd.var('z')
u = bdd.add_expr('x & y & z')
u_ = bdd.cube(dict(x=True, y=True, z=True))
assert u == u_, (u, u_)
# x & !y & z
u = bdd.add_expr('x & !y & z')
u_ = bdd.cube(dict(x=True, y=False, z=True))
assert u == u_, (u, u_)
# \E x: x & y = y
y = bdd.var('y')
u = bdd.add_expr('\E x: x & y')
assert u == y, (str(u), str(y))
# \A x: x | !x = 1
u = bdd.add_expr('\A x: !x | x')
assert u == bdd.true, u
def test_quantify():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
x = bdd.var('x')
# \E x: x = 1
r = bdd.quantify(x, ['x'], forall=False)
assert r == bdd.true, r
# \A x: x = 0
r = bdd.quantify(x, ['x'], forall=True)
assert r == bdd.false, r
# \E y: x = x
r = bdd.quantify(x, ['y'], forall=False)
assert r == x, (r, x)
# \A y: x = x
r = bdd.quantify(x, ['y'], forall=True)
assert r == x, (r, x)
# \E x: x & y = y
y = bdd.var('y')
u = bdd.apply('and', x, y)
r = bdd.quantify(u, ['x'], forall=False)
assert r == y, (r, y)
assert r != x, (r, x)
# \A x: x & y = 0
r = bdd.quantify(u, ['x'], forall=True)
assert r == bdd.false, r
# \A x: !x | y = y
not_x = bdd.apply('not', x)
u = bdd.apply('or', not_x, y)
r = bdd.quantify(u, ['x'], forall=True)
assert r == y, (r, y)
def solve_pg_bdd_partial_debug(pg_path, timeout_value):
"""
Load and solve the parity game whose path is provided in parameter using the bdd implementation of the combination
of the recursive algorithm and a partial solver. This is Clement's implementation.
"""
player0_won = "TIMEOUT"
winning_0, winning_1 = None, None
start_time = time.time()
with timeout(timeout_value):
manager = _bdd.BDD()
arena, all_vertices = bdd_pg_loader.pg2bdd(pg_path, manager)
winning_0, winning_1 = bdd_pg_recursive.recursive_with_buchi(
arena, manager)
vertex_0_dict_rep = next(manager.pick_iter(all_vertices[0]))
player0_won = manager.let(vertex_0_dict_rep, winning_0) == manager.true
end_time = "%.5f" % (time.time() - start_time)
if player0_won == "TIMEOUT":
end_time = "TIMEOUT"
return player0_won, end_time, winning_0, winning_1
def test_rename():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# x -> y
x = bdd.var('x')
supp = bdd.support(x)
assert supp == set(['x']), supp
d = dict(x='y')
f = cudd.rename(x, bdd, d)
supp = bdd.support(f)
assert supp == set(['y']), supp
y = bdd.var('y')
assert f == y, (f, y)
# x, y -> z, w
for var in ['z', 'w']:
bdd.add_var(var)
not_y = bdd.apply('not', y)
u = bdd.apply('or', x, not_y)
supp = bdd.support(u)
assert supp == set(['x', 'y']), supp
d = dict(x='z', w='y')
f = cudd.rename(u, bdd, d)
supp = bdd.support(f)
assert supp == set(['z', 'w']), supp
z = bdd.var('z')
w = bdd.var('w')
not_w = bdd.apply('not', w)
f_ = bdd.apply('or', z, not_w)
assert f == f_, (f, f_)
# x -> x
d = dict(x='y', y='x')
with assert_raises(AssertionError):
cudd.rename(u, bdd, d)
del x, y, not_y, z, w, not_w, u, f, f_
def test_compose():
bdd = cudd.BDD()
for var in ['x', 'y', 'z']:
bdd.add_var(var)
u = bdd.add_expr('x /\ ~ y')
# x |-> y
sub = dict(x=bdd.var('y'))
v = bdd.let(sub, u)
v_ = bdd.false
assert v == v_, v
# x |-> y, y |-> x
sub = dict(x=bdd.var('y'), y=bdd.var('x'))
v = bdd.let(sub, u)
v_ = bdd.add_expr('y /\ ~ x')
assert v == v_, v
# x |-> z
sub = dict(x=bdd.var('z'))
v = bdd.let(sub, u)
v_ = bdd.add_expr('z /\ ~ y')
assert v == v_, v
# x |-> z, y |-> x
sub = dict(x=bdd.var('z'), y=bdd.var('x'))
v = bdd.let(sub, u)
v_ = bdd.add_expr('z /\ ~ x')
assert v == v_, v
# x |-> (y \/ z)
sub = dict(x=bdd.add_expr('y \/ z'))
v = bdd.let(sub, u)
v_ = bdd.add_expr('(y \/ z) /\ ~ y')
assert v == v_, v
def test_quantify():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
x = bdd.var('x')
# (\E x: x) \equiv TRUE
r = bdd.quantify(x, ['x'], forall=False)
assert r == bdd.true, r
# (\A x: x) \equiv FALSE
r = bdd.quantify(x, ['x'], forall=True)
assert r == bdd.false, r
# (\E y: x) \equiv x
r = bdd.quantify(x, ['y'], forall=False)
assert r == x, (r, x)
# (\A y: x) \equiv x
r = bdd.quantify(x, ['y'], forall=True)
assert r == x, (r, x)
# (\E x: x /\ y) \equiv y
y = bdd.var('y')
u = bdd.apply('and', x, y)
r = bdd.quantify(u, ['x'], forall=False)
assert r == y, (r, y)
assert r != x, (r, x)
# (\A x: x /\ y) \equiv FALSE
r = bdd.quantify(u, ['x'], forall=True)
assert r == bdd.false, r
# (\A x: ~ x \/ y) \equiv y
not_x = bdd.apply('not', x)
u = bdd.apply('or', not_x, y)
r = bdd.quantify(u, ['x'], forall=True)
assert r == y, (r, y)
def main():
b = cudd.BDD()
b.declare('x', 'y', 'z')
u = b.add_expr('x & y & z')
u = b.add_expr('x | y | ~ z')
stats = b.statistics()
pprint.pprint(format_dict(stats))
def __init__(self):
warnings.warn(
'Deprecated; use the class '
'`omega.symbolic.temporal.Automaton` instead.',
category=PendingDeprecationWarning)
self.players = dict(env=0, sys=1) # name -> turn
self.vars = dict()
self.moore = True
self.plus_one = True
self.qinit = '\A \A'
# formulas
self.init = dict(env=list(), sys=list())
self.action = dict(env=list(), sys=list())
self.win = {'<>[]': list(), '[]<>': list()}
self.acceptance = 'Streett(1)'
# auto-populated
self.turns = list() # inverse of `self.players`
# subsets of bits
self.uvars = set() # unprimed env
self.upvars = set() # primed env
self.ubvars = set() # both primed and unprimed env
self.evars = set() # unprimed sys
self.epvars = set() # primed sys
self.ebvars = set() # both primed and unprimed env
self.uevars = set() # all unprimed vars
self.uepvars = set() # all primed vars
# future: hidden, node vars
# map between primed and unprimed
self.prime = dict() # unprimed -> primed
self.unprime = dict() # primed -> unprimed
# aux
# init only to aid static analysis
self.bdd = _bdd.BDD()
def test_prob_negated_edge_basic():
r_expr = "a & ~b"
bdd = _bdd.BDD()
bdd.declare('a', 'b')
r = bdd.add_expr(r_expr)
x = {"a": 0.5, "b": 0.25}
assert (bdd_prob(bdd, r, x, dict()) == 0.375)
def test_prob_negated_edge_basic_2():
r_expr = "a & ~(b | ~c)"
bdd = _bdd.BDD()
bdd.declare('a', 'b', 'c')
r = bdd.add_expr(r_expr)
x = {"a": 0.5, "b": 0.25, "c": 0.125}
assert (bdd_prob(bdd, r, x, dict()) == 0.046875)
def test_true_false():
bdd = cudd.BDD()
true = bdd.true
false = bdd.false
assert false != true
assert false == ~true
assert false == false & true
assert true == true | false
def main():
assert cudd.GB == 2**30, cudd.GB
b = cudd.BDD()
b.configure(
# number of bytes
max_memory=2 * cudd.GB,
# number of entries, not memory units!
max_cache_hard=2**25)
def test_dump_load():
bdd = cudd.BDD()
for var in ['x', 'y', 'z', 'w']:
bdd.add_var(var)
u = bdd.add_expr('(x & !w) | z')
fname = 'bdd.txt'
bdd.dump(u, fname)
u_ = bdd.load(fname)
assert u == u_
def test_true_false():
bdd = cudd.BDD()
true = bdd. True
false = bdd. False
assert false != true
assert false == ~true
assert false == false & true
assert true == true | false
del true, false
def test_dump_load():
bdd = cudd.BDD()
for var in ['x', 'y', 'z', 'w']:
bdd.add_var(var)
u = bdd.add_expr('(x /\ ~ w) \/ z')
fname = 'bdd.txt'
bdd.dump(fname, [u], filetype='dddmp')
u_ = bdd.load(fname)
assert u == u_
def test_function():
bdd = cudd.BDD()
bdd.add_var('x')
# x
x = bdd.var('x')
assert not x.negated
# ~ x
not_x = ~x
assert not_x.negated
def _init_bdd(use_cudd):
if _bdd is None:
raise ImportError('Failed to import `dd.bdd`.\n'
'Install package `dd`.')
if not use_cudd:
return _bdd.BDD()
if cudd is None:
raise ImportError('Failed to import module `dd.cudd`.\n'
'Compile the Cython bindings of `dd` to CUDD.')
return cudd.BDD()
def test_or_forall():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# \A x y: x | ! y = 0
x = bdd.var('x')
not_y = bdd.add_expr('!y')
qvars = ['x', 'y']
r = cudd.or_forall(x, not_y, qvars, bdd)
assert r == bdd.false, r
def test_or_forall():
bdd = cudd.BDD()
for var in ['x', 'y']:
bdd.add_var(var)
# (\A x, y: x \/ ~ y) \equiv FALSE
x = bdd.var('x')
not_y = bdd.add_expr('~ y')
qvars = ['x', 'y']
r = cudd.or_forall(x, not_y, qvars)
assert r == bdd.false, r
def test_var_cofactor():
bdd = cudd.BDD()
bdd.add_var('x')
x = bdd.var('x')
values = dict(x=False)
u = bdd.let(values, x)
assert u == bdd.false, u
values = dict(x=True)
u = bdd.let(values, x)
assert u == bdd.true, u
def test_function_support():
bdd = cudd.BDD()
bdd.add_var('x')
u = bdd.var('x')
r = u.support
assert r == {'x'}, r
bdd.add_var('y')
u = bdd.add_expr('y /\ x')
r = u.support
assert r == {'x', 'y'}, r
