def queens(n):
solution = Robdd.true()
# create the rule "there must be at least one queen at each line"
for j in range(1, n + 1):
line = Robdd.false()
for i in range(1, n + 1):
queen = Robdd.make_x(index_of(i, j))
line = synth(line, Bdd.OR, queen)
solution = synth(solution, Bdd.AND, line)
# create a list of "NOT" expressions
not_expressions = {}
for j in range(1, n + 1):
for i in range(1, n + 1):
not_expressions[(i, j)] = Robdd.make_not_x(index_of(i, j))
# create conditions for each position
for j in range(1, n + 1):
for i in range(1, n + 1):
queen = queen_conditions(not_expressions, i, j, n)
solution = synth(solution, Bdd.AND, queen)
return solution
def queens(n):
solution = Robdd.true()
# create the rule "there must be at least one queen at each line"
for j in range(1, n + 1):
line = Robdd.false()
for i in range(1, n + 1):
queen = Robdd.make_x(index_of(i, j))
line = synth(line, Bdd.OR, queen)
solution = synth(solution, Bdd.AND, line)
# create a list of "NOT" expressions
not_expressions = {}
for j in range(1, n + 1):
for i in range(1, n + 1):
not_expressions[(i, j)] = Robdd.make_not_x(index_of(i, j))
# create conditions for each position
for j in range(1, n + 1):
for i in range(1, n + 1):
queen = queen_conditions(not_expressions, i, j, n)
solution = synth(solution, Bdd.AND, queen)
return solution
def remove_interval_up(original, s):
r = Robdd.false()
for i, b in enumerate(s):
if b == '0':
current_var = Robdd.make_x(i)
r = synth(r, Bdd.OR, current_var)
return synth(original, Bdd.AND, r)
def blah():
v = [
'1000000000000001', '1100000000000011', '1010000000000101',
'1000000110000001', '1000100000010001', '1001000000001001',
'1000010000100001', '1000001001000001', '1111000000001111',
'1010010110100101', '1001100110011001', '1100110000110101',
'1010101001010101', '1100001111000011', '1111111111111111'
]
#
# '''
# 1000010000100001
# 1000000110000001
# 1010000000000101
# 1010010110100101
# '''
# print v[2]
solution = None
for __v__ in v:
if solution is None:
solution = add_restriction(__v__)
else:
solution = synth(solution, Bdd.OR, add_restriction(__v__))
# solution = add_restriction(v[0])
# for i in range(len(v)):
# if i in [0, 1, 13]:
# continue
# solution = synth(solution, Bdd.AND, add_negated(v[i]))
# solution = remove_interval_down(solution, v[6])
# solution = remove_interval_down(solution, v[2])
# solution = remove_interval_down(solution, v[4])
# solution = remove_interval_down(solution, v[5])
#
# solution = remove_interval_up(solution, v[1])
# solution = Robdd.make_x(0)
# solution = synth(solution, Bdd.OR, Robdd.make_not_x(0))
# solution = synth(solution, Bdd.OR, Robdd.make_x(1))
solution = Robdd.false()
solution = synth(solution, Bdd.OR, Robdd.make_not_x(0))
with open('/tmp/graph.dot', 'w') as fh:
fh.write(solution.graphviz())
return solution
def add_restriction(s):
r = Robdd.true()
for i, b in enumerate(s):
# if i == 0:
# continue
# if i >= 8 :
# continue
if b == '1':
current_var = Robdd.make_x(i)
else:
current_var = Robdd.make_not_x(i)
r = synth(r, Bdd.AND, current_var)
return r
def add_negated(s):
r = Robdd.false()
for i, b in enumerate(s):
# if i == 0:
# continue
# if i >= 8:
# continue
if b == '0':
current_var = Robdd.make_x(i)
else:
current_var = Robdd.make_not_x(i)
r = synth(r, Bdd.OR, current_var)
return r
def queen_conditions(not_x, i, j, n) :
queen = Robdd.make_x(index_of(i, j))
# creates the rule "none in the same column"
a = Robdd.true()
for y in range(1, n + 1) :
if y == j : continue
a_ = synth(queen, Bdd.IMPL, not_x[(i, y)])
a = synth(a, Bdd.AND, a_)
# creates the rule "none in the same line"
b = Robdd.true()
for x in range(1, n + 1) :
if x == i : continue
b_ = synth(queen, Bdd.IMPL, not_x[(x, j)])
b = synth(b, Bdd.AND, b_)
# creates the rule "none in the diagonals"
c = Robdd.true()
x = 1
while (i - x) > 0 and (j - x) > 0 :
c_ = synth(queen, Bdd.IMPL, not_x[(i - x, j - x)])
c = synth(c, Bdd.AND, c_)
x += 1
x = 1
while (i + x) <= n and (j + x) <= n :
c_ = synth(queen, Bdd.IMPL, not_x[(i + x, j + x)])
c = synth(c, Bdd.AND, c_)
x += 1
d = Robdd.true()
x = 1
while (i - x) > 0 and (j + x) <= n :
d_ = synth(queen, Bdd.IMPL, not_x[(i - x, j + x)])
d = synth(d, Bdd.AND, d_)
x += 1
x = 1
while (i + x) <= n and (j - x) > 0 :
d_ = synth(queen, Bdd.IMPL, not_x[(i + x, j - x)])
d = synth(d, Bdd.AND, d_)
x += 1
return synth(synth(a, Bdd.AND, b), Bdd.AND, synth(c, Bdd.AND, d))
def queen_conditions(not_x, i, j, n):
queen = Robdd.make_x(index_of(i, j))
# creates the rule "none in the same column"
a = Robdd.true()
for y in range(1, n + 1):
if y == j: continue
a_ = synth(queen, Bdd.IMPL, not_x[(i, y)])
a = synth(a, Bdd.AND, a_)
# creates the rule "none in the same line"
b = Robdd.true()
for x in range(1, n + 1):
if x == i: continue
b_ = synth(queen, Bdd.IMPL, not_x[(x, j)])
b = synth(b, Bdd.AND, b_)
# creates the rule "none in the diagonals"
c = Robdd.true()
x = 1
while (i - x) > 0 and (j - x) > 0:
c_ = synth(queen, Bdd.IMPL, not_x[(i - x, j - x)])
c = synth(c, Bdd.AND, c_)
x += 1
x = 1
while (i + x) <= n and (j + x) <= n:
c_ = synth(queen, Bdd.IMPL, not_x[(i + x, j + x)])
c = synth(c, Bdd.AND, c_)
x += 1
d = Robdd.true()
x = 1
while (i - x) > 0 and (j + x) <= n:
d_ = synth(queen, Bdd.IMPL, not_x[(i - x, j + x)])
d = synth(d, Bdd.AND, d_)
x += 1
x = 1
while (i + x) <= n and (j - x) > 0:
d_ = synth(queen, Bdd.IMPL, not_x[(i + x, j - x)])
d = synth(d, Bdd.AND, d_)
x += 1
return synth(synth(a, Bdd.AND, b), Bdd.AND, synth(c, Bdd.AND, d))
def synthesize(self):
if self.expression_a == None or not isinstance(self.expression_a,
Robdd):
raise "Expression A is not a Robdd object."
if self.expression_b == None or not isinstance(self.expression_b,
Robdd):
raise "Expression B is not a Robdd object."
if self.operator not in [Bdd.AND, Bdd.OR, Bdd.IMPL, Bdd.BIIMPL]:
raise "Invalid operator."
self.result = Robdd()
self.result.root = self._synth(self.expression_a.root,
self.expression_b.root)
return self.result
def test_evaluate_should_return_true_for_x1(self):
robdd = Robdd.false()
v = robdd.make_x(0)
robdd = synth(robdd, Bdd.OR, v)
self.assertTrue(robdd.evaluate([1]))
self.assertTrue(robdd.evaluate([1, 0]))
self.assertTrue(robdd.evaluate([1, 1, 0, 1]))
self.assertFalse(robdd.evaluate([0]))
self.assertFalse(robdd.evaluate([0, 1]))
self.assertFalse(robdd.evaluate([0, 1, 1, 1]))
def synthesize(self):
if self.expression_a == None or not isinstance(self.expression_a, Robdd):
raise "Expression A is not a Robdd object."
if self.expression_b == None or not isinstance(self.expression_b, Robdd):
raise "Expression B is not a Robdd object."
if self.operator not in [Bdd.AND, Bdd.OR, Bdd.IMPL, Bdd.BIIMPL]:
raise "Invalid operator."
self.result = Robdd()
self.result.root = self._synth(self.expression_a.root, self.expression_b.root)
return self.result
def negate_bdd(bdd):
neg_bdd = synthesize(bdd, Bdd.AND, Robdd.true())
for i in xrange(len(neg_bdd.items)):
neg_bdd.items[i] = tuple(
(neg_bdd.items[i][0], not neg_bdd.items[i][1]
if neg_bdd.items[i][1] in (True, False) else neg_bdd.items[i][1],
not neg_bdd.items[i][2]
if neg_bdd.items[i][2] in (True, False) else neg_bdd.items[i][2]))
# invert root, if root is a leaf
if neg_bdd.root in (0, 1):
neg_bdd.root ^= 1
return neg_bdd
def negate_bdd(bdd):
neg_bdd = synthesize(bdd, Bdd.AND, Robdd.true())
for i in xrange(len(neg_bdd.items)):
neg_bdd.items[i] = tuple((neg_bdd.items[i][0],
not neg_bdd.items[i][1] if neg_bdd.items[i][1] in (True, False) else neg_bdd.items[i][
1],
not neg_bdd.items[i][2] if neg_bdd.items[i][2] in (True, False) else neg_bdd.items[i][
2]))
# invert root, if root is a leaf
if neg_bdd.root in (0, 1):
neg_bdd.root ^= 1
return neg_bdd
def get_minimal_element(robdd: Robdd,
mapping_partition_to_boolean,
mapping_boolean_to_partition,
expected_value=1):
bool_representation = robdd.get_random_solution(expected_value)
if bool_representation is None:
return None
partition = Partition(
mask=mapping_boolean_to_partition[tuple(bool_representation)].mask)
while True:
can_continue = False
for partition_child in partition.subset_generator():
boolean_representation = mapping_partition_to_boolean[
partition_child.mask]
if robdd.evaluate(boolean_representation) == expected_value:
can_continue = True
partition = partition_child
if not can_continue:
break
return partition.mask
def test_get_minimal_element_should_work2(self):
robdd = Robdd.false()
a = (1, 1, 1, 1)
pa = Partition(mask=(0, 0, 0))
b = (1, 1, 0, 0)
pb = Partition(mask=(0, 0, 1))
c = (1, 0, 1, 0)
pc = Partition(mask=(0, 1, 0))
d = (1, 0, 0, 1)
pd = Partition(mask=(0, 1, 1))
e = (1, 0, 0, 0)
pe = Partition(mask=(0, 1, 2))
robdd = synth(robdd, Bdd.OR, add_restriction(a))
robdd = synth(robdd, Bdd.OR, add_restriction(b))
robdd = synth(robdd, Bdd.OR, add_restriction(c))
robdd = synth(robdd, Bdd.OR, add_restriction(d))
mapping_partition_to_boolean = dict()
mapping_partition_to_boolean[pa.mask] = a
mapping_partition_to_boolean[pb.mask] = b
mapping_partition_to_boolean[pc.mask] = c
mapping_partition_to_boolean[pd.mask] = d
mapping_partition_to_boolean[pe.mask] = e
mapping_boolean_to_partition = dict()
mapping_boolean_to_partition[a] = pa
mapping_boolean_to_partition[b] = pb
mapping_boolean_to_partition[c] = pc
mapping_boolean_to_partition[d] = pd
mapping_boolean_to_partition[e] = pe
minimal_element = get_minimal_element(robdd, mapping_partition_to_boolean, mapping_boolean_to_partition)
self.assertTrue(minimal_element == (0, 0, 1) or minimal_element == (0, 1, 0) or minimal_element == (0, 1, 1))
def main():
#Parse the command line arguments provided at run time.
parser = argparse.ArgumentParser(description='ROBDD')
parser.add_argument('-b',
'--boolean_expr',
dest='expr_1',
metavar='B',
type=str,
nargs='?',
help='Provide a boolean expression')
parser.add_argument('-b2',
'--boolean_expr2',
dest='expr_2',
metavar='B2',
type=str,
nargs='?',
help='Provide a boolean expression')
parser.add_argument(
'-a',
'--apply',
dest='apply_expr',
metavar='A',
type=str,
nargs='?',
help='Provide the operation to apply (And, Or, Equal, Implies)')
parser.add_argument('-r',
'--restrict',
dest='restrict_expr',
metavar='R',
type=str,
nargs='?',
help='Provide the restriction "var,val"')
parser.add_argument('-s',
'--sat',
dest='sat',
action='store_true',
help='Return SAT on ROBDD')
# Parse the input arguments
args = parser.parse_args()
if args.expr_1 is not None:
expression1 = str(expr(args.expr_1))
print("Expression1: " + expression1)
r1 = Robdd(find_large_var(expression1))
r1.build(expression1)
r1.print_graph("r1")
if args.expr_2 is not None:
expression2 = str(expr(args.expr_2))
print("Expression2: " + expression2)
r2 = Robdd(find_large_var(expression2))
r2.build(expression2)
r2.print_graph("r2")
if args.apply_expr is not None:
r3 = Robdd_apply(
max(find_large_var(expression1), find_large_var(expression2)))
r3.apply(convert_apply(args.apply_expr), r1, r2)
r3.print_graph("r3_apply")
if args.restrict_expr is not None:
r4 = Robdd_restrict(r1)
r4.restrict(int(args.restrict_expr.split(',')[0]),
int(args.restrict_expr.split(',')[1]))
r4.print_graph('r4_restrict')
if args.sat:
r4 = Robdd_sat(r1)
r4.print_SAT()
class Synthesis:
def __init__(self):
self.memo = {}
self.operator = None
self.expression_a = None
self.expression_b = None
self.result = None
def synthesize(self):
if self.expression_a == None or not isinstance(self.expression_a, Robdd):
raise "Expression A is not a Robdd object."
if self.expression_b == None or not isinstance(self.expression_b, Robdd):
raise "Expression B is not a Robdd object."
if self.operator not in [Bdd.AND, Bdd.OR, Bdd.IMPL, Bdd.BIIMPL]:
raise "Invalid operator."
self.result = Robdd()
self.result.root = self._synth(self.expression_a.root, self.expression_b.root)
return self.result
def _synth(self, a_index, b_index):
if (a_index, b_index) in self.memo:
return self.memo[(a_index, b_index)]
# print "_synth {}, {}".format(a_index, b_index)
# print " A is leaf:", self._is_leaf(a_index)
# print " B is leaf:", self._is_leaf(b_index)
i_a, t_a, f_a = self.expression_a.items[a_index]
i_b, t_b, f_b = self.expression_b.items[b_index]
if self._is_leaf(a_index) and self._is_leaf(b_index):
# print " operating leaves"
result = self._operate(a_index, b_index)
elif i_a == i_b:
# print " operating nodes"
result = self.result.insert(i_a, self._synth(t_a, t_b), self._synth(f_a, f_b))
elif i_a < i_b:
# print " advancing A"
result = self.result.insert(i_a, self._synth(t_a, b_index), self._synth(f_a, b_index))
# elif i_a > i_b:
else:
# print " advancing B"
result = self.result.insert(i_b, self._synth(a_index, t_b), self._synth(a_index, f_b))
self.memo[(a_index, b_index)] = result
return result
def _operate(self, a_index, b_index):
a = self._index_to_bool(a_index)
b = self._index_to_bool(b_index)
if self.operator == Bdd.AND:
return a and b
if self.operator == Bdd.OR:
return a or b
if self.operator == Bdd.IMPL:
return False if (a and not b) else True
if self.operator == Bdd.BIIMPL:
return a == b
raise "Unknown operator."
def _is_leaf(self, index):
return index == 0 or index == 1
def _index_to_bool(self, index):
return index == 1
def test_get_minimal_element_should_return_none_if_empty(self):
robdd = Robdd.false()
self.assertIsNone(get_minimal_element(robdd, dict(), dict()))
def test_evaluate_should_always_return_false(self):
robdd = Robdd.false()
self.assertFalse(robdd.evaluate([0]))
self.assertFalse(robdd.evaluate([1]))
self.assertFalse(robdd.evaluate([0, 0]))
self.assertFalse(robdd.evaluate([0, 1, 1, 0]))
class Synthesis:
def __init__(self):
self.memo = {}
self.operator = None
self.expression_a = None
self.expression_b = None
self.result = None
def synthesize(self):
if self.expression_a == None or not isinstance(self.expression_a,
Robdd):
raise "Expression A is not a Robdd object."
if self.expression_b == None or not isinstance(self.expression_b,
Robdd):
raise "Expression B is not a Robdd object."
if self.operator not in [Bdd.AND, Bdd.OR, Bdd.IMPL, Bdd.BIIMPL]:
raise "Invalid operator."
self.result = Robdd()
self.result.root = self._synth(self.expression_a.root,
self.expression_b.root)
return self.result
def _synth(self, a_index, b_index):
if (a_index, b_index) in self.memo:
return self.memo[(a_index, b_index)]
# print "_synth {}, {}".format(a_index, b_index)
# print " A is leaf:", self._is_leaf(a_index)
# print " B is leaf:", self._is_leaf(b_index)
i_a, t_a, f_a = self.expression_a.items[a_index]
i_b, t_b, f_b = self.expression_b.items[b_index]
if self._is_leaf(a_index) and self._is_leaf(b_index):
# print " operating leaves"
result = self._operate(a_index, b_index)
elif i_a == i_b:
# print " operating nodes"
result = self.result.insert(i_a, self._synth(t_a, t_b),
self._synth(f_a, f_b))
elif i_a < i_b:
# print " advancing A"
result = self.result.insert(i_a, self._synth(t_a, b_index),
self._synth(f_a, b_index))
# elif i_a > i_b:
else:
# print " advancing B"
result = self.result.insert(i_b, self._synth(a_index, t_b),
self._synth(a_index, f_b))
self.memo[(a_index, b_index)] = result
return result
def _operate(self, a_index, b_index):
a = self._index_to_bool(a_index)
b = self._index_to_bool(b_index)
if self.operator == Bdd.AND:
return a and b
if self.operator == Bdd.OR:
return a or b
if self.operator == Bdd.IMPL:
return False if (a and not b) else True
if self.operator == Bdd.BIIMPL:
return a == b
raise "Unknown operator."
def _is_leaf(self, index):
return index == 0 or index == 1
def _index_to_bool(self, index):
return index == 1
def test_evaluate_should_always_return_true(self):
robdd = Robdd.true()
self.assertTrue(robdd.evaluate([0]))
self.assertTrue(robdd.evaluate([1]))
self.assertTrue(robdd.evaluate([0, 0]))
self.assertTrue(robdd.evaluate([0, 1, 1, 0]))