def to_cnf(self, x_vars, cnf):
d_vars = [[cnf.nv + 1 + j + (j * i) for j in range(self.out_dim)]
for i in range(self.out_dim)]
cnf.nv += self.out_dim**2
for j in range(self.out_dim):
for i in range(self.out_dim):
E_ij = np.ceil((self.b[i] - self.b[j] + np.sum(self.A[i]) -
np.sum(self.A[j])) / 2)
lits = [
x if (ai > 0 and aj < 0) else -x
for (x, ai, aj) in zip(x_vars, self.A[i], self.A[j])
if not (np.sign(ai) == np.sign(aj))
]
ale = CardEnc.atleast(lits, np.ceil(E_ij / 2.0), cnf.nv,
EncType.seqcounter)
r = ale.nv # TODO: Check assumption that this is "r(n, D)" of AAAI paper
cnf.extend(ale.clauses)
cnf.append([-r, d_vars[i][j]])
cnf.append([r, -d_vars[i][j]])
return d_vars
def get_constraint(idpool: IDPool, id2varmap,
constraint: tConstraint) -> CNFPlus:
""" Generate formula for a given cardinality constraint"""
validate_constraint(constraint)
lits = []
for ta in constraint.tas:
t1 = tuple((constraint.course_name, ta))
if t1 not in id2varmap.keys():
id1 = idpool.id(t1)
id2varmap[t1] = id1
else:
id1 = id2varmap[t1]
lits.append(id1)
if constraint.type == tCardType.GREATEROREQUALS:
if (constraint.bound == 1):
cnf = CNFPlus()
cnf.append(lits)
elif (constraint.bound > len(lits)):
msg = "Num TAs available for constraint:" + constraint.con_str + "is more than the bound in the constraint. \
Changing the bound to " + str(len(lits)) + ".\n"
print(msg, file=sys.stderr)
constraint.bound = len(lits)
cnf = CardEnc.atleast(lits, vpool=idpool, bound=constraint.bound)
elif constraint.type == tCardType.LESSOREQUALS:
cnf = CardEnc.atmost(lits, vpool=idpool, bound=constraint.bound)
return cnf
def closest_string(bitarray_list, distance=4):
"""
Return if a bitarray exists of distance at most 'distance'.
Use example:
s1=bitarray('0010')
s2=bitarray('0011')
closest_string([s1,s2], distance=0)
> False
closest_string([s1,s2], distance=2)
> True
"""
if distance < 0:
raise ValueError('Distance must be positive integer')
logging.info('\nCodifying SAT Solver...')
length = max(len(bit_arr) for bit_arr in bitarray_list)
solver = Solver(name='mcm')
vpool = IDPool()
local_list = bitarray_list.copy()
logging.info(' -> Codifying: normalizing strings')
for index, bitarr in enumerate(bitarray_list):
aux = (length - len(bitarr)) * bitarray('0')
local_list[index] = bitarr + aux
logging.info(' -> Codifying: imposing distance condition')
for index, word in enumerate(local_list):
for pos in range(length):
vpool.id(ut.xvar(index, pos))
for pos in range(length):
vpool.id(ut.yvar(pos))
for index, word in enumerate(local_list):
for pos in range(length):
vpool.id(ut.zvar(index, pos))
for index, word in enumerate(local_list):
for pos in range(length):
for clause in ut.triple_equal(ut.xvar(index, pos),
ut.yvar(pos),
ut.zvar(index, pos),
vpool=vpool):
solver.add_clause(clause)
cnf = CardEnc.atleast(
lits=[vpool.id(ut.zvar(index, pos)) for pos in range(length)],
bound=length - distance,
vpool=vpool)
solver.append_formula(cnf)
logging.info(' -> Codifying: Words Value')
assumptions = []
for index, word in enumerate(local_list):
for pos in range(length):
assumptions += [
vpool.id(ut.xvar(index, pos)) * (-1)**(not word[pos])
]
logging.info('Running SAT Solver...')
return solver.solve(assumptions=assumptions)