def test_long(self) :
for l in range(10,30) :
solver = Solver()
toadd = []
toassume = []
solution_expected = [None]
for i in range(1,l) :
toadd.append(i)
solution_expected.append(False)
if i != l-1 :
toassume.append(i*-1)
solver.add_xor_clause(toadd, False)
res, solution = solver.solve(toassume)
self.assertEqual(res, True)
self.assertEqual(solution, tuple(solution_expected))
def is_system_uniquely_satisfiable(self, system, n):
"""
Tests unique satisfiable by banning all zero solution
:param system:
:param n:
:return:
"""
if not system:
return False
# Prep solver
solver = Solver()
for clause in system:
solver.add_xor_clause(clause, False)
# Ban all zero
solver.add_clause(range(1, n + 1))
sat, sol = solver.solve()
# print "Found system is {0}".format(sat)
return not sat
class TestXor(unittest.TestCase) :
def setUp(self) :
self.solver = Solver(threads = 2);
def test_wrong_args(self) :
self.assertRaises(TypeError, self.solver.add_xor_clause, [1, 2])
self.assertRaises(ValueError, self.solver.add_xor_clause, [1, 0], True)
self.assertRaises(ValueError, self.solver.add_xor_clause, [-1, 2], True)
def test_binary(self) :
self.solver.add_xor_clause([1,2], False)
res, solution = self.solver.solve([1])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, True))
def test_unit(self) :
self.solver.add_xor_clause([1], False)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertEqual(solution, (None, False))
def test_unit2(self) :
self.solver.add_xor_clause([1], True)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertEqual(solution, (None, True))
def test_3_long(self) :
self.solver.add_xor_clause([1, 2, 3], False)
res, solution = self.solver.solve([1, 2])
self.assertEqual(res, True)
#self.assertEqual(solution, (None, True, True, False))
def test_3_long2(self) :
self.solver.add_xor_clause([1, 2, 3], True)
res, solution = self.solver.solve([1, -2])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, False, False))
def test_long(self) :
for l in range(10,30) :
self.setUp()
toadd = []
toassume = []
solution_expected = [None]
for i in range(1,l) :
toadd.append(i)
solution_expected.append(False)
if i != l-1 :
toassume.append(i*-1)
self.solver.add_xor_clause(toadd, False)
res, solution = self.solver.solve(toassume)
self.assertEqual(res, True)
self.assertEqual(solution, tuple(solution_expected))
class TestXor(unittest.TestCase):
def setUp(self):
self.solver = Solver(threads=2)
def test_wrong_args(self):
self.assertRaises(TypeError, self.solver.add_xor_clause, [1, 2])
self.assertRaises(ValueError, self.solver.add_xor_clause, [1, 0], True)
self.assertRaises(ValueError, self.solver.add_xor_clause, [-1, 2],
True)
def test_binary(self):
self.solver.add_xor_clause([1, 2], False)
res, solution = self.solver.solve([1])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, True))
def test_unit(self):
self.solver.add_xor_clause([1], False)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertEqual(solution, (None, False))
def test_unit2(self):
self.solver.add_xor_clause([1], True)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertEqual(solution, (None, True))
def test_3_long(self):
self.solver.add_xor_clause([1, 2, 3], False)
res, solution = self.solver.solve([1, 2])
self.assertEqual(res, True)
# self.assertEqual(solution, (None, True, True, False))
def test_3_long2(self):
self.solver.add_xor_clause([1, 2, 3], True)
res, solution = self.solver.solve([1, -2])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, False, False))
def test_long(self):
for l in range(10, 30):
self.setUp()
toadd = []
toassume = []
solution_expected = [None]
for i in range(1, l):
toadd.append(i)
solution_expected.append(False)
if i != l - 1:
toassume.append(i * -1)
self.solver.add_xor_clause(toadd, False)
res, solution = self.solver.solve(toassume)
self.assertEqual(res, True)
self.assertEqual(solution, tuple(solution_expected))
class ProgramSolver():
def __init__(self,filename):
self.s = Solver(threads = 3)
self.tt = 0
h2v = {} # hole 2 variable
self.maximum_variable = -1
with open(filename,'r') as f:
for l in f:
if len(l) > len('c hole ') and l[:len('c hole ')] == 'c hole ':
ms = re.findall(r'(\d+) \- (\d+)', l)[0]
assert int(ms[0]) == int(ms[1])
ms = int(ms[0])
n = int(re.findall(r'H__\S+_(\S+)\s',l)[0])
h2v[n] = ms
elif len(l) > 0 and not 'c' in l and not 'p' in l:
vs = re.findall(r'(\-?\d+)',l)
assert vs[-1] == '0'
clause = [int(v) for v in vs[:-1] ]
self.maximum_variable = max([self.maximum_variable] +
[abs(v) for v in clause ])
self.s.add_clause(clause)
print "Loaded",filename," with",len(h2v),"holes"
# convert the tape index into a sat variable
self.tape2variable = [ v for h,v in sorted(h2v.items()) ]
# converts a sat variable to a tape index
self.variable2tape = dict([ (v,h) for h,v in h2v.items() ])
def generate_variable(self):
self.maximum_variable += 1
return self.maximum_variable
def random_projection(self):
self.s.add_xor_clause([v for v in self.variable2tape if random.random() > 0.5 ],random.random() > 0.5)
def try_solving(self,assumptions = None):
print "About to run solver == == == > "
start_time = time.time()
if assumptions != None:
result = self.s.solve(assumptions)
else:
result = self.s.solve()
dt = (time.time() - start_time)
self.tt += dt
print "Ran solver in time",dt
if result[0]:
bindings = {}
for v in range(len(result[1])):
if v in self.variable2tape:
bindings[v] = result[1][v]
print "Satisfiable."
return bindings
else:
print "Unsatisfiable."
return False
def uniqueness_clause(self,tape):
p,bit_mask = parse_tape(tape)
clause = []
for j in range(len(tape)):
if bit_mask[j] == 1:
# jth tape position
v = self.tape2variable[j]
if tape[j] == 1: v = -v
clause += [v]
return clause
def is_solution_unique(self,tape):
d = self.generate_variable()
clause = [d] + self.uniqueness_clause(tape)
print "uniqueness clause",clause
self.s.add_clause(clause)
result = self.try_solving([-d])
self.s.add_clause([d]) # make the clause documents they satisfied
if result:
tp = self.holes2tape(result)
print "alternative:",parse_tape(tp)
print "alternative tape:",tp
return False
else:
return True
def holes2tape(self,result):
return [ (1 if result[v] else 0) for v in self.tape2variable ]
def try_sampling(self,subspace_dimension):
for j in range(subspace_dimension):
self.random_projection()
result = self.try_solving()
if result:
print "Random projection satisfied"
tp = self.holes2tape(result)
print parse_tape(tp)[0]
if self.is_solution_unique(tp):
print "Unique. Accepted."
else:
print "Sample rejected"
def adaptive_sample(self):
subspace_dimension = 1
result = self.try_solving()
if result:
print "Formula satisfied"
for j in range(subspace_dimension):
self.random_projection()
while True:
print "\n\niterating:"
result = self.try_solving()
if result:
print "Satisfied %d constraints" % subspace_dimension
tp = self.holes2tape(result)
print parse_tape(tp)
print "tape = ",tp
if self.is_solution_unique(tp):
print "UNIQUE"
print "<<< == == == >>>"
self.random_projection()
subspace_dimension += 1
else:
print "Rejected %d projections" % subspace_dimension
print "total time = ",self.tt
break
def enumerate_solutions(self):
solutions = []
result = self.try_solving()
d = self.generate_variable()
logZ = float('-inf')
while result:
tp = self.holes2tape(result)
program,mask = parse_tape(tp)
solutions = solutions + [program]
specified = sum(mask)
logZ = lse(logZ, -specified * 0.693)
print "Enumerated program", program, "with", specified, "specified bits."
self.s.add_clause([d] + self.uniqueness_clause(tp))
result = self.try_solving([-d])
print "log(z) = ",logZ, "\t1/p = ", math.exp(-logZ)
return solutions
class CryptoMiniSat(SatSolver):
r"""
CryptoMiniSat Solver.
INPUT:
- ``verbosity`` -- an integer between 0 and 15 (default: 0). Verbosity.
- ``confl_limit`` -- an integer (default: ``None``). Abort after this many
conflicts. If set to ``None``, never aborts.
- ``threads`` -- an integer (default: None). The number of thread to
use. If set to ``None``, the number of threads used corresponds to the
number of cpus.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
"""
def __init__(self, verbosity=0, confl_limit=None, threads=None):
r"""
Constuct a new CryptoMiniSat instance.
See the documentation class for the description of inputs.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat(threads=1) # optional - cryptominisat
"""
if threads is None:
from sage.parallel.ncpus import ncpus
threads = ncpus()
if confl_limit is None:
from sys import maxint
confl_limit = maxint
try:
from pycryptosat import Solver
except ImportError:
from sage.misc.package import PackageNotFoundError
raise PackageNotFoundError("cryptominisat")
self._solver = Solver(verbose=int(verbosity), confl_limit=int(confl_limit), threads=int(threads))
self._nvars = 0
self._clauses = []
def var(self, decision=None):
r"""
Return a *new* variable.
INPUT:
- ``decision`` -- accepted for compatibility with other solvers, ignored.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.var() # optional - cryptominisat
1
sage: solver.add_clause((-1,2,-4)) # optional - cryptominisat
sage: solver.var() # optional - cryptominisat
5
"""
return self._nvars + 1
def nvars(self):
r"""
Return the number of variables. Note that for compatibility with DIMACS
convention, the number of variables corresponds to the maximal index of
the variables used.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.nvars() # optional - cryptominisat
0
If a variable with intermediate index is not used, it is still
considered as a variable::
sage: solver.add_clause((1,-2,4)) # optional - cryptominisat
sage: solver.nvars() # optional - cryptominisat
4
"""
return self._nvars
def add_clause(self, lits):
r"""
Add a new clause to set of clauses.
INPUT:
- ``lits`` -- a tuple of nonzero integers.
.. note::
If any element ``e`` in ``lits`` has ``abs(e)`` greater
than the number of variables generated so far, then new
variables are created automatically.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.add_clause((1, -2 , 3)) # optional - cryptominisat
"""
if 0 in lits:
raise ValueError("0 should not appear in the clause: {}".format(lits))
# cryptominisat does not handle Sage integers
lits = tuple(int(i) for i in lits)
self._nvars = max(self._nvars, max(abs(i) for i in lits))
self._solver.add_clause(lits)
self._clauses.append((lits, False, None))
def add_xor_clause(self, lits, rhs=True):
r"""
Add a new XOR clause to set of clauses.
INPUT:
- ``lits`` -- a tuple of positive integers.
- ``rhs`` -- boolean (default: ``True``). Whether this XOR clause should
be evaluated to ``True`` or ``False``.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.add_xor_clause((1, 2 , 3), False) # optional - cryptominisat
"""
if 0 in lits:
raise ValueError("0 should not appear in the clause: {}".format(lits))
# cryptominisat does not handle Sage integers
lits = tuple(int(i) for i in lits)
self._nvars = max(self._nvars, max(abs(i) for i in lits))
self._solver.add_xor_clause(lits, rhs)
self._clauses.append((lits, True, rhs))
def __call__(self, assumptions=None):
r"""
Solve this instance.
OUTPUT:
- If this instance is SAT: A tuple of length ``nvars()+1``
where the ``i``-th entry holds an assignment for the
``i``-th variables (the ``0``-th entry is always ``None``).
- If this instance is UNSAT: ``False``.
EXAMPLES::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.add_clause((1,2)) # optional - cryptominisat
sage: solver.add_clause((-1,2)) # optional - cryptominisat
sage: solver.add_clause((-1,-2)) # optional - cryptominisat
sage: solver() # optional - cryptominisat
(None, False, True)
sage: solver.add_clause((1,-2)) # optional - cryptominisat
sage: solver() # optional - cryptominisat
False
"""
satisfiable, assignments = self._solver.solve()
if satisfiable:
return assignments
else:
return False
def __repr__(self):
r"""
TESTS::
sage: from sage.sat.solvers.cryptominisat import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver # optional - cryptominisat
CryptoMiniSat solver: 0 variables, 0 clauses.
"""
return "CryptoMiniSat solver: {} variables, {} clauses.".format(self.nvars(), len(self.clauses()))
def clauses(self, filename=None):
r"""
Return original clauses.
INPUT:
- ``filename`` -- if not ``None`` clauses are written to ``filename`` in
DIMACS format (default: ``None``)
OUTPUT:
If ``filename`` is ``None`` then a list of ``lits, is_xor, rhs``
tuples is returned, where ``lits`` is a tuple of literals,
``is_xor`` is always ``False`` and ``rhs`` is always ``None``.
If ``filename`` points to a writable file, then the list of original
clauses is written to that file in DIMACS format.
EXAMPLES::
sage: from sage.sat.solvers import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.add_clause((1,2,3,4,5,6,7,8,-9)) # optional - cryptominisat
sage: solver.add_xor_clause((1,2,3,4,5,6,7,8,9), rhs=True) # optional - cryptominisat
sage: solver.clauses() # optional - cryptominisat
[((1, 2, 3, 4, 5, 6, 7, 8, -9), False, None),
((1, 2, 3, 4, 5, 6, 7, 8, 9), True, True)]
DIMACS format output::
sage: from sage.sat.solvers import CryptoMiniSat
sage: solver = CryptoMiniSat() # optional - cryptominisat
sage: solver.add_clause((1, 2, 4)) # optional - cryptominisat
sage: solver.add_clause((1, 2, -4)) # optional - cryptominisat
sage: fn = tmp_filename() # optional - cryptominisat
sage: solver.clauses(fn) # optional - cryptominisat
sage: print(open(fn).read()) # optional - cryptominisat
p cnf 4 2
1 2 4 0
1 2 -4 0
<BLANKLINE>
Note that in cryptominisat, the DIMACS standard format is augmented with
the following extension: having an ``x`` in front of a line makes that
line an XOR clause::
sage: solver.add_xor_clause((1,2,3), rhs=True) # optional - cryptominisat
sage: solver.clauses(fn) # optional - cryptominisat
sage: print(open(fn).read()) # optional - cryptominisat
p cnf 4 3
1 2 4 0
1 2 -4 0
x1 2 3 0
<BLANKLINE>
Note that inverting an xor-clause is equivalent to inverting one of the
variables::
sage: solver.add_xor_clause((1,2,5),rhs=False) # optional - cryptominisat
sage: solver.clauses(fn) # optional - cryptominisat
sage: print(open(fn).read()) # optional - cryptominisat
p cnf 5 4
1 2 4 0
1 2 -4 0
x1 2 3 0
x1 2 -5 0
<BLANKLINE>
"""
if filename is None:
return self._clauses
else:
from sage.sat.solvers.dimacs import DIMACS
DIMACS.render_dimacs(self._clauses, filename, self.nvars())
class ProgramSolver():
def __init__(self, filename):
self.s = Solver(threads=3)
self.tt = 0
h2v = {} # hole 2 variable
self.maximum_variable = -1
with open(filename, 'r') as f:
for l in f:
if len(l) > len('c hole ') and l[:len('c hole ')] == 'c hole ':
ms = re.findall(r'(\d+) \- (\d+)', l)[0]
assert int(ms[0]) == int(ms[1])
ms = int(ms[0])
n = int(re.findall(r'H__\S+_(\S+)\s', l)[0])
h2v[n] = ms
elif len(l) > 0 and not 'c' in l and not 'p' in l:
vs = re.findall(r'(\-?\d+)', l)
assert vs[-1] == '0'
clause = [int(v) for v in vs[:-1]]
self.maximum_variable = max([self.maximum_variable] +
[abs(v) for v in clause])
self.s.add_clause(clause)
print "Loaded", filename, " with", len(h2v), "holes"
# convert the tape index into a sat variable
self.tape2variable = [v for h, v in sorted(h2v.items())]
# converts a sat variable to a tape index
self.variable2tape = dict([(v, h) for h, v in h2v.items()])
def generate_variable(self):
self.maximum_variable += 1
return self.maximum_variable
def random_projection(self):
self.s.add_xor_clause(
[v for v in self.variable2tape if random.random() > 0.5],
random.random() > 0.5)
def try_solving(self, assumptions=None):
print "About to run solver == == == > "
start_time = time.time()
if assumptions != None:
result = self.s.solve(assumptions)
else:
result = self.s.solve()
dt = (time.time() - start_time)
self.tt += dt
print "Ran solver in time", dt
if result[0]:
bindings = {}
for v in range(len(result[1])):
if v in self.variable2tape:
bindings[v] = result[1][v]
print "Satisfiable."
return bindings
else:
print "Unsatisfiable."
return False
def uniqueness_clause(self, tape):
p, bit_mask = parse_tape(tape)
clause = []
for j in range(len(tape)):
if bit_mask[j] == 1:
# jth tape position
v = self.tape2variable[j]
if tape[j] == 1: v = -v
clause += [v]
return clause
def is_solution_unique(self, tape):
d = self.generate_variable()
clause = [d] + self.uniqueness_clause(tape)
print "uniqueness clause", clause
self.s.add_clause(clause)
result = self.try_solving([-d])
self.s.add_clause([d]) # make the clause documents they satisfied
if result:
tp = self.holes2tape(result)
print "alternative:", parse_tape(tp)
print "alternative tape:", tp
return False
else:
return True
def holes2tape(self, result):
return [(1 if result[v] else 0) for v in self.tape2variable]
def try_sampling(self, subspace_dimension):
for j in range(subspace_dimension):
self.random_projection()
result = self.try_solving()
if result:
print "Random projection satisfied"
tp = self.holes2tape(result)
print parse_tape(tp)[0]
if self.is_solution_unique(tp):
print "Unique. Accepted."
else:
print "Sample rejected"
def adaptive_sample(self):
subspace_dimension = 1
result = self.try_solving()
if result:
print "Formula satisfied"
for j in range(subspace_dimension):
self.random_projection()
while True:
print "\n\niterating:"
result = self.try_solving()
if result:
print "Satisfied %d constraints" % subspace_dimension
tp = self.holes2tape(result)
print parse_tape(tp)
print "tape = ", tp
if self.is_solution_unique(tp):
print "UNIQUE"
print "<<< == == == >>>"
self.random_projection()
subspace_dimension += 1
else:
print "Rejected %d projections" % subspace_dimension
print "total time = ", self.tt
break
def enumerate_solutions(self):
solutions = []
result = self.try_solving()
d = self.generate_variable()
logZ = float('-inf')
while result:
tp = self.holes2tape(result)
program, mask = parse_tape(tp)
solutions = solutions + [program]
specified = sum(mask)
logZ = lse(logZ, -specified * 0.693)
print "Enumerated program", program, "with", specified, "specified bits."
self.s.add_clause([d] + self.uniqueness_clause(tp))
result = self.try_solving([-d])
print "log(z) = ", logZ, "\t1/p = ", math.exp(-logZ)
return solutions
def solve_xor(model):
s = Solver()
for clause in model.clauses:
s.add_xor_clause(_only_positive(clause), rhs=_get_clause_parity(clause))
return s.solve()
def test_binary(self) :
solver = Solver()
solver.add_xor_clause([1,2], False)
res, solution = solver.solve([1])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, True))
def test_3_long2(self) :
solver = Solver()
solver.add_xor_clause([1, 2, 3], True)
res, solution = solver.solve([1, -2])
self.assertEqual(res, True)
self.assertEqual(solution, (None, True, False, False))
def test_unit2(self) :
solver = Solver()
solver.add_xor_clause([1], True)
res, solution = solver.solve()
self.assertEqual(res, True)
self.assertEqual(solution, (None, True))
