class TestSolve(unittest.TestCase):
def setUp(self) :
self.solver = Solver(threads = 2)
def test_wrong_args(self):
self.assertRaises(TypeError, self.solver.add_clause, 'A')
self.assertRaises(TypeError, self.solver.add_clause, 1)
self.assertRaises(TypeError, self.solver.add_clause, 1.0)
self.assertRaises(TypeError, self.solver.add_clause, object())
self.assertRaises(TypeError, self.solver.add_clause, ['a'])
self.assertRaises(TypeError, self.solver.add_clause, [[1, 2], [3, None]])
self.assertRaises(ValueError, self.solver.add_clause, [1, 0])
def test_no_clauses(self):
for n in range(7):
self.assertEqual(self.solver.solve([]), (True, (None,)))
def test_cnf1(self):
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses1, solution))
def test_bad_iter(self):
class Liar:
def __iter__(self): return None
self.assertRaises(TypeError, self.solver.add_clause, Liar())
def test_cnf2(self):
for cl in clauses2:
self.solver.add_clause(cl)
self.assertEqual(self.solver.solve(), (False, None))
def test_cnf3(self):
for cl in clauses3:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses3, solution))
def test_cnf1_confl_limit(self):
for lim in range(1, 20):
self.setUp()
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertTrue(res == None or check_solution(clauses1, solution))
class TestDump(unittest.TestCase):
def setUp(self):
self.solver = Solver()
def test_max_glue_missing(self):
self.assertRaises(TypeError,
self.solver.start_getting_small_clauses, 4)
def test_one_dump(self):
with open("tests/test.cnf", "r") as x:
for line in x:
line = line.strip()
if "p" in line or "c" in line:
continue
out = [int(x) for x in line.split()[:-1]]
self.solver.add_clause(out)
res, _ = self.solver.solve()
self.assertEqual(res, True)
self.solver.start_getting_small_clauses(4, max_glue=10)
x = self.solver.get_next_small_clause()
self.assertNotEquals(x, None)
self.solver.end_getting_small_clauses()
def test_cnf3(self):
solver = Solver()
for cl in clauses3:
solver.add_clause(cl)
res, solution = solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses3, solution))
def test_cnf1_confl_limit(self):
for lim in range(1, 20):
solver = Solver(confl_limit=lim)
for cl in clauses1:
solver.add_clause(cl)
res, solution = solver.solve()
self.assertTrue(res == None or check_solution(clauses1, solution))
def cryptominisat_solve(self):
s = Solver()
for clause in self.clauses:
s.add_clause(clause)
sat, solution = s.solve()
if sat:
return solution
else:
return 'UNSAT'
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))
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))
class TestDump(unittest.TestCase):
def setUp(self):
self.solver = Solver()
def test_one_dump(self):
with open("tests/test.cnf", "r") as x:
for line in x:
line = line.strip()
if "p" in line or "c" in line:
continue
out = [int(x) for x in line.split()[:-1]]
self.solver.add_clause(out)
res, _ = self.solver.solve()
self.assertEqual(res, True)
self.solver.start_getting_small_clauses(4)
x = self.solver.get_next_small_clause()
self.assertNotEquals(x, None)
self.solver.end_getting_small_clauses()
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 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())
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))
def test_no_clauses(self):
solver = Solver()
for n in range(7):
self.assertEqual(solver.solve([]), (True, (None,)))
class TestSolve(unittest.TestCase):
def setUp(self):
self.solver = Solver(threads=2)
def test_wrong_args(self):
self.assertRaises(TypeError, self.solver.add_clause, 'A')
self.assertRaises(TypeError, self.solver.add_clause, 1)
self.assertRaises(TypeError, self.solver.add_clause, 1.0)
self.assertRaises(TypeError, self.solver.add_clause, object())
self.assertRaises(TypeError, self.solver.add_clause, ['a'])
self.assertRaises(TypeError, self.solver.add_clause,
[[1, 2], [3, None]])
self.assertRaises(ValueError, self.solver.add_clause, [1, 0])
def test_no_clauses(self):
for _ in range(7):
self.assertEqual(self.solver.solve([]), (True, (None, )))
def test_cnf1(self):
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses1, solution))
def test_bad_iter(self):
class Liar:
def __iter__(self):
return None
self.assertRaises(TypeError, self.solver.add_clause, Liar())
def test_cnf2(self):
for cl in clauses2:
self.solver.add_clause(cl)
self.assertEqual(self.solver.solve(), (False, None))
def test_cnf3(self):
for cl in clauses3:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses3, solution))
def test_cnf1_confl_limit(self):
for _ in range(1, 20):
self.setUp()
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertTrue(res is None or check_solution(clauses1, solution))
def test_by_re_curse(self):
self.solver.add_clause([-1, -2, 3])
res, _ = self.solver.solve()
self.assertEqual(res, True)
self.solver.add_clause([-5, 1])
self.solver.add_clause([4, -3])
self.solver.add_clause([2, 3, 5])
res, _ = self.solver.solve()
self.assertEqual(res, True)
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 Solvatore(object):
def __init__(self):
'''
Create a new Solvatore instance
'''
self.cipher = None
self.round_states =[]
self.rounds = None
self.fresh_conditions = False
self.sbox_cnfs = {}
self.model_size = 0
return
def load_cipher(self, cipher):
'''
Load a cipher description to Solvatore
'''
self.model_size = 0
self.cipher = cipher
self.state_size = cipher.state_size
self.fresh_conditions = False
self.set_rounds(cipher.rounds)
self.sbox_cnfs = {}
return
def addclause(self,clause):
self.solver.add_clause(clause)
self.model_size +=1
return
def set_rounds(self, rounds):
'''
Specify the number of times the round transition is applied
'''
rounds = int(rounds)
if not rounds >= 0:
print('The number of rounds needs to be positive')
sys.exit(1)
self.rounds = rounds
self.fresh_conditions = False
return
def create_conditions(self):
'''
Create conditions for solver from cipher description
'''
if self.cipher == None:
print('You need to load a cipher.')
sys.exit(1)
if self.rounds == None:
print('You need to specify the number of rounds.')
sys.exit(1)
if self.fresh_conditions:
return
self.solver = Solver()
self.next_variable = 1
self.state_bit = [i + 1 for i in range(self.state_size)]
state = [self.state_bit[i] for i in range(self.state_size)]
self.round_states.append(state)
self.next_variable += self.state_size
self.temporary = {i: None for i in self.cipher.temporaries}
self.sbox_tmps = {}
for rnd in range(self.rounds):
for step in self.cipher.transition:
if step[-1] == 'XOR':
self.apply_xor(step[0], step[1], step[2])
elif step[-1] == 'AND':
self.apply_and(step[0], step[1], step[2])
elif step[-1] == 'PERM':
self.apply_permutation(step[0])
elif step[-1] == 'SBOX':
self.apply_sbox(step[0], step[1], step[2])
elif step[-1] == 'MOV':
self.apply_mov(step[0], step[1])
self.set_temporaries_to_zero()
state = [self.state_bit[i] for i in range(self.state_size)]
self.round_states.append(state)
self.fresh_conditions = True
return
def apply_mov(self, target, source):
""" When target != source, we have the following allowed trails
on source, target:
0 0 -> 0 0
1 0 -> 0 1
1 0 -> 1 0
In particular, when the target is a state bit, it cannot be equal
to 1.
"""
if target == source:
return
old_source, new_source = self.get_variables(source)
old_target, new_target = self.get_variables(target)
#Ensure old target is 0
if old_target != None:
self.addclause([-old_target])
self.addclause([-old_source, new_source, new_target])
self.addclause([old_source, -new_source])
self.addclause([old_source, -new_target])
self.addclause([-new_source, -new_target])
return
def apply_xor(self, target, source_1, source_2):
""" First move source_2 to target, then apply the following
rules on source_1, target:
0 0 -> 0 0
0 1 -> 0 1
1 0 -> 1 0
1 0 -> 0 1
1 1 -> 1 1
"""
if source_1 == source_2:
old_target, new_target = self.get_variables(target)
self.addclause([-new_target])
return
if source_1 != target:
self.apply_mov(target, source_2)
source = source_1
else:
source = source_2
old_source, new_source = self.get_variables(source)
old_target, new_target = self.get_variables(target)
self.addclause([-new_source, old_source])
self.addclause([new_target, -old_target])
self.addclause([-new_source, -new_target, old_target])
self.addclause([new_source, new_target, -old_source])
self.addclause([-new_target, old_source, old_target])
self.addclause([new_source, -old_source, -old_target])
return
def apply_and(self, target, source_1, source_2):
""" First move source_2 to target, then apply the following
rules on source_1, target:
0 0 -> 0 0
0 1 -> 0 1
1 0 -> 1 0
1 0 -> 0 1
1 1 -> 0 1
"""
if source_1 == source_2:
self.apply_mov(target, source_1)
return
if source_1 != target:
self.apply_mov(target, source_2)
source = source_1
else:
source = source_2
old_source, new_source = self.get_variables(source)
old_target, new_target = self.get_variables(target)
self.addclause([-new_source, old_source])
self.addclause([new_target, -old_target])
self.addclause([-new_source, -new_target])
self.addclause([new_source, new_target, -old_source])
self.addclause([-new_target, old_source, old_target])
return
def apply_permutation(self, permutation):
'''
Relabel the state bits according to the permutation
'''
last_value = int(permutation[-1][1:])
tmp = self.state_bit[last_value]
for bit in permutation:
number = int(bit[1:])
self.state_bit[number], tmp = tmp, self.state_bit[number]
return
def apply_sbox(self, sbox_name, input_bits, output_bits):
cnf = self.get_sbox_cnf(sbox_name, len(input_bits), len(output_bits))
for bit in input_bits:
self.apply_mov('copy_' + bit, bit)
sources = [self.get_variables('copy_' + bit) for bit in input_bits]
targets = [self.get_variables(bit) for bit in output_bits]
for in_clause, out_clause in cnf:
clause = [sources[i][0] if in_clause[i] == 1 else \
-sources[i][0] for i in range(len(sources))]
clause += [targets[i][1] if out_clause[i] == 1 else \
-targets[i][1] for i in range(len(targets))]
self.addclause(clause)
# Ensure that the target bits did not contain 1s
for i in range(len(targets)):
self.addclause([-targets[i][0]])
def get_sbox_cnf(self, sbox_name, n, m):
if sbox_name in self.sbox_cnfs:
return self.sbox_cnfs[sbox_name]
if sbox_name not in self.cipher.sboxes:
raise KeyError('sbox_name not in cipher.sboxes')
sbox = self.cipher.sboxes[sbox_name]
anf = self.get_anf(sbox)
# Store the products of the output anfs in products
products = []
for output_dp in range(2**m):
# Set the empty product to the constant 1
prod = [0 for _ in range(2**n)]
prod[0] = 1
# Multiply the anfs of the selected output bits
for i in range(m):
if (output_dp >> i) & 1:
# multiply prod with output bit
result = [0 for _ in range(2**n)]
for j in range(2**n):
for k in range(2**n):
result[j|k] ^= prod[j] * ((anf[k] >> i) & 1)
prod = result
products.append(prod)
# Store guaranteed zero derivatives
zero_derivatives = []
for input_dp in range(2**n):
for output_dp in range(2**m):
prod = products[output_dp]
# If not term in the output product contains all selected
# input bits, the derivative is zero, so we store it.
if not any(input_dp & i == input_dp for i in range(2**n) if prod[i]):
zero_derivatives.append((input_dp, output_dp))
# As the zero derivatives are the transitions we want to exclude,
# we can use them to generate the CNF.
cnf = []
for in_dp, out_dp in zero_derivatives:
cnf.append((tuple(((in_dp >> i) & 1) ^ 1 for i in range(n)),\
tuple(((out_dp >> i) & 1) ^ 1 for i in range(m))))
self.sbox_cnfs[sbox_name] = cnf
return cnf
def get_anf(self, sbox):
n = int(log(len(sbox), 2))
anf = [x for x in sbox]
for i in range(n):
mask = (1 << i)
for j in range(len(anf)):
if j & mask:
anf[j] ^= anf[j^mask]
return anf
def is_sbox_bijective(self, sbox, n, m):
if n != m:
return False
if len(set(sbox[i & (2**n-1)] for i in range(2**n))) != 2**n:
return False
return True
def set_temporaries_to_zero(self):
'''
To guarantee that temporaries are zero at end of rounds
'''
for tmp in self.temporary.values():
self.addclause([-tmp])
return
def get_variables(self, bit):
if bit[0] == 's':
number = int(bit[1:])
old_bit = self.state_bit[number]
new_bit = self.next_variable
self.state_bit[number] = new_bit
self.next_variable += 1
elif bit[0] == 't':
old_bit = self.temporary[bit]
new_bit = self.next_variable
self.temporary[bit] = new_bit
self.next_variable += 1
else:
if bit in self.sbox_tmps:
old_bit = self.sbox_tmps[bit]
else:
old_bit = None
new_bit = self.next_variable
self.next_variable += 1
self.sbox_tmps[bit] = new_bit
return old_bit, new_bit
def is_bit_balanced(self, bit, rnd, active):
self.create_conditions()
if bit >= self.state_size:
raise ValueError("There are only {} state bits."\
.format(self.state_size))
active_bits = map(int, active)
for active_bit in active_bits:
if active_bit >= self.state_size or active_bit < 0:
print('Bit {} designated as active bit, but there are only '
'{} state bits.'.format(active_bit, self.state_size))
sys.exit(1)
conditions = []
for i in range(self.state_size):
if i in active_bits:
conditions.append(self.round_states[0][i])
else:
conditions.append(-self.round_states[0][i])
for i in range(self.state_size):
if i != bit:
conditions.append(-self.round_states[rnd][i])
else:
conditions.append(self.round_states[rnd][i])
unbalanced, _ = self.solver.solve(conditions)
return not unbalanced
def distinguisher_exists(self, rnd):
#TODO: not working at the moment
self.create_conditions()
# No all zero input, no all active input
input_allzero = [self.round_states[0][i] for i in range(self.state_size)]
input_allone = [-self.round_states[0][i] for i in range(self.state_size)]
self.addclause(input_allzero)
self.addclause(input_allone)
# At least one unit vector reachable
out_cond = [self.round_states[rnd][i] for i in range(self.state_size)]
self.addclause(out_cond)
# No pair should be sat together
for pair in combinations(range(self.state_size), 2):
exclude_pair = [-self.round_states[rnd][pair[0]],
-self.round_states[rnd][pair[1]]]
self.addclause(exclude_pair)
sat, solution = self.solver.solve()
# for r in range(rnd + 1):
# print("\nRound {}: ".format(r))
# for i in self.round_states[r]:
# print int(solution[i]),
return sat, solution
def is_reachable(self, output_bits, rnd, active_bits):
self.create_conditions()
conditions = []
for i in range(self.state_size):
if i in active_bits:
conditions.append(self.round_states[0][i])
else:
conditions.append(-self.round_states[0][i])
for i in range(self.state_size):
if i not in output_bits:
conditions.append(-self.round_states[rnd][i])
else:
conditions.append(self.round_states[rnd][i])
reachable, _ = self.solver.solve(conditions)
return reachable
def solve_or(model):
s = Solver()
for clause in model.clauses:
s.add_clause(clause)
return s.solve()
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))
class SatHandler:
def __init__(self, tracesList, numOfInputs, usePyCrypto=False):
self.numOfInputs = numOfInputs
self.tracesList = tracesList
self.usePyCrypto = usePyCrypto
self.s = None
if self.usePyCrypto and PyCryptoSat_Import_Successful:
self.s = Solver()
print("Initialized solver")
self.clauses = ClauseHandler()
## Creates the acyclic Fsm of trace nodes.
self.constructTraceTree() # self.traceTree is created and filled
self.numOfTraceNodes = len(self.traceTree.nodes)
###
#This variable is used as global, handle with care
self.numOfNodes = 0
###
def varToNum(self, var):
x, s = var.split("_")
return int(x) * self.numOfNodes + int(s) + 1
def numToVar(self, num):
num -= 1
return "{}_{}".format(int(num / self.numOfNodes), num % self.numOfNodes)
def newVarToNum(self, newVar):
## newVar syntax is "y_a_i_j"
y, a, i, j = newVar.split("_")
a = int(a)
# a+1 so that it doesn't clash with normal vars
offset = (self.numOfTraceNodes * self.numOfNodes) * (a+1)
return offset + self.varToNum(i+"_"+j)
def numToNewVar(self, num):
offset = self.numOfTraceNodes * self.numOfNodes
offsetCount = int(num/offset)
a = offsetCount - 1
num = num - offset * offsetCount
x, s = self.numToVar(num).split("_")
return "y_{}_{}_{}".format(a, x, s)
def constructTraceTree(self, nameInBreathFirst = True):
self.traceTree = FSM(0, self.numOfInputs, 0) # numOfNodes, numOfInputs, numOfOutputs
rootNode = FSM.Node(self.numOfInputs, 0) # 0 is the index
self.traceTree.nodes.append(rootNode)
currentNode = rootNode
temp = None
for trace in self.tracesList:
currentNode = rootNode #reset this
temp = None
for ioTuple in trace:
# This transition exists
if currentNode.transitions[ioTuple[0]][0] != None:
currentNode = currentNode.transitions[ioTuple[0]][0] # Keep moving
# This transition is new, create new branch
else:
temp = FSM.Node(self.numOfInputs, len(self.traceTree.nodes))
self.traceTree.nodes.append(temp)
currentNode.transitions[ioTuple[0]] = (temp, ioTuple[1])
currentNode = temp
### Name the nodes in a BDF way if the argument is true
if nameInBreathFirst:
newNodeList = []
nodeQ = deque()
nodeQ.append(rootNode)
while len(nodeQ) != 0:
currentNode = nodeQ.popleft()
for transition in currentNode.transitions:
if transition[0] != None:
transition[0].parent = currentNode
nodeQ.append(transition[0])
## Set the index and append to the list
currentNode.index = len(newNodeList)
newNodeList.append(currentNode)
self.traceTree.nodes = newNodeList
def constructClauses(self, writeToFile=False, filename="SatFile", numOfNodes=-1):
#This is for debugging
if numOfNodes != -1:
self.numOfNodes = numOfNodes
countClauses = 0
#
#Each trace node must correspond to at least one node
#Does not the 0_0 condition
#
for i in range(self.numOfTraceNodes):
tempList = []
for k in range(self.numOfNodes):
tempList.append("x_{}_{}".format(i, k))
self.clauses.addClause(tempList)
countClauses += 1
#
#Each trace node must correspond to at most one node
#
for i in range(self.numOfTraceNodes):
for k in range(self.numOfNodes - 1):
for j in range(k + 1, self.numOfNodes):
self.clauses.addClause(["-x_{}_{}".format(i,k), "-x_{}_{}".format(i,j)])
countClauses += 1
#
#Check each transition between tracenodes and act accordingly
#
for i in range(self.numOfTraceNodes - 1):
for j in range(i + 1, self.numOfTraceNodes):
for k in range(len(self.traceTree.nodes[i].transitions)):
# if outputs are not None
if (self.traceTree.nodes[i].transitions[k][1] != None and self.traceTree.nodes[j].transitions[k][1] != None):
#if outputs are different
if (self.traceTree.nodes[i].transitions[k][1] != self.traceTree.nodes[j].transitions[k][1]):
for h in range(self.numOfNodes):
self.clauses.addClause(["-x_{}_{}".format(i,h), "-x_{}_{}".format(j,h)])
countClauses += 1
break
for x in range(self.numOfTraceNodes):
for a in range(len(self.traceTree.nodes[x].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[x].transitions[a][0] != None:
#file.write("y_a_i_j -x_i -x.transitions[a][0]_j")
self.clauses.addClause(["y_{}_{}_{}".format(a,i,j), "-x_{}_{}".format(x,i), "-x_{}_{}".format(self.traceTree.nodes[x].transitions[a][0].index, j)])
countClauses += 1
for a in range(len(self.traceTree.nodes[0].transitions)):
for i in range(self.numOfNodes):
for h in range(self.numOfNodes - 1):
for j in range(h + 1, self.numOfNodes):
self.clauses.addClause(["-y_{}_{}_{}".format(a,i,h), "-y_{}_{}_{}".format(a,i,j)])
countClauses += 1
for a in range(len(self.traceTree.nodes[0].transitions)):
for i in range(self.numOfNodes):
tempList = []
for j in range(self.numOfNodes):
tempList.append("y_{}_{}_{}".format(a,i,j))
self.clauses.addClause(tempList)
countClauses += 1
for x in range(self.numOfTraceNodes):
for a in range(len(self.traceTree.nodes[x].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[x].transitions[a][0] != None:
self.clauses.addClause(["-y_{}_{}_{}".format(a,i,j), "-x_{}_{}".format(x,i), "x_{}_{}".format(self.traceTree.nodes[x].transitions[a][0].index, j)])
countClauses += 1
if not self.usePyCrypto:
varCount = self.numOfNodes * self.numOfTraceNodes * (len(self.traceTree.nodes[0].transitions) + 1)
self.clauses.addFirstLine("p cnf {} {}".format(varCount, countClauses))
self.clauses.writeTheFile()
def constructSatFile(self, writeFile=True, filename="SatFile", verbose=True, numOfNodes=-1):
#This is for debugging
if numOfNodes != -1:
self.numOfNodes = numOfNodes
file = FileHandler(filename)
clauseHandler = ClauseHandler(filename)
countClauses = 0
#
#Each trace node must correspond to at least one node
#Contains the 0_0 condition
#
if verbose:
file.writeComment("##### Each must correspond to at least one node #####")
for i in range(self.numOfTraceNodes):
tempStr = ""
commentStr = ""
for k in range(self.numOfNodes): #min(i+1, self.numOfNodes
tempStr += "{} ".format(self.varToNum("{}_{}".format(i, k)))
commentStr += "{}_{} ".format(i, k)
if verbose:
file.writeComment(commentStr)
file.write(tempStr)
countClauses += 1
#
#Each trace node must correspond to at most one node
#
if verbose:
file.writeComment("##### Each must correspond to at most one node #####")
for i in range(self.numOfTraceNodes):
for k in range(self.numOfNodes - 1):
for j in range(k + 1, self.numOfNodes):
if verbose:
file.writeComment("-{}_{} -{}_{}".format(i, k, i, j))
file.write("-{} -{}".format(self.varToNum("{}_{}".format(i, k)), self.varToNum("{}_{}".format(i, j))))
countClauses += 1
#
#Check each trasition between tracenodes and act accordingly
#
for i in range(self.numOfTraceNodes - 1):
for j in range(i + 1, self.numOfTraceNodes):
for k in range(len(self.traceTree.nodes[i].transitions)):
# if outputs are not None
if (self.traceTree.nodes[i].transitions[k][1] != None and self.traceTree.nodes[j].transitions[k][1] != None):
#if outputs are different
if (self.traceTree.nodes[i].transitions[k][1] != self.traceTree.nodes[j].transitions[k][1]):
for h in range(self.numOfNodes):
if verbose:
file.writeComment("-{}_{} -{}_{}".format(i, h, j, h))
file.write("-{} -{}".format(self.varToNum("{}_{}".format(i, h)), self.varToNum("{}_{}".format(j, h))))
countClauses += 1
break
#if outputs are same
"""
# The Auxiliary variables will replace these
else:
iP = self.traceTree.nodes[i].transitions[k][0].index
jP = self.traceTree.nodes[j].transitions[k][0].index
for h in range(self.numOfNodes):
for hP in range(self.numOfNodes):
if verbose:
file.writeComment("-{}_{} -{}_{} -{}_{} {}_{}".format(i, h, j, h, iP, hP, jP, hP))
file.write("-{} -{} -{} {}".format(self.varToNum("{}_{}".format(i, h)),\
self.varToNum("{}_{}".format(j, h)),\
self.varToNum("{}_{}".format(iP, hP)),\
self.varToNum("{}_{}".format(jP, hP))))
countClauses += 1
"""
for x in range(self.numOfTraceNodes):
for a in range(len(self.traceTree.nodes[x].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[x].transitions[a][0] != None:
#file.write("y_a_i_j -x_i -x.transitions[a][0]_j")
file.writeComment("y_{}_{}_{} -{}_{} -{}_{}".format(a, i, j, \
x, i, \
self.traceTree.nodes[x].transitions[a][0].index, j))
file.write("{} -{} -{}".format(self.newVarToNum("y_{}_{}_{}".format(a, i, j)), \
self.varToNum("{}_{}".format(x, i)), \
self.varToNum("{}_{}".format(self.traceTree.nodes[x].transitions[a][0].index, j))))
countClauses += 1
for a in range(len(self.traceTree.nodes[0].transitions)):
for i in range(self.numOfNodes):
for h in range(self.numOfNodes - 1):
for j in range(h + 1, self.numOfNodes):
file.writeComment("-y_{}_{}_{} -y_{}_{}_{}".format(a,i,h,\
a,i,j))
file.write("-{} -{}".format(self.newVarToNum("-y_{}_{}_{}".format(a,i,h)), \
self.newVarToNum("-y_{}_{}_{}".format(a,i,j))))
countClauses += 1
for a in range(len(self.traceTree.nodes[0].transitions)):
for i in range(self.numOfNodes):
tempStr = ""
commentStr = ""
for j in range(self.numOfNodes):
commentStr += "y_{}_{}_{} ".format(a, i, j)
tempStr += "{} ".format(self.newVarToNum("y_{}_{}_{}".format(a, i, j)))
file.writeComment(commentStr)
file.write(tempStr)
countClauses += 1
for x in range(self.numOfTraceNodes):
for a in range(len(self.traceTree.nodes[x].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[x].transitions[a][0] != None:
#file.write("y_a_i_j -x_i -x.transitions[a][0]_j")
file.writeComment("-y_{}_{}_{} -{}_{} {}_{}".format(a, i, j, \
x, i, \
self.traceTree.nodes[x].transitions[a][0].index, j))
file.write("-{} -{} {}".format(self.newVarToNum("y_{}_{}_{}".format(a, i, j)), \
self.varToNum("{}_{}".format(x, i)), \
self.varToNum("{}_{}".format(self.traceTree.nodes[x].transitions[a][0].index, j))))
countClauses += 1
varCount = self.numOfNodes * self.numOfTraceNodes * (len(self.traceTree.nodes[0].transitions) + 1)
file.addFirstLine("p cnf {} {}".format(varCount, countClauses))
file.writeTheFile()
def checkOutput(self, filename="satOutput", onlyCheck=False):
with open(filename, "r") as f:
#if the output has no solution, dont continue
if f.readline().strip() != "s SATISFIABLE":
return (False, None)
#if the output has a solution BUT the onlyCheck parameter is true, dont read the output
elif onlyCheck:
return (True, None)
output = []
for line in f.readlines():
for var in line.split()[1:]:
if var[0] != "-" and var != "0":
output.append(self.numToVar(int(var)))
return (True, output)
def addFormulasForSingleVariable(self, traceNo=0, numOfNodes=-1):
if numOfNodes == -1:
self.numOfNodes = numOfNodes
if traceNo == 0:
print("addFormulasForSingleVariable -> You should gice the traceNo to use this function!")
return
#This trace must be at least one of the nodes
tempList = []
for k in range(self.numOfNodes):
tempList.append("x_{}_{}".format(traceNo, k))
self.clauses.addClause(tempList)
for k in range(self.numOfNodes - 1):
for j in range(k + 1, self.numOfNodes):
self.clauses.addClause(["-x_{}_{}".format(traceNo,k), "-x_{}_{}".format(traceNo,j)])
countClauses += 1
for j in range(traceNo):
for k in range(len(self.traceTree.nodes[traceNo].transitions)):
# if outputs are not None
if (self.traceTree.nodes[traceNo].transitions[k][1] != None and self.traceTree.nodes[j].transitions[k][1] != None):
#if outputs are different
if (self.traceTree.nodes[traceNo].transitions[k][1] != self.traceTree.nodes[j].transitions[k][1]):
for h in range(self.numOfNodes):
self.clauses.addClause(["-x_{}_{}".format(traceNo,h), "-x_{}_{}".format(j,h)])
countClauses += 1
break
for a in range(len(self.traceTree.nodes[traceNo].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[traceNo].transitions[a][0] != None:
#file.write("y_a_i_j -x_i -x.transitions[a][0]_j")
self.clauses.addClause(["y_{}_{}_{}".format(a,i,j), "-x_{}_{}".format(traceNo,i), "-x_{}_{}".format(self.traceTree.nodes[traceNo].transitions[a][0].index, j)])
countClauses += 1
#Auxiliary for this
for a in range(len(self.traceTree.nodes[traceNo].transitions)):
for i in range(self.numOfNodes):
for j in range(self.numOfNodes):
if self.traceTree.nodes[traceNo].transitions[a][0] != None:
self.clauses.addClause(["-y_{}_{}_{}".format(a,i,j), "-x_{}_{}".format(traceNo,i), "x_{}_{}".format(self.traceTree.nodes[traceNo].transitions[a][0].index, j)])
countClauses += 1
def oldfindFsmConsecutive(self, filename="SatFile", outputFile="satOutput"):
self.numOfNodes = 1
FOUND = False
startTime = time.time()
totalSolveTime = 0
totalFileTime = 0
while not FOUND:
print("Trying with", self.numOfNodes, "nodes...")
if self.usePyCrypto:
self.s = Solver() #Reinitialize
sTime = time.time()
self.constructClauses()
self.clauses.addToSolver(self.s)
endTime = time.time()-sTime
totalFileTime += endTime
print("Sat preperations took", endTime, "seconds")
sTime = time.time()
isSatisfiable, output = self.s.solve()
solveEnd = time.time()-sTime
totalSolveTime += solveEnd
print("Solving took", solveEnd, "seconds")
else:
sFileTime = time.time()
self.constructClauses()
fileEnd = time.time()-sFileTime
totalFileTime += fileEnd
print("Sat file construction took", fileEnd, "seconds")
solveTime = time.time()
subprocess.run("cryptominisat5 --verb 0 {} > {}".format(filename, outputFile), shell=True)
solveEnd = time.time()-solveTime
totalSolveTime += solveEnd
print("Solving took", solveEnd, "seconds")
isSatisfiable, output = self.checkOutput()
if isSatisfiable:
print("Satisfiable with", self.numOfNodes, "nodes!")
print("Total construction time:", totalFileTime, "seconds")
print("Total solving time:", totalSolveTime, "seconds")
print("\nConsecutive approach took", time.time()-startTime, "seconds.")
print()
FOUND = True
self.numOfNodes += 1
return output
def getFsmFromSolution(self, output):
switchValueKey = {}
for key, value in self.clauses.clausedict.items():
if key[0] == "x":
switchValueKey[value] = key[2:]
#init the fsm
traceFsm = FSM(self.numOfNodes, self.numOfInputs, 0)
traceToNode = {}
for i in range(1, len(output)):
if output[i]: # only check true ones
## continu here
def findFsmConsecutive(self, filename="SatFile", outputFile="satOutput"):
self.numOfNodes = 7
FOUND = False
startTime = time.time()
totalSolveTime = 0
totalFileTime = 0
while not FOUND:
def findFsmBinary(self, filename="SatFile", outputFile="satOutput"):
minNumOfNodes = 0
maxNumOfNodes = -1
self.numOfNodes = 1
lastOutput = None
FOUND = False
startTime = time.time()
while not FOUND:
if maxNumOfNodes == -1:
self.numOfNodes *= 2
else:
self.numOfNodes = int((minNumOfNodes + maxNumOfNodes)/2)
print("Trying with", self.numOfNodes, "nodes...")
self.constructSatFile()
subprocess.run("cryptominisat5 --verb 0 {} > {}".format(filename, outputFile), shell=True)
isSatisfiable, output = self.checkOutput()
if isSatisfiable:
print("Satisfiable with", self.numOfNodes, "nodes!")
lastOutput = output
maxNumOfNodes = self.numOfNodes
else:
print("Not satisfiable with", self.numOfNodes, "nodes.")
minNumOfNodes = self.numOfNodes
if minNumOfNodes == maxNumOfNodes - 1:
print("Merged at", self.numOfNodes, "nodes!")
print("\nBinary approach took", time.time()-startTime, "seconds.")
FOUND = True
return lastOutput
def findFsm(self, tryBinarySearch=False, filename="SatFile", outputFile="satOutput"):
if tryBinarySearch:
return self.findFsmBinary(filename, outputFile)
else:
return self.findFsmConsecutive(filename, outputFile)
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))
class TestSolve(unittest.TestCase):
def setUp(self):
self.solver = Solver(threads=2)
def test_wrong_args(self):
self.assertRaises(TypeError, self.solver.add_clause, 'A')
self.assertRaises(TypeError, self.solver.add_clause, 1)
self.assertRaises(TypeError, self.solver.add_clause, 1.0)
self.assertRaises(TypeError, self.solver.add_clause, object())
self.assertRaises(TypeError, self.solver.add_clause, ['a'])
self.assertRaises(TypeError, self.solver.add_clause,
[[1, 2], [3, None]])
self.assertRaises(ValueError, self.solver.add_clause, [1, 0])
def test_no_clauses(self):
for _ in range(7):
self.assertEqual(self.solver.solve([]), (True, (None, )))
def test_cnf1(self):
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses1, solution))
def test_add_clauses(self):
self.solver.add_clauses([[1], [-1]])
res, solution = self.solver.solve()
self.assertEqual(res, False)
def test_add_clauses_wrong_zero(self):
self.assertRaises(TypeError, self.solver.add_clause, [[1, 0], [-1]])
def test_add_clauses_array_SAT(self):
cls = array('i', [1, 2, 0, 1, 2, 0])
self.solver.add_clauses(cls)
res, solution = self.solver.solve()
self.assertEqual(res, True)
def test_add_clauses_array_UNSAT(self):
cls = array('i', [-1, 0, 1, 0])
self.solver.add_clauses(cls)
res, solution = self.solver.solve()
self.assertEqual(res, False)
def test_add_clauses_array_unterminated(self):
cls = array('i', [1, 2, 0, 1, 2])
self.assertRaises(ValueError, self.solver.add_clause, cls)
def test_bad_iter(self):
class Liar:
def __iter__(self):
return None
self.assertRaises(TypeError, self.solver.add_clause, Liar())
def test_get_conflict(self):
self.solver.add_clauses([[-1], [2], [3], [-4]])
assume = [-2, 3, 4]
res, model = self.solver.solve(assumptions=assume)
self.assertEqual(res, False)
confl = self.solver.get_conflict()
self.assertEqual(isinstance(confl, list), True)
self.assertNotIn(3, confl)
if 2 in confl:
self.assertIn(2, confl)
elif -4 in confl:
self.assertIn(-4, confl)
else:
self.assertEqual(False,
True,
msg="Either -2 or 4 should be conflicting!")
assume = [2, 4]
res, model = self.solver.solve(assumptions=assume)
self.assertEqual(res, False)
confl = self.solver.get_conflict()
self.assertEqual(isinstance(confl, list), True)
self.assertNotIn(2, confl)
self.assertIn(-4, confl)
def test_cnf2(self):
for cl in clauses2:
self.solver.add_clause(cl)
self.assertEqual(self.solver.solve(), (False, None))
def test_cnf3(self):
for cl in clauses3:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses3, solution))
def test_cnf1_confl_limit(self):
for _ in range(1, 20):
self.setUp()
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertTrue(res is None or check_solution(clauses1, solution))
def test_by_re_curse(self):
self.solver.add_clause([-1, -2, 3])
res, _ = self.solver.solve()
self.assertEqual(res, True)
self.solver.add_clause([-5, 1])
self.solver.add_clause([4, -3])
self.solver.add_clause([2, 3, 5])
res, _ = self.solver.solve()
self.assertEqual(res, True)
class TestSolve(unittest.TestCase):
def setUp(self):
self.solver = Solver(threads=2)
def test_wrong_args(self):
self.assertRaises(TypeError, self.solver.add_clause, 'A')
self.assertRaises(TypeError, self.solver.add_clause, 1)
self.assertRaises(TypeError, self.solver.add_clause, 1.0)
self.assertRaises(TypeError, self.solver.add_clause, object())
self.assertRaises(TypeError, self.solver.add_clause, ['a'])
self.assertRaises(
TypeError, self.solver.add_clause, [[1, 2], [3, None]])
self.assertRaises(ValueError, self.solver.add_clause, [1, 0])
def test_no_clauses(self):
for _ in range(7):
self.assertEqual(self.solver.solve([]), (True, (None,)))
def test_cnf1(self):
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses1, solution))
def test_add_clauses(self):
self.solver.add_clauses([[1], [-1]])
res, solution = self.solver.solve()
self.assertEqual(res, False)
def test_add_clauses_wrong_zero(self):
self.assertRaises(TypeError, self.solver.add_clause, [[1, 0], [-1]])
def test_add_clauses_array_SAT(self):
cls = array('i', [1, 2, 0, 1, 2, 0])
self.solver.add_clauses(cls)
res, solution = self.solver.solve()
self.assertEqual(res, True)
def test_add_clauses_array_UNSAT(self):
cls = array('i', [-1, 0, 1, 0])
self.solver.add_clauses(cls)
res, solution = self.solver.solve()
self.assertEqual(res, False)
def test_add_clauses_array_unterminated(self):
cls = array('i', [1, 2, 0, 1, 2])
self.assertRaises(ValueError, self.solver.add_clause, cls)
def test_bad_iter(self):
class Liar:
def __iter__(self):
return None
self.assertRaises(TypeError, self.solver.add_clause, Liar())
def test_get_conflict(self):
self.solver.add_clauses([[-1], [2], [3], [-4]])
assume = [-2, 3, 4]
res, model = self.solver.solve(assumptions=assume)
self.assertEqual(res, False)
confl = self.solver.get_conflict()
self.assertEqual(isinstance(confl, list), True)
self.assertNotIn(3, confl)
if 2 in confl:
self.assertIn(2, confl)
elif -4 in confl:
self.assertIn(-4, confl)
else:
self.assertEqual(False, True, msg="Either -2 or 4 should be conflicting!")
assume = [2, 4]
res, model = self.solver.solve(assumptions=assume)
self.assertEqual(res, False)
confl = self.solver.get_conflict()
self.assertEqual(isinstance(confl, list), True)
self.assertNotIn(2, confl)
self.assertIn(-4, confl)
def test_cnf2(self):
for cl in clauses2:
self.solver.add_clause(cl)
self.assertEqual(self.solver.solve(), (False, None))
def test_cnf3(self):
for cl in clauses3:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertEqual(res, True)
self.assertTrue(check_solution(clauses3, solution))
def test_cnf1_confl_limit(self):
for _ in range(1, 20):
self.setUp()
for cl in clauses1:
self.solver.add_clause(cl)
res, solution = self.solver.solve()
self.assertTrue(res is None or check_solution(clauses1, solution))
def test_by_re_curse(self):
self.solver.add_clause([-1, -2, 3])
res, _ = self.solver.solve()
self.assertEqual(res, True)
self.solver.add_clause([-5, 1])
self.solver.add_clause([4, -3])
self.solver.add_clause([2, 3, 5])
res, _ = self.solver.solve()
self.assertEqual(res, True)
def solve_sat(self):
solver = Solver()
for clause in self.formula:
solver.add_clause(clause)
sat, assignments = solver.solve()
return sat
def test_cnf2(self):
solver = Solver()
for cl in clauses2:
solver.add_clause(cl)
self.assertEqual(solver.solve(), (False, None))