def test_AMONE():
my_TEST(my_AMONE, Clauses.AtMostOne_NSQ, 0,3, True)
my_TEST(my_AMONE, Clauses.AtMostOne_BDD, 0,3, True)
my_TEST(my_AMONE, Clauses.AtMostOne, 0,3, True)
C1 = Clauses(10)
x1 = C1.AtMostOne_BDD((1,2,3,4,5,6,7,8,9,10))
C2 = Clauses(10)
x2 = C2.AtMostOne((1,2,3,4,5,6,7,8,9,10))
assert x1 == x2 and C1.as_list() == C2.as_list()
def test_AMONE():
my_TEST(my_AMONE, Clauses.AtMostOne_NSQ, 0, 3, True)
my_TEST(my_AMONE, Clauses.AtMostOne_BDD, 0, 3, True)
my_TEST(my_AMONE, Clauses.AtMostOne, 0, 3, True)
C1 = Clauses(10)
x1 = C1.AtMostOne_BDD((1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
C2 = Clauses(10)
x2 = C2.AtMostOne((1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
assert x1 == x2 and C1.as_list() == C2.as_list()
def test_AMONE():
my_TEST(my_AMONE, Clauses.AtMostOne_NSQ, 0, 3, True)
my_TEST(my_AMONE, Clauses.AtMostOne_BDD, 0, 3, True)
my_TEST(my_AMONE, Clauses.AtMostOne, 0, 3, True)
C1 = Clauses(10)
x1 = C1.AtMostOne_BDD(tuple(range(1, 11)))
C2 = Clauses(10)
x2 = C2.AtMostOne(tuple(range(1, 11)))
assert x1 == x2 and C1.as_list() == C2.as_list()
def test_minimize():
# minimize x1 + 2 x2 + 3 x3 + 4 x4 + 5 x5
# subject to x1 + x2 + x3 + x4 + x5 == 1
C = Clauses(15)
C.Require(C.ExactlyOne, range(1, 6))
sol = C.sat()
C._clauses.unsat = True
# Unsatisfiable constraints
assert C.minimize([(k, k) for k in range(1, 6)], sol)[1] == 16
C._clauses.unsat = False
sol, sval = C.minimize([(k, k) for k in range(1, 6)], sol)
assert sval == 1
C.Require(C.ExactlyOne, range(6, 11))
# Supply an initial vector that is too short, forcing recalculation
sol, sval = C.minimize([(k, k) for k in range(6, 11)], sol)
assert sval == 6
C.Require(C.ExactlyOne, range(11, 16))
# Don't supply an initial vector
sol, sval = C.minimize([(k, k) for k in range(11, 16)])
assert sval == 11
def test_minimize():
# minimize x1 + 2 x2 + 3 x3 + 4 x4 + 5 x5
# subject to x1 + x2 + x3 + x4 + x5 == 1
C = Clauses(15)
C.Require(C.ExactlyOne, range(1,6))
sol = C.sat()
C.unsat = True
# Unsatisfiable constraints
assert C.minimize([(k,k) for k in range(1,6)], sol)[1] == 16
C.unsat = False
sol, sval = C.minimize([(k,k) for k in range(1,6)], sol)
assert sval == 1
C.Require(C.ExactlyOne, range(6,11))
# Supply an initial vector that is too short, forcing recalculation
sol, sval = C.minimize([(k,k) for k in range(6,11)], sol)
assert sval == 6
C.Require(C.ExactlyOne, range(11,16))
# Don't supply an initial vector
sol, sval = C.minimize([(k,k) for k in range(11,16)])
assert sval == 11
def sat(val):
return Clauses(max(abs(v) for v in chain(*val))).sat(val)
def test_sat():
C = Clauses()
C.new_var('x1')
C.new_var('x2')
assert C.sat() is not None
assert C.sat([]) is not None
assert C.sat([()]) is None
assert C.sat([(False, )]) is None
assert C.sat([(True, ), ()]) is None
assert C.sat([(True, False, -1)]) is not None
assert C.sat([(+1, False), (+2, ), (True, )], names=True) == {'x1', 'x2'}
assert C.sat([(-1, False), (True, ), (+2, )], names=True) == {'x2'}
assert C.sat([(True, ), (-1, ), (-2, False)], names=True) == set()
assert C.sat([(+1, ), (-1, False)], names=True) is None
C.unsat = True
assert C.sat() is None
assert C.sat([]) is None
assert C.sat([(True, )]) is None
assert len(Clauses(10).sat([[1]])) == 10
def test_LinearBound():
L = [
([], [0, 1], 10),
([], [1, 2], 10),
({
'x1': 2,
'x2': 2
}, [3, 3], 10),
({
'x1': 2,
'x2': 2
}, [0, 1], 1000),
({
'x1': 1,
'x2': 2
}, [0, 2], 1000),
({
'x1': 2,
'!x2': 2
}, [0, 2], 1000),
([(1, 1), (2, 2), (3, 3)], [3, 3], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7)], [0,
2], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7), (3, False),
(2, True)], [2, 4], 1000),
([(1, 15), (2, 16), (3, 17), (4, 18), (5, 6), (5, 19), (6, 7), (6, 20),
(7, 8), (7, 21), (7, 28), (8, 9), (8, 22), (8, 29), (8, 41), (9, 10),
(9, 23), (9, 30), (9, 42), (10, 1), (10, 11), (10, 24), (10, 31),
(10, 34), (10, 37), (10, 43), (10, 46), (10, 50), (11, 2), (11, 12),
(11, 25), (11, 32), (11, 35), (11, 38), (11, 44), (11, 47), (11, 51),
(12, 3), (12, 4), (12, 5), (12, 13), (12, 14), (12, 26), (12, 27),
(12, 33), (12, 36), (12, 39), (12, 40), (12, 45), (12, 48), (12, 49),
(12, 52), (12, 53), (12, 54)], [192, 204], 100),
]
for eq, rhs, max_iter in L:
if isinstance(eq, dict):
N = len(eq)
else:
N = max([0] +
[a for c, a in eq if a is not True and a is not False])
C = Clauses(N)
Cpos = Clauses(N)
Cneg = Clauses(N)
if isinstance(eq, dict):
for k in range(1, N + 1):
nm = 'x%d' % k
C.name_var(k, nm)
Cpos.name_var(k, nm)
Cneg.name_var(k, nm)
eq2 = [(v, C.from_name(c)) for c, v in iteritems(eq)]
else:
eq2 = eq
x = C.LinearBound(eq, rhs[0], rhs[1])
Cpos.Require(Cpos.LinearBound, eq, rhs[0], rhs[1])
Cneg.Prevent(Cneg.LinearBound, eq, rhs[0], rhs[1])
if x is not False:
for _, sol in zip(range(max_iter),
C.itersolve([] if x is True else [(x, )], N)):
assert rhs[0] <= my_EVAL(eq2, sol) <= rhs[1], C.as_list()
if x is not True:
for _, sol in zip(
range(max_iter),
C.itersolve([] if x is True else [(C.Not(x), )], N)):
assert not (rhs[0] <= my_EVAL(eq2, sol) <= rhs[1]), C.as_list()
for _, sol in zip(range(max_iter), Cpos.itersolve([], N)):
assert rhs[0] <= my_EVAL(eq2, sol) <= rhs[1], ('Cpos',
Cpos.as_list())
for _, sol in zip(range(max_iter), Cneg.itersolve([], N)):
assert not (rhs[0] <= my_EVAL(eq2, sol) <= rhs[1]), (
'Cneg', Cneg.as_list())
def my_TEST(Mfunc, Cfunc, mmin, mmax, is_iter):
for m in range(mmin, mmax + 1):
if m == 0:
ijprod = [()]
else:
ijprod = (True, False) + sum(
((k, my_NOT(k)) for k in range(1, m + 1)), ())
ijprod = product(ijprod, repeat=m)
for ij in ijprod:
C = Clauses()
Cpos = Clauses()
Cneg = Clauses()
for k in range(1, m + 1):
nm = 'x%d' % k
C.new_var(nm)
Cpos.new_var(nm)
Cneg.new_var(nm)
ij2 = tuple(C.from_index(k) if type(k) is int else k for k in ij)
if is_iter:
x = Cfunc.__get__(C, Clauses)(ij2)
Cpos.Require(Cfunc.__get__(Cpos, Clauses), ij)
Cneg.Prevent(Cfunc.__get__(Cneg, Clauses), ij)
else:
x = Cfunc.__get__(C, Clauses)(*ij2)
Cpos.Require(Cfunc.__get__(Cpos, Clauses), *ij)
Cneg.Prevent(Cfunc.__get__(Cneg, Clauses), *ij)
tsol = Mfunc(*ij)
if type(tsol) is bool:
assert x is tsol, (ij2, Cfunc.__name__, C.as_list())
assert Cpos.unsat == (not tsol) and not Cpos.as_list(), (
ij, 'Require(%s)')
assert Cneg.unsat == tsol and not Cneg.as_list(), (
ij, 'Prevent(%s)')
continue
for sol in C.itersolve([(x, )]):
qsol = Mfunc(*my_SOL(ij, sol))
assert qsol is True, (ij2, sol, Cfunc.__name__, C.as_list())
for sol in Cpos.itersolve([]):
qsol = Mfunc(*my_SOL(ij, sol))
assert qsol is True, (ij, sol, 'Require(%s)' % Cfunc.__name__,
Cpos.as_list())
for sol in C.itersolve([(C.Not(x), )]):
qsol = Mfunc(*my_SOL(ij, sol))
assert qsol is False, (ij2, sol, Cfunc.__name__, C.as_list())
for sol in Cneg.itersolve([]):
qsol = Mfunc(*my_SOL(ij, sol))
assert qsol is False, (ij, sol, 'Prevent(%s)' % Cfunc.__name__,
Cneg.as_list())
def test_sat():
C = Clauses()
C.new_var('x1')
C.new_var('x2')
assert C.sat() is not None
assert C.sat([]) is not None
assert C.sat([()]) is None
assert C.sat([(False,)]) is None
assert C.sat([(True,),()]) is None
assert C.sat([(True,False,-1)]) is not None
assert C.sat([(+1,False),(+2,),(True,)], names=True) == {'x1','x2'}
assert C.sat([(-1,False),(True,),(+2,)], names=True) == {'x2'}
assert C.sat([(True,),(-1,),(-2,False)], names=True) == set()
assert C.sat([(+1,),(-1,False)], names=True) is None
C.unsat = True
assert C.sat() is None
assert C.sat([]) is None
assert C.sat([(True,)]) is None
assert len(Clauses(10).sat([[1]])) == 10
def test_LinearBound():
L = [
([], [0, 1], 10),
([], [1, 2], 10),
({'x1':2, 'x2':2}, [3, 3], 10),
({'x1':2, 'x2':2}, [0, 1], 1000),
({'x1':1, 'x2':2}, [0, 2], 1000),
({'x1':2, '!x2':2}, [0, 2], 1000),
([(1, 1), (2, 2), (3, 3)], [3, 3], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7)], [0, 2], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7),
(3, False), (2, True)], [2, 4], 1000),
([(1, 15), (2, 16), (3, 17), (4, 18), (5, 6), (5, 19), (6, 7),
(6, 20), (7, 8), (7, 21), (7, 28), (8, 9), (8, 22), (8, 29), (8, 41), (9,
10), (9, 23), (9, 30), (9, 42), (10, 1), (10, 11), (10, 24), (10, 31),
(10, 34), (10, 37), (10, 43), (10, 46), (10, 50), (11, 2), (11, 12), (11,
25), (11, 32), (11, 35), (11, 38), (11, 44), (11, 47), (11, 51), (12, 3),
(12, 4), (12, 5), (12, 13), (12, 14), (12, 26), (12, 27), (12, 33), (12,
36), (12, 39), (12, 40), (12, 45), (12, 48), (12, 49), (12, 52), (12, 53),
(12, 54)], [192, 204], 100),
]
for eq, rhs, max_iter in L:
if isinstance(eq, dict):
N = len(eq)
else:
N = max([0]+[a for c,a in eq if a is not True and a is not False])
C = Clauses(N)
Cpos = Clauses(N)
Cneg = Clauses(N)
if isinstance(eq, dict):
for k in range(1,N+1):
nm = 'x%d'%k
C.name_var(k, nm)
Cpos.name_var(k, nm)
Cneg.name_var(k, nm)
eq2 = [(v,C.from_name(c)) for c,v in iteritems(eq)]
else:
eq2 = eq
x = C.LinearBound(eq, rhs[0], rhs[1])
Cpos.Require(Cpos.LinearBound, eq, rhs[0], rhs[1])
Cneg.Prevent(Cneg.LinearBound, eq, rhs[0], rhs[1])
if x is not False:
for _, sol in zip(range(max_iter), C.itersolve([] if x is True else [(x,)],N)):
assert rhs[0] <= my_EVAL(eq2,sol) <= rhs[1], C.clauses
if x is not True:
for _, sol in zip(range(max_iter), C.itersolve([] if x is True else [(C.Not(x),)],N)):
assert not(rhs[0] <= my_EVAL(eq2,sol) <= rhs[1]), C.clauses
for _, sol in zip(range(max_iter), Cpos.itersolve([],N)):
assert rhs[0] <= my_EVAL(eq2,sol) <= rhs[1], ('Cpos',Cpos.clauses)
for _, sol in zip(range(max_iter), Cneg.itersolve([],N)):
assert not(rhs[0] <= my_EVAL(eq2,sol) <= rhs[1]), ('Cneg',Cneg.clauses)
def my_TEST(Mfunc, Cfunc, mmin, mmax, is_iter):
for m in range(mmin,mmax+1):
if m == 0:
ijprod = [()]
else:
ijprod = (True,False)+sum(((k,my_NOT(k)) for k in range(1,m+1)),())
ijprod = product(ijprod, repeat=m)
for ij in ijprod:
C = Clauses()
Cpos = Clauses()
Cneg = Clauses()
for k in range(1,m+1):
nm = 'x%d' % k
C.new_var(nm)
Cpos.new_var(nm)
Cneg.new_var(nm)
ij2 = tuple(C.from_index(k) if type(k) is int else k for k in ij)
if is_iter:
x = Cfunc.__get__(C,Clauses)(ij2)
Cpos.Require(Cfunc.__get__(Cpos,Clauses), ij)
Cneg.Prevent(Cfunc.__get__(Cneg,Clauses), ij)
else:
x = Cfunc.__get__(C,Clauses)(*ij2)
Cpos.Require(Cfunc.__get__(Cpos,Clauses), *ij)
Cneg.Prevent(Cfunc.__get__(Cneg,Clauses), *ij)
tsol = Mfunc(*ij)
if type(tsol) is bool:
assert x is tsol, (ij2, Cfunc.__name__, C.clauses)
assert Cpos.unsat == (not tsol) and not Cpos.clauses, (ij, 'Require(%s)')
assert Cneg.unsat == tsol and not Cneg.clauses, (ij, 'Prevent(%s)')
continue
for sol in C.itersolve([(x,)]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is True, (ij2, sol, Cfunc.__name__, C.clauses)
for sol in Cpos.itersolve([]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is True, (ij, sol,'Require(%s)' % Cfunc.__name__, Cpos.clauses)
for sol in C.itersolve([(C.Not(x),)]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is False, (ij2, sol, Cfunc.__name__, C.clauses)
for sol in Cneg.itersolve([]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is False, (ij, sol,'Prevent(%s)' % Cfunc.__name__, Cneg.clauses)