/usr/lib/python2.7/dist-packages/brial/cnf.py is in python-brial 1.2.0-2.
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from .PyPolyBoRi import (Monomial, BooleSet, Polynomial, if_then_else
as ite, lp, gauss_on_polys, ll_red_nf_redsb)
from .ll import ll_encode
from .statistics import used_vars_set
class CNFEncoder(object):
def __init__(self, r, random_seed=16):
self.random_generator = Random(random_seed)
self.one_set = r.one().set()
self.empty_set = r.zero().set()
self.r = r
def zero_blocks(self, f):
"""divides the zero set of f into blocks
>>> from brial import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.zero_blocks(r.variable(0)*r.variable(1)*r.variable(2))
[{y: 0}, {z: 0}, {x: 0}]
"""
f = Polynomial(f)
variables = f.vars_as_monomial()
space = variables.divisors()
variables = list(variables.variables())
zeros = f.zeros_in(space)
rest = zeros
res = list()
def choose_old(s):
return next(iter(rest)) # somewhat
#inefficient compared to polynomials lex_lead
def choose(s):
indices = []
assert not s.empty()
nav = s.navigation()
while not nav.constant():
e = nav.else_branch()
t = nav.then_branch()
if e.constant() and not e.terminal_one():
indices.append(nav.value())
nav = t
else:
if self.random_generator.randint(0, 1):
indices.append(nav.value())
nav = t
else:
nav = e
assert nav.terminal_one()
res = self.one_set
for i in reversed(indices):
res = ite(i, res, self.empty_set)
return next(iter(res))
while not rest.empty():
l = choose(rest)
l_variables = set(l.variables())
def get_val(var):
if var in l_variables:
return 1
return 0
block_dict = dict([(v, get_val(v)) for v in variables])
l = l.set()
self.random_generator.shuffle(variables)
for v in variables:
candidate = l.change(v.index())
if candidate.diff(zeros).empty():
l = l.union(candidate)
del block_dict[v]
rest = rest.diff(l)
res.append(block_dict)
return res
def clauses(self, f):
"""
>>> from brial import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.clauses(r.variable(0)*r.variable(1)*r.variable(2)) # doctest:+ELLIPSIS
[{...x: 0...}]
>>> e.clauses(r.variable(1)+r.variable(0)) # doctest:+ELLIPSIS
[{...x: 1...}, {...y: 1...}]
>>> [sorted(c.iteritems()) for c in e.clauses(r.variable(0)*r.variable(1)*r.variable(2))]
[[(z, 0), (y, 0), (x, 0)]]
>>> [sorted(c.iteritems()) for c in e.clauses(r.variable(1)+r.variable(0))]
[[(y, 1), (x, 0)], [(y, 0), (x, 1)]]
"""
f_plus_one = f + 1
blocks = self.zero_blocks(f + 1)
negated_blocks = [dict([(variable, 1 - value) for (variable, value)
in b.items()]) for b in blocks]
# we form an expression for a var configuration *not* lying in the
# block it is evaluated to 0 by f, iff it is not lying in any zero
# block of f+1
return negated_blocks
def polynomial_clauses(self, f):
"""
>>> from brial import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.polynomial_clauses(r.variable(0)*r.variable(1)*r.variable(2))
[x*y*z]
>>> v = r.variable
>>> p = v(1)*v(2)+v(2)*v(0)+1
>>> groebner_basis([p], heuristic = False)==groebner_basis(e.polynomial_clauses(p), heuristic = False)
True
"""
def product(l):
res = l[0]
for p in l[1:]:
res = res * p
# please care about the order of these multiplications for
# performance
return res
return [product([variable + value for (variable, value)
in b.items()]) for b in self.clauses(f)]
def to_dimacs_index(self, v):
return v.index() + 1
def dimacs_encode_clause(self, c):
def get_sign(val):
if value == 1:
return 1
return -1
items = sorted(c.items(), reverse=True)
return " ".join(
[str(v) for v in
[
get_sign(value) * self.to_dimacs_index(variable)
for (variable, value) in items] + [0]])
def dimacs_encode_polynomial(self, p):
"""
>>> from brial import *
>>> d=dict()
>>> r = declare_ring(["x", "y", "z"], d)
>>> e = CNFEncoder(r)
>>> e.dimacs_encode_polynomial(d["x"]+d["y"]+d["z"])
['1 2 -3 0', '1 -2 3 0', '-1 -2 -3 0', '-1 2 3 0']
"""
clauses = self.clauses(p)
res = []
for c in clauses:
res.append(self.dimacs_encode_clause(c))
return res
def dimacs_cnf(self, polynomial_system):
r"""
>>> from brial import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.dimacs_cnf([r.variable(0)*r.variable(1)*r.variable(2)])
'c cnf generated by PolyBoRi\np cnf 3 1\n-1 -2 -3 0'
>>> e.dimacs_cnf([r.variable(1)+r.variable(0)])
'c cnf generated by PolyBoRi\np cnf 3 2\n1 -2 0\n-1 2 0'
>>> e.dimacs_cnf([r.variable(0)*r.variable(1)*r.variable(2), r.variable(1)+r.variable(0)])
'c cnf generated by PolyBoRi\np cnf 3 3\n-1 -2 -3 0\n-1 2 0\n1 -2 0'
"""
clauses_list = [c for p in polynomial_system for c in self.
dimacs_encode_polynomial(p)]
res = ["c cnf generated by PolyBoRi"]
r = polynomial_system[0].ring()
n_variables = r.n_variables()
res.append("p cnf %s %s" % (n_variables, len(clauses_list)))
for c in clauses_list:
res.append(c)
return "\n".join(res)
class CryptoMiniSatEncoder(CNFEncoder):
group_counter = 0
def dimacs_encode_polynomial(self, p):
r"""
>>> from brial import *
>>> d=dict()
>>> r = declare_ring(["x", "y", "z"], d)
>>> e = CryptoMiniSatEncoder(r)
>>> p = d["x"]+d["y"]+d["z"]
>>> p.deg()
1
>>> len(p)
3
>>> e.dimacs_encode_polynomial(p)
['x1 2 3 0\nc g 1 x + y + z']
>>> e.dimacs_encode_polynomial(p+1)
['x1 2 -3 0\nc g 2 x + y + z + 1']
"""
if p.deg() != 1 or len(p) <= 1:
res = super(CryptoMiniSatEncoder, self).dimacs_encode_polynomial(p)
else:
if p.has_constant_part():
invert_last = True
else:
invert_last = False
variables = list(p.vars_as_monomial().variables())
indices = [self.to_dimacs_index(v) for v in variables]
if invert_last:
indices[-1] = -indices[-1]
indices.append(0)
res = ["x" + " ".join([str(v) for v in indices])]
self.group_counter = self.group_counter + 1
group_comment = "\nc g %s %s" % (self.group_counter, str(p)[:30])
return [c + group_comment for c in res]
def dimacs_cnf(self, polynomial_system):
r"""
>>> from brial import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CryptoMiniSatEncoder(r)
>>> e.dimacs_cnf([r.variable(0)*r.variable(1)*r.variable(2)])
'c cnf generated by PolyBoRi\np cnf 3 1\n-1 -2 -3 0\nc g 1 x*y*z\nc v 1 x\nc v 2 y\nc v 3 z'
>>> e.dimacs_cnf([r.variable(1)+r.variable(0)])
'c cnf generated by PolyBoRi\np cnf 3 1\nx1 2 0\nc g 2 x + y\nc v 1 x\nc v 2 y'
>>> e.dimacs_cnf([r.variable(0)*r.variable(1)*r.variable(2), r.variable(1)+r.variable(0)])
'c cnf generated by PolyBoRi\np cnf 3 2\n-1 -2 -3 0\nc g 3 x*y*z\nx1 2 0\nc g 4 x + y\nc v 1 x\nc v 2 y\nc v 3 z'
"""
uv = list(used_vars_set(polynomial_system).variables())
res = super(CryptoMiniSatEncoder, self).dimacs_cnf(polynomial_system)
res = res + "\n" + "\n".join(["c v %s %s" % (self.to_dimacs_index(v),
v) for v in uv])
return res
def _test():
import doctest
doctest.testmod()
if __name__ == "__main__":
_test()
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