def cnf_from_variables_and_clauses(variables, clauses) :
cnf = CNF()
for variable in variables :
cnf.add_variable(variable)
for clause in clauses :
cnf.add_clause(clause)
return cnf
def test_polarity_shuffle_vs_flip(self) :
cnf = CNF([[(True,'x'),(True,'y'),(False,'z')]])
variable_permutation = list(cnf.variables())
clause_permutation = range(len(cnf))
polarity_flip = [-1]*len(variable_permutation)
shuffled = Shuffle(cnf, variable_permutation, clause_permutation, polarity_flip)
flipped = FlipPolarity(cnf)
self.assertCnfEqual(flipped,shuffled)
def test_single_vertex_graph(self):
"""Singleton graph has no nontrivial automorphism."""
G1=nx.Graph()
G1.add_node(0)
cnf1 = GraphAutomorphism(G1)
v = list(cnf1.variables())[0]
cnf2 = CNF()
cnf2.add_clause([(True,v)])
cnf2.add_clause([(False,v)])
self.assertCnfEqual(cnf1,cnf2)
def test_polarity_shuffle_vs_flip(self):
cnf = CNF([[(True, 'x'), (True, 'y'), (False, 'z')]])
variable_permutation = list(cnf.variables())
clause_permutation = list(range(len(cnf)))
polarity_flip = [-1] * len(variable_permutation)
shuffled = Shuffle(cnf, variable_permutation, clause_permutation,
polarity_flip)
flipped = FlipPolarity(cnf)
self.assertCnfEqual(flipped, shuffled)
def test_one_clause(self):
dimacs = """\
p cnf 4 1
1 2 -3 -4 0
"""
opb = """\
* #variable= 4 #constraint= 1
*
+1 x1 +1 x2 -1 x3 -1 x4 >= -1;
"""
F = CNF()
F.add_clause([(True, "a"), (True, "b"), (False, "c"), (False, "d")])
F = Expand(F)
self.assertCnfEqualsDimacs(F, dimacs)
self.assertCnfEqualsOPB(F, opb)
def test_contradiction(self):
dimacs = """\
p cnf 3 1
0
"""
opb = """\
* #variable= 3 #constraint= 1
*
>= 1;
"""
F = CNF()
F.add_greater_or_equal(["a", "b", "c"], 4)
F = Expand(F)
self.assertCnfEqualsDimacs(F, dimacs)
self.assertCnfEqualsOPB(F, opb)
def test_subset_sum(self):
dimacs = """\
p cnf 3 7
-1 -2 -3 0
-1 2 -3 0
-1 2 3 0
1 -2 -3 0
1 -2 3 0
1 2 -3 0
1 2 3 0
"""
F = CNF()
F.add_linear(3, "a", 5, "b", 7, "c", "==", 8)
F = Expand(F)
self.assertCnfEqualsDimacs(F, dimacs)
def test_subset_sum(self) :
dimacs="""\
p cnf 3 7
-1 -2 -3 0
-1 2 -3 0
-1 2 3 0
1 -2 -3 0
1 -2 3 0
1 2 -3 0
1 2 3 0
"""
F=CNF()
F.add_linear(3,"a",5,"b",7,"c","==",8)
F = Expand(F)
self.assertCnfEqualsDimacs(F,dimacs)
def test_contradiction(self) :
dimacs="""\
p cnf 3 1
0
"""
opb="""\
* #variable= 3 #constraint= 1
*
>= 1;
"""
F=CNF()
F.add_greater_or_equal(["a","b","c"],4)
F = Expand(F)
self.assertCnfEqualsDimacs(F,dimacs)
self.assertCnfEqualsOPB(F,opb)
def test_one_clause(self) :
dimacs="""\
p cnf 4 1
1 2 -3 -4 0
"""
opb="""\
* #variable= 4 #constraint= 1
*
+1 x1 +1 x2 -1 x3 -1 x4 >= -1;
"""
F=CNF()
F.add_clause([(True,"a"),(True,"b"),(False,"c"),(False,"d")])
F = Expand(F)
self.assertCnfEqualsDimacs(F,dimacs)
self.assertCnfEqualsOPB(F,opb)
def test_empty_vs_empty(self):
"""Empty graphs are isomorphic."""
G1 = nx.Graph()
G2 = nx.Graph()
cnf1 = CNF()
cnf2 = GraphIsomorphism(G1, G2)
self.assertCnfEqual(cnf1, cnf2)
def test_empty_vs_non_empty(self):
"""Empty graph is not isomorphic to a non empty graph."""
G1 = nx.Graph()
G2 = nx.complete_graph(3)
cnf1 = CNF([[]]) # one empty clause
cnf2 = GraphIsomorphism(G1, G2)
self.assertCnfEqual(cnf1, cnf2)
def test_empty(self):
G = CNF()
graph=nx.Graph()
for functional in (True,False):
for onto in (True,False):
F = GraphPigeonholePrinciple(graph,functional,onto)
self.assertCnfEqual(F,G)
def build_cnf(args):
"""Build a conjunction
Arguments:
- `args`: command line options
"""
clauses = [ [(True,"x_{}".format(i))] for i in range(args.P) ] + \
[ [(False,"y_{}".format(i))] for i in range(args.N) ]
return CNF(clauses,
header="""Singleton clauses: {} positive and {} negative""".format(args.P,args.N))
def test_one_inequality(self) :
dimacs="""\
p cnf 3 3
1 2 0
1 3 0
2 3 0
"""
opb="""\
* #variable= 3 #constraint= 3
*
+1 x1 +1 x2 >= 1;
+1 x1 +1 x3 >= 1;
+1 x2 +1 x3 >= 1;
"""
F=CNF()
F.add_greater_or_equal(["a","b","c"],2)
F = Expand(F)
self.assertCnfEqualsDimacs(F,dimacs)
self.assertCnfEqualsOPB(F,opb)
def test_one_inequality(self):
dimacs = """\
p cnf 3 3
1 2 0
1 3 0
2 3 0
"""
opb = """\
* #variable= 3 #constraint= 3
*
+1 x1 +1 x2 >= 1;
+1 x1 +1 x3 >= 1;
+1 x2 +1 x3 >= 1;
"""
F = CNF()
F.add_greater_or_equal(["a", "b", "c"], 2)
F = Expand(F)
self.assertCnfEqualsDimacs(F, dimacs)
self.assertCnfEqualsOPB(F, opb)
def build_cnf(args):
"""Build an disjunction
Arguments:
- `args`: command line options
"""
clause = [ (True,"x_{}".format(i)) for i in range(args.P) ] + \
[ (False,"y_{}".format(i)) for i in range(args.N) ]
return CNF([clause],
header="""Single clause with {} positive and {} negative literals""".format(args.P,args.N))
def cnf_from_variables_and_clauses(variables, clauses):
cnf = CNF()
for variable in variables:
cnf.add_variable(variable)
for clause in clauses:
cnf.add_clause(clause)
return cnf
def test_single_vertex_graph(self):
"""Singleton graph has no nontrivial automorphism."""
G1 = nx.Graph()
G1.add_node(0)
cnf1 = GraphAutomorphism(G1)
v = list(cnf1.variables())[0]
cnf2 = CNF()
cnf2.add_clause([(True, v)])
cnf2.add_clause([(False, v)])
self.assertCnfEqual(cnf1, cnf2)
def test_simple_flip(self):
flipped = FlipPolarity(CNF([[(False, 'x'), (False, 'y'),
(True, 'z')]]))
expected = CNF([[(True, 'x'), (True, 'y'), (False, 'z')]])
self.assertCnfEqual(expected, flipped)
def test_empty(self):
G = CNF()
graph = nx.Graph()
F = EvenColoringFormula(graph)
self.assertCnfEqual(F, G)
def test_empty_graph(self):
"""Empty graph has no nontrivial automorphism."""
G1 = nx.Graph()
cnf1 = CNF([[]]) # one empty clause
cnf2 = GraphAutomorphism(G1)
self.assertCnfEqual(cnf1, cnf2)
def test_empty(self):
cnf = CNF()
lift = Expand(cnf)
self.assertCnfEqual(cnf, lift)
def reshuffle(cnf,
variable_permutation=None,
clause_permutation=None,
polarity_flip=None
):
""" Reshuffle the given cnf. Returns a formula logically
equivalent to the input with the following transformations
applied in order:
1. Polarity flips. polarity_flip is a {-1,1}^n vector. If the i-th
entry is -1, all the literals with the i-th variable change its
sign.
2. Variable permutations. variable_permutation is a permutation of
[vars(cnf)]. All the literals with the old i-th variable are
replaced with the new i-th variable.
3. Clause permutations. clause_permutation is a permutation of
[0..m-1]. The resulting clauses are reordered according to the
permutation.
"""
# empty cnf
out=CNF(header='')
out.header="Reshuffling of:\n\n"+cnf.header
variables=list(cnf.variables())
N=len(variables)
M=len(cnf)
# variable permutation
if variable_permutation==None:
variable_permutation=variables
random.shuffle(variable_permutation)
else:
assert len(variable_permutation)==N
# polarity flip
if polarity_flip==None:
polarity_flip=[random.choice([-1,1]) for x in xrange(N)]
else:
assert len(polarity_flip)==N
#
# substitution of variables
#
for v in variable_permutation:
out.add_variable(v)
substitution=[None]*(2*N+1)
reverse_idx=dict([(v,i) for (i,v) in enumerate(out.variables(),1)])
polarity_flip = [None]+polarity_flip
for i,v in enumerate(cnf.variables(),1):
substitution[i]= polarity_flip[i]*reverse_idx[v]
substitution[-i]= -substitution[i]
#
# permutation of clauses
#
if clause_permutation==None:
clause_permutation=range(M)
random.shuffle(clause_permutation)
# load clauses
out._clauses = [None]*M
for (old,new) in enumerate(clause_permutation):
out._clauses[new]=tuple( substitution[l] for l in cnf._clauses[old])
# return the formula
assert out._check_coherence(force=True)
return out
def reshuffle(cnf,
variable_permutation=None,
clause_permutation=None,
polarity_flip=None):
""" Reshuffle the given cnf. Returns a formula logically
equivalent to the input with the following transformations
applied in order:
1. Polarity flips. polarity_flip is a {-1,1}^n vector. If the i-th
entry is -1, all the literals with the i-th variable change its
sign.
2. Variable permutations. variable_permutation is a permutation of
[vars(cnf)]. All the literals with the old i-th variable are
replaced with the new i-th variable.
3. Clause permutations. clause_permutation is a permutation of
[0..m-1]. The resulting clauses are reordered according to the
permutation.
"""
# empty cnf
out = CNF(header='')
out.header = "Reshuffling of:\n\n" + cnf.header
variables = list(cnf.variables())
N = len(variables)
M = len(cnf)
# variable permutation
if variable_permutation == None:
variable_permutation = variables
random.shuffle(variable_permutation)
else:
assert len(variable_permutation) == N
# polarity flip
if polarity_flip == None:
polarity_flip = [random.choice([-1, 1]) for x in xrange(N)]
else:
assert len(polarity_flip) == N
#
# substitution of variables
#
for v in variable_permutation:
out.add_variable(v)
substitution = [None] * (2 * N + 1)
reverse_idx = dict([(v, i) for (i, v) in enumerate(out.variables(), 1)])
polarity_flip = [None] + polarity_flip
for i, v in enumerate(cnf.variables(), 1):
substitution[i] = polarity_flip[i] * reverse_idx[v]
substitution[-i] = -substitution[i]
#
# permutation of clauses
#
if clause_permutation == None:
clause_permutation = range(M)
random.shuffle(clause_permutation)
# load clauses
out._clauses = [None] * M
for (old, new) in enumerate(clause_permutation):
out._clauses[new] = tuple(substitution[l] for l in cnf._clauses[old])
# return the formula
assert out._check_coherence(force=True)
return out
def test_empty(self):
G = CNF()
graph = nx.Graph()
F = SubsetCardinalityFormula(graph)
self.assertCnfEqual(F, G)
def test_empty(self):
G = CNF()
graph = nx.Graph()
F = GraphOrderingPrinciple(graph)
self.assertCnfEqual(F, G)
def test_empty(self):
G = CNF()
graph = nx.Graph()
F = PerfectMatchingPrinciple(graph)
self.assertCnfEqual(F, G)
def test_null_graph(self):
G = nx.DiGraph()
peb = PebblingFormula(G)
self.assertTrue(peb._check_coherence())
self.assertCnfEqual(peb, CNF())