def test_parity(self):
opb = """\
* #variable= 3 #constraint= 4
*
+1 x1 +1 x2 +1 x3 >= 1;
+1 x1 -1 x2 -1 x3 >= -1;
-1 x1 +1 x2 -1 x3 >= -1;
-1 x1 -1 x2 +1 x3 >= -1;
"""
F = CNF()
F.add_parity(["a", "b", "c"], 1)
self.assertCnfEqualsOPB(F, opb)
def test_parity(self) :
opb="""\
* #variable= 3 #constraint= 4
*
+1 x1 +1 x2 +1 x3 >= 1;
+1 x1 -1 x2 -1 x3 >= -1;
-1 x1 +1 x2 -1 x3 >= -1;
-1 x1 -1 x2 +1 x3 >= -1;
"""
F=CNF()
F.add_parity(["a","b","c"],1)
self.assertCnfEqualsOPB(F,opb)
def TseitinFormula(graph,charges=None):
"""Build a Tseitin formula based on the input graph.
Odd charge is put on the first vertex by default, unless other
vertices are is specified in input.
Arguments:
- `graph`: input graph
- `charges': odd or even charge for each vertex
"""
V=enumerate_vertices(graph)
if charges==None:
charges=[1]+[0]*(len(V)-1) # odd charge on first vertex
else:
charges = [bool(c) for c in charges] # map to boolean
if len(charges)<len(V):
charges=charges+[0]*(len(V)-len(charges)) # pad with even charges
# init formula
tse=CNF()
edgename = { }
for (u,v) in sorted(graph.edges(),key=sorted):
edgename[(u,v)] = "E_{{{0},{1}}}".format(u,v)
edgename[(v,u)] = "E_{{{0},{1}}}".format(u,v)
tse.add_variable(edgename[(u,v)])
tse.mode_strict()
# add constraints
for v,charge in zip(V,charges):
# produce all clauses and save half of them
names = [ edgename[(u,v)] for u in neighbors(graph,v) ]
tse.add_parity(names,charge)
return tse
def TseitinFormula(graph, charges=None, encoding=None):
"""Build a Tseitin formula based on the input graph.
Odd charge is put on the first vertex by default, unless other
vertices are is specified in input.
Arguments:
- `graph`: input graph
- `charges': odd or even charge for each vertex
"""
V = enumerate_vertices(graph)
if charges == None:
charges = [1] + [0] * (len(V) - 1) # odd charge on first vertex
else:
charges = [bool(c) for c in charges] # map to boolean
if len(charges) < len(V):
charges = charges + [0] * (len(V) - len(charges)
) # pad with even charges
# init formula
tse = CNF()
edgename = {}
for (u, v) in sorted(graph.edges(), key=sorted):
edgename[(u, v)] = "E_{{{0},{1}}}".format(u, v)
edgename[(v, u)] = "E_{{{0},{1}}}".format(u, v)
tse.add_variable(edgename[(u, v)])
tse.mode_strict()
# add constraints
for v, charge in zip(V, charges):
# produce all clauses and save half of them
names = [edgename[(u, v)] for u in neighbors(graph, v)]
if encoding == None:
tse.add_parity(names, charge)
else:
def toArgs(listOfTuples, operator, degree):
return list(sum(listOfTuples, ())) + [operator, degree]
terms = list(map(lambda x: (1, x), names))
w = len(terms)
k = w // 2
if encoding == "extendedPBAnyHelper":
for i in range(k):
helper = ("xor_helper", i, v)
tse.add_variable(helper)
terms.append((2, helper))
elif encoding == "extendedPBOneHelper":
helpers = list()
for i in range(k):
helper = ("xor_helper", i, v)
helpers.append(helper)
tse.add_variable(helper)
terms.append(((i + 1) * 2, helper))
tse.add_linear(*toArgs([(1, x) for x in helpers], "<=", 1))
elif encoding == "extendedPBExpHelper":
for i in range(math.ceil(math.log(k, 2)) + 1):
helper = ("xor_helper", i, v)
tse.add_variable(helper)
terms.append((2**i * 2, helper))
else:
raise ValueError("Invalid encoding '%s'" % encoding)
degree = 2 * k + (charge % 2)
tse.add_linear(*toArgs(terms, "==", degree))
return tse
