Exemple #1
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 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
Exemple #2
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    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)
Exemple #4
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    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)
Exemple #5
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 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)
Exemple #6
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 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)
Exemple #7
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 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)
Exemple #8
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 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)
Exemple #9
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 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)
Exemple #10
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 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)
Exemple #14
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    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))
Exemple #15
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 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)
Exemple #16
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 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)
Exemple #17
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    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))
Exemple #18
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 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)
Exemple #20
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 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)
Exemple #23
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 def test_empty(self):
     cnf = CNF()
     lift = Expand(cnf)
     self.assertCnfEqual(cnf, lift)
Exemple #24
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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
Exemple #25
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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)
Exemple #27
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 def test_empty(self):
     G = CNF()
     graph = nx.Graph()
     F = GraphOrderingPrinciple(graph)
     self.assertCnfEqual(F, G)
Exemple #28
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 def test_empty(self):
     G = CNF()
     graph = nx.Graph()
     F = PerfectMatchingPrinciple(graph)
     self.assertCnfEqual(F, G)
Exemple #29
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 def test_null_graph(self):
     G = nx.DiGraph()
     peb = PebblingFormula(G)
     self.assertTrue(peb._check_coherence())
     self.assertCnfEqual(peb, CNF())