def test_up_unsat():
# (x1|~x2|x3)&x2&(~x1|x3)&(x2|~x3) --> UNSAT
x1_var = Variable('x1')
x2_var = Variable('x2')
x3_var = Variable('x3')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
x3 = Literal(x3_var, negated=False)
not_x3 = Literal(x3_var, negated=True)
clauses = [[x1, not_x2, x3], [x2], [not_x1, x3], [not_x2, not_x3]]
# literal_to_clauses = {x1: {0}, not_x1: {2}, not_x2: {0, 3}, x2: {1}, x3: {0, 2}, not_x3: {3}}
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
actual_cnf = dpll.unit_propagation()
assert actual_cnf is None
assert not dpll.get_full_assignment()[x3_var]
assert dpll.get_full_assignment()[x2_var]
def test_search_complex():
# (~x|z) & (~x|~z|~y) & (~z|w) & (~w|~y) (lec3, slide 18)
# (~x1 | x2) & (~x1 | ~x2 | ~x3) & (~x2 | x4) & (~x4| ~x3)
x1_var = Variable('x1')
x2_var = Variable('x2')
x3_var = Variable('x3')
x4_var = Variable('x4')
x5_var = Variable('x5')
x6_var = Variable('x6')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
x3 = Literal(x3_var, negated=False)
not_x3 = Literal(x3_var, negated=True)
x4 = Literal(x4_var, negated=False)
not_x4 = Literal(x4_var, negated=True)
x5 = Literal(x5_var, negated=False)
not_x5 = Literal(x5_var, negated=True)
x6 = Literal(x6_var, negated=False)
not_x6 = Literal(x6_var, negated=True)
# (~x1 | x2) & (~x1 | ~x2 | ~x3) & (~x2 | x4) & (~x4| ~x3)
clauses = [[not_x1, x2], [not_x1, not_x2, not_x3], [not_x2, x4],
[not_x4, not_x3], [x5, x6], [not_x5, not_x6]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
assert search_result
def test_find_all_paths():
vars = [Variable('x{}'.format(i + 1)) for i in range(8)]
pos_l = [None] + [Literal(v, negated=False) for v in vars]
neg_l = [None] + [Literal(v, negated=True) for v in vars]
clauses = [[pos_l[1]], [neg_l[1], pos_l[5]], [neg_l[1], pos_l[3]],
[neg_l[2], neg_l[3], pos_l[4]], [neg_l[5], pos_l[2]]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
g = ImplicationGraph(cnf)
g.add_decide_node(1, pos_l[1])
g.add_node(1, pos_l[3], None, 2)
g.add_node(1, pos_l[5], None, 1)
g.add_node(1, pos_l[2], None, 4)
# g.add_node(1, pos_l[2], None, 3)
g.add_node(1, pos_l[4], None, 3)
source_node = g._nodes[pos_l[1]]
target_node = g._nodes[pos_l[4]]
actual_paths = g._find_all_paths(source_node, target_node)
expected_paths = [[
pos_l[1].variable, pos_l[5].variable, pos_l[2].variable,
pos_l[4].variable
], [pos_l[1].variable, pos_l[3].variable, pos_l[4].variable]]
assert {(frozenset(item))
for item in actual_paths} == {(frozenset(item))
for item in expected_paths}
def get_complicated_graph() -> (ImplicationGraph, int, List[Variable]):
variables = [Variable('TEMP')
] + [Variable('x{}'.format(i + 1)) for i in range(10)]
pos_l = [Literal(v, negated=False) for v in variables]
neg_l = [Literal(v, negated=True) for v in variables]
c0 = [pos_l[10]
] # unused clause to keep the numbering aligned to the slides
c1 = [pos_l[2], pos_l[3]]
c2 = [pos_l[9]
] # unused clause to keep the numbering aligned to the slides
c3 = [neg_l[3], neg_l[4]]
c4 = [neg_l[4], neg_l[2], neg_l[1]]
c5 = [neg_l[6], neg_l[5], pos_l[4]]
c6 = [pos_l[7], pos_l[5]]
c7 = [neg_l[8], pos_l[7], pos_l[6]]
conflict = [c0, c1, c2, c3, c4, c5, c6, c7]
clauses = conflict
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
g = ImplicationGraph(cnf)
g.add_decide_node(1, pos_l[1])
g.add_decide_node(2, pos_l[8])
g.add_decide_node(3, pos_l[7])
g.add_node(3, pos_l[6], None, 7)
g.add_node(3, pos_l[5], None, 6)
g.add_node(3, pos_l[4], None, 5)
g.add_node(3, neg_l[3], None, 3)
g.add_node(3, neg_l[2], None, 4)
return g, 1, variables
def test_search_complex_unsat():
variables = [Variable('TEMP')
] + [Variable('x{}'.format(i + 1)) for i in range(10)]
pos_l = [Literal(v, negated=False) for v in variables]
neg_l = [Literal(v, negated=True) for v in variables]
# x1 = T, x2 = F, x3 =
# x3 != x2 /\ x1 != x2 /\ (!x1 \/ x2 \/ !x3) /\ (x1 \/ !x2 \/ x3)
clauses = [[pos_l[1], pos_l[2]], [neg_l[1], neg_l[2]],
[pos_l[3], pos_l[2]], [neg_l[3], neg_l[2]],
[neg_l[1], pos_l[2], neg_l[3]], [pos_l[3], neg_l[2], pos_l[1]]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
# print(dpll.get_assignment())
assert not search_result
def test_search_simple_unsat():
# (x1|~x2) | (~x1 | x2)
x1_var = Variable('x1')
x2_var = Variable('x2')
# x3_var = Variable('x3')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
clauses = [[x1], [x2], [not_x1, not_x2]]
# literal_to_clauses = {x1: {0}, x2: {0}, x3: {0}} #not_x1: {2}, not_x2: {0}
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
assert not search_result
def test_search_simple():
# (x1|x2|~x3) | (x3 | ~x2)
x1_var = Variable('x1')
x2_var = Variable('x2')
x3_var = Variable('x3')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
x3 = Literal(x3_var, negated=False)
not_x3 = Literal(x3_var, negated=True)
clauses = [[x1, x2, not_x3], [x3, not_x2]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
assert search_result
def test_multi_level_deduction_sat():
x1_var = Variable('x1')
x2_var = Variable('x2')
x3_var = Variable('x3')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
x3 = Literal(x3_var, negated=False)
not_x3 = Literal(x3_var, negated=True)
clauses = [[x1], [x3, x2], [not_x2, not_x3, not_x1]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
assert search_result
def get_simple_graph() -> (ImplicationGraph, int, List[Variable]):
variables = [Variable('TEMP')
] + [Variable('x{}'.format(i + 1)) for i in range(8)]
pos_l = [Literal(v, negated=False) for v in variables]
neg_l = [Literal(v, negated=True) for v in variables]
# x1 =True --> x3=True, x5=True --> x2 = True,
clauses = [[pos_l[1]], [neg_l[1], pos_l[5]], [neg_l[1], pos_l[3]],
[neg_l[2], neg_l[3]], [neg_l[5], pos_l[2]]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
g = ImplicationGraph(cnf)
g.add_decide_node(1, pos_l[1])
g.add_node(1, pos_l[3], None, 2)
g.add_node(1, pos_l[5], None, 1)
g.add_node(1, neg_l[2], None, 4)
# g.add_node(1, pos_l[2], None, 3)
# g.add_node(1, pos_l[4], None, 3)
return g, 3, variables
def test_multi_level_conflict_sat():
vars = [Variable('x{}'.format(i + 1)) for i in range(8)]
pos_l = [None] + [Literal(v, negated=False) for v in vars]
neg_l = [None] + [Literal(v, negated=True) for v in vars]
c1 = [pos_l[2], pos_l[3]]
# c2 = [pos_l[1], pos_l[4], neg_l[8]]
c3 = [neg_l[3], neg_l[4]]
c4 = [neg_l[4], neg_l[2], neg_l[1]]
c5 = [neg_l[6], neg_l[5], pos_l[4]]
c6 = [pos_l[7], pos_l[5]]
c7 = [neg_l[8], pos_l[7], pos_l[6]]
conflict = [c3, c4, c5, c6, c7, c1] # c2,
# If we implement pure_literal will need to change this
# this is just to make sure the order decisions will be: x1=True, x2=True, x3=True, the conflict is because x1
n_temps = 4
temp_literals = [
Literal(Variable('x1_temp{}'.format(idx)), negated=False)
for idx in range(n_temps)
]
x1_clauses = [[pos_l[1], l] for l in temp_literals]
temp_literals = [
Literal(Variable('x8_temp{}'.format(idx)), negated=False)
for idx in range(n_temps)
]
x8_clauses = [[pos_l[8], l] for l in temp_literals[:-1]]
temp_literals = [
Literal(Variable('x7_temp{}'.format(idx)), negated=False)
for idx in range(n_temps)
]
x7_clauses = [[neg_l[7], l] for l in temp_literals[:-2]]
clauses = x1_clauses + x8_clauses + x7_clauses + conflict
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
assert search_result
def test_up_simple():
# (x1|~x2|x3)&x2&(~x1|x3) --> (x1|x3) & (~x1|x3)
x1_var = Variable('x1')
x2_var = Variable('x2')
x3_var = Variable('x3')
x1 = Literal(x1_var, negated=False)
not_x1 = Literal(x1_var, negated=True)
x2 = Literal(x2_var, negated=False)
not_x2 = Literal(x2_var, negated=True)
x3 = Literal(x3_var, negated=False)
clauses = [[x1, not_x2, x3], [x2], [not_x1, x3]]
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
actual_cnf = dpll.unit_propagation()
expected_cnf = [[x1, not_x2, x3], [not_x1, x3]]
assert dpll.get_full_assignment()[x2_var]
actual_cnf_real = [cl for cl in actual_cnf.clauses if cl != []]
assert actual_cnf_real == expected_cnf, dpll.get_full_assignment()
def perform_test(clauses: List[List[Literal]], debug=False):
z3_time_start = timer()
z3_res = get_z3_result(clauses, debug)
z3_time_end = timer()
our_time_start = timer()
cnf = CnfFormula(clauses)
cnf = preprocess(cnf)
dpll = DPLL(cnf)
search_result = dpll.search()
if debug:
print(dpll.get_full_assignment())
our_time_end = timer()
assert search_result == z3_res, "Our: {}, Z3: {}".format(
search_result, z3_res)
res_str = 'Sat ' if search_result else 'UNSAT '
all_vars = set([lit.variable for clause in clauses for lit in clause])
res_str += "#var: {}, #clauses: {} #per_clause: {} ".format(
len(all_vars), len(clauses), len(clauses[0]))
res_str += "Time(sec): Our {:0.2f}, z3: {:0.2f}".format(
our_time_end - our_time_start, z3_time_end - z3_time_start)
print(res_str)