def test_sat_negative(self):
solver = self.get_solver()
solver.add(expr.And(*self.pos))
solver.add(expr.And(*(~p for p in self.pos)))
solution = solver.solve()
self.assertIsNone(solution)
def test_not_at_most_one(self):
self.function = expr.And(self.pos, expr.exprvar("b"),
~expr.Or(*self.neg))
cardinality = constraint.at_most_one(self.function.support)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNone(sat)
def test_equals_one(self, function):
cardinality_a = constraint.equals_one(function.support)
sat_a = expr.And(function, *cardinality_a).to_cnf().satisfy_one()
cardinality_b = constraint.equals(function.support, 1)
sat_b = expr.And(function, *cardinality_b).to_cnf().satisfy_one()
self.assertEqual(sat_a is None, sat_b is None)
def test_sat_positive(self):
solver = self.get_solver()
solver.add(expr.And(*self.pos))
solver.add(expr.And(*(~n for n in self.neg)))
solution = solver.solve()
expected = dict(it.chain(((p, True) for p in self.pos),
((n, False) for n in self.neg)))
self.assertIsNotNone(solution)
self.assertEqual(expected, solution)
def test_not_at_most_one_not_equivalent(self):
self.function = expr.And(self.pos, expr.exprvar("b"),
~expr.Or(*self.neg))
at_most = expr.exprvar("at_most")
cardinality = constraint.at_most_one(self.function.support, ~at_most)
sat = expr.And(self.function, at_most,
*cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(at_most), 1)
def test_at_least_one_not_equivalent(self, function):
equivalent = expr.exprvar("equivalent")
cardinality_a = constraint.at_least_one(function.support, ~equivalent)
sat_a = expr.And(function, ~equivalent,
*cardinality_a).to_cnf().satisfy_one()
cardinality_b = constraint.at_least(function.support, 1, ~equivalent)
sat_b = expr.And(function, ~equivalent,
*cardinality_b).to_cnf().satisfy_one()
self.assertEqual(sat_a is None, sat_b is None)
if sat_a or sat_b:
self.assertEqual(sat_a.get(equivalent), sat_b.get(equivalent))
def satisfies(spc, f):
"""
Return True if the spec (which must be BOTH) satisfies formula f.
"""
assert spc.spec_type == spec.ShapeSpecTypes.BOTH, "must pass in both type"
spc_expr = spc.to_expr()
return expr.And(spc_expr, f).satisfy_one() is not None
def expr_is_vacuous(f):
"""
Vacuous if every shape applies to this.
"""
return all(
expr_is_satisfiable(expr.And(f, spc.to_expr()))
for spc in spec.ShapeSpec.enumerate_both())
def test_at_least_one(self):
cardinality = cardnet.at_least(self.function.support, 1)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
solution = {x: sat.get(x) for x in self.pos}
self.assertEqual(solution, {x: 1 for x in self.pos})
def test_qbf_negative(self):
solver = self.get_solver()
solver.forall(self.pos)
solver.add(expr.And(*self.pos))
solution = solver.solve()
self.assertIsNone(solution)
def test_at_most_one_zero(self):
self.function = ~expr.Or(*self.neg)
cardinality = constraint.at_most_one(self.function.support)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
def test_at_most_zero_small(self):
(a, _b, _c) = self.pos
self.function = a
cardinality = cardnet.at_most(self.function.support, 0)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNone(sat)
def at_most_one(inputs, equivalent=None):
assert inputs, "inputs must not be empty"
count = next(_counter)
def a(i):
return expr.exprvar("sinz", (i, count))
def clauses(variables):
length = len(variables)
(first, rest, last) = (variables[0], variables[1:-1], variables[-1])
yield expr.Or(~first, a(1))
yield expr.Or(~last, ~a(length - 1))
for (i, x) in zip(range(2, length), rest):
yield expr.Or(~x, a(i))
yield expr.Or(~a(i - 1), a(i))
yield expr.Or(~x, ~a(i - 1))
if equivalent is None:
yield from clauses(tuple(inputs))
else:
auxiliaries = list()
for clause in clauses(tuple(inputs)):
aux = expr.exprvar(("sinz", "eq"), next(_counter))
yield expr.Implies(aux, clause).to_cnf()
yield expr.Implies(clause, aux).to_cnf()
auxiliaries.append(aux)
constraint = expr.And(*auxiliaries)
yield expr.Implies(constraint, equivalent).to_cnf()
yield expr.Implies(equivalent, constraint).to_cnf()
def __init__(self, *args, **kwargs):
self.formula_dnf = self.formula.to_dnf()
self.formula_onehot = onehot_f(self.formula)
self.pos_assignments = []
self.neg_assignments = []
for spc in spec.ShapeSpec.enumerate_both():
if satisfies(spc, self.formula_onehot):
self.pos_assignments.append(spc)
else:
self.neg_assignments.append(spc)
self.disjunction = isinstance(self.formula, expr.OrOp)
self.conjunction = isinstance(self.formula, expr.AndOp)
# Get assignments by which part they satisfy
self.left_assignments = []
self.right_assignments = []
self.both_assignments = []
self.neither_assignments = []
if self.conjunction or self.disjunction:
left_formula, right_formula = self.formula.xs
only_left = onehot_f(
expr.And(left_formula, expr.Not(right_formula)))
only_right = onehot_f(
expr.And(right_formula, expr.Not(left_formula)))
for spc in spec.ShapeSpec.enumerate_both():
if satisfies(spc, only_left):
self.left_assignments.append(spc)
elif satisfies(spc, only_right):
self.right_assignments.append(spc)
elif satisfies(spc, self.formula_onehot): # Both
self.both_assignments.append(spc)
else:
self.neither_assignments.append(spc)
if self.disjunction:
assert set(self.neither_assignments) == set(
self.neg_assignments)
assert set(self.left_assignments + self.right_assignments +
self.both_assignments) == set(self.pos_assignments)
else:
assert set(self.both_assignments) == set(self.pos_assignments)
assert set(self.left_assignments + self.right_assignments +
self.neither_assignments) == set(
self.neg_assignments)
def test_sat_negative_assumption(self):
solver = self.get_solver()
solver.add(expr.And(*(~p for p in self.pos)))
assumptions = {v: True for v in self.pos}
solution = solver.solve(assumptions=assumptions)
self.assertIsNone(solution)
def test_not_equals_higher(self):
equals = expr.exprvar("equals")
cardinality = cardnet.equals(self.function.support,
len(self.pos) + 1,
~equals)
sat = expr.And(self.function, equals, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(equals), 1)
def test_at_most_one_small(self):
self.function = self.pos
cardinality = constraint.at_most_one(self.function.support)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(self.pos), 1)
def test_not_at_most_is_not_equivalent(self):
at_most = expr.exprvar("at_most")
cardinality = cardnet.at_most(self.function.support,
len(self.pos) - 1,
~at_most)
sat = expr.And(self.function, at_most, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(at_most), 1)
def test_at_least_one_equivalent(self):
at_least = expr.exprvar("at_least")
cardinality = constraint.at_least_one(self.function.support, at_least)
sat = expr.And(self.function, at_least,
*cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(at_least), 1)
def test_equals_one_small(self):
(a, _b, _c) = self.pos
self.function = a
cardinality = cardnet.equals(self.function.support, 1)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(a), 1)
def test_not_equals_one_not_equivalent(self):
self.function = ~expr.Or(*self.neg)
equals = expr.exprvar("equals")
cardinality = constraint.equals_one(self.function.support, ~equals)
sat = expr.And(self.function, equals,
*cardinality).to_cnf().satisfy_one()
self.assertIsNotNone(sat)
self.assertEqual(sat.get(equals), 1)
def to_expr(self):
if self.spec_type == ShapeSpecTypes.SHAPE:
return shape.S2V[self.shape]
elif self.spec_type == ShapeSpecTypes.COLOR:
return color.C2V[self.color]
else:
return expr.And(
color.C2V[self.color],
shape.S2V[self.shape],
)
def recurse(expression):
if expression.ASTOP == "or":
return expr.And(*(recurse(e) for e in expression.xs))
if expression.ASTOP == "and":
return expr.Or(*(recurse(e) for e in expression.xs))
elif expression.ASTOP == "lit":
return expression
elif expression.is_one() or expression.is_zero():
return ~expression
else:
raise NotImplementedError(str(expression))
def convert_to_pyeda(term):
"""Converts a term object to a PyEDA expression.
Args:
term (Term): A term object.
Returns:
expr: The corresponding PyEDA expression.
"""
if term.operator is None:
return expr.exprvar(escape_var_name(term.operands[0]), None)
elif term.operator == "NEG":
return expr.Not(convert_to_pyeda(term.operands[0]), simplify=False)
elif term.operator == "AND":
return expr.And(
*[convert_to_pyeda(operand) for operand in term.operands],
simplify=False)
elif term.operator == "OR":
return expr.Or(
*[convert_to_pyeda(operand) for operand in term.operands],
simplify=False)
elif term.operator == "IMP":
return expr.Implies(convert_to_pyeda(term.operands[0]),
convert_to_pyeda(term.operands[0]),
simplify=False)
elif term.operator == "EQV":
return expr.Equal(
*[convert_to_pyeda(operand) for operand in term.operands],
simplify=False)
elif term.operator == "ADD":
return expr.exprvar(
"___ADD___".join([
escape_var_name(operand.operands[0])
for operand in term.operands
]), None)
def onehot_f(f):
return expr.And(f, color.ONEHOT_VAR, shape.ONEHOT_VAR)
def _cover_to_expression(cover):
inputs = (inp for (inp, outputs) in cover if outputs == (1, ))
terms = (expr.And(*Function._vector_to_vars(v)) for v in inputs)
return expr.Or(*terms)
def setUp(self):
self.pos = tuple(expr.exprvar(p) for p in "abc")
self.neg = tuple(expr.exprvar(p) for p in "uvwxyz")
self.function = expr.And(*self.pos, ~expr.Or(*self.neg))
def test_at_most_lower(self):
cardinality = cardnet.at_most(self.function.support,
len(self.pos) - 1)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNone(sat)
def test_equals_higher(self):
cardinality = cardnet.equals(self.function.support,
len(self.pos) + 1)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNone(sat)
def test_at_most_zero(self):
cardinality = cardnet.at_most(self.function.support, 0)
sat = expr.And(self.function, *cardinality).to_cnf().satisfy_one()
self.assertIsNone(sat)
