def solver(self):
solver = z3.Solver()
# Cheat a bit to randomize possible solution by adding constraints in a random order
undetermined = list(self.tiles(determined=False))
revealed_boundary = list(self.tiles(revealed=True, on_boundary=True))
shuffle(undetermined)
shuffle(revealed_boundary)
# The sum of all undetermined tiles that are a mine must equal the number of unplaced mines
solver.add(
z3.PbEq([(t.var, 1) for t in undetermined], self.num_undetermined_mines)
)
# The sum of all undetermined tiles touching a revealed number must equal that number
for t in revealed_boundary:
known_mine_neighbors = sum(
1 for n in t.neighbors if n.determined and n.mine
)
solver.add(
z3.PbEq(
[(n.var, 1) for n in t.neighbors if n.undetermined],
t.num_adjacent_mines - known_mine_neighbors,
)
)
return solver
def cons_rowcol(self):
'''Return basic structural constraints.
The returned list of constraints will require every row and column of
every grid to have exactly one 1.
'''
for grid in self.all_grids:
for i in range(self.num_items):
yield z3.PbEq([(g, 1) for g in grid[i, :]], 1)
yield z3.PbEq([(g, 1) for g in grid[:, i]], 1)
def solve_vortorb_flip(col_constraints, row_constraints, cell_constraints):
'''
col_constraints: [Constraint], left-to-right
row_constraints: [Constraint], top-to-bottom
cell_constraints: {(row, col): val}
returns num_solutions, 2d-array[row][col]{val: probability}
'''
cel_val_upper_bound = max(c.sum_ for c in col_constraints)
cel_val_upper_bound = max(cel_val_upper_bound, max(c.sum_ for c in row_constraints))
cel_val_upper_bound = min(cel_val_upper_bound, 3)
s = z3.Solver()
n = len(col_constraints)
xss = [[z3.Int('x{}{}'.format(i, j)) for j in range(n)] for i in range(n)]
# cell constraints
for i in range(n):
for j in range(n):
val = cell_constraints.get((i, j))
if val is not None:
s.add(xss[i][j] == val)
else:
s.add(0 <= xss[i][j], xss[i][j] <= cel_val_upper_bound)
# row constraints
for i in range(n):
s.add(z3.Sum(xss[i]) == row_constraints[i].sum_)
s.add(z3.PbEq([(xss[i][j]==0, 1) for j in range(n)], row_constraints[i].zeros))
# col constraints
for j in range(n):
s.add(z3.Sum([xss[i][j] for i in range(n)]) == col_constraints[j].sum_)
s.add(z3.PbEq([(xss[i][j]==0, 1) for i in range(n)], col_constraints[j].zeros))
num_soln = 0
soln = [[collections.defaultdict(int) for j in range(n)] for i in range(n)]
while s.check() == z3.sat:
num_soln += 1
m = s.model()
for i in range(n):
for j in range(n):
soln[i][j][m[xss[i][j]].as_long()] += 1
s.add(z3.Or([xss[i][j] != m[xss[i][j]] for i in range(n) for j in range(n)]))
for i in range(n):
for j in range(n):
for k, v in list(soln[i][j].items()):
soln[i][j][k] = v/num_soln
return num_soln, soln
def visitBFactorOneOnly(self, ctx):
formulas = []
for i in range(2, ctx.getChildCount() - 1, 2):
formulas.append(ctx.getChild(i).accept(self))
if not formulas:
return z3.BoolVal(False)
elif len(formulas) == 1:
return formulas[0]
return z3.PbEq([(i, 1) for i in formulas], 1)
def to_z3_(self):
return z3.PbEq(*[a.to_z3_() for a in self.children], 1)
def run_feature_analysis_forall(features,
features_as_boolean,
contexts,
attributes,
constraints,
optional_features,
non_incremental_solver,
out_stream,
time_context=""):
"""
Performs the feature analysis task.
A quantifier formula is solved to detect the anomalies
"""
data = {"dead_features": {}, "false_optionals": {}}
solver = z3.Solver()
#solver.set("smt.relevancy", 0)
if non_incremental_solver:
solver.set("combined_solver.solver2_timeout", 1)
# if time variable is not defined, create a fictional one
time_context = get_time_context(time_context, optional_features)
# add it in context if not present
if time_context not in contexts:
contexts[time_context] = {}
contexts[time_context]['min'] = 0
contexts[time_context]['max'] = 0
# these constraints will also be added in the forall formula and are redundant
# hopefully they will help the SMT solver to solve the forall formula
solver.add(contexts[time_context]["min"] <= z3.Int(time_context))
solver.add(z3.Int(time_context) <= contexts[time_context]["max"])
log.info("Building the FM formula")
# will repeat the constraints about the bounds on the environment but that is OK
formulas = get_basic_formula_list(features, attributes, contexts,
constraints, features_as_boolean)
if not non_incremental_solver:
log.debug("Preliminary check")
solver.check()
log.info(
"Computing dead or false optional features considering {} optional features"
.format(len(optional_features)))
opt_features_ls = optional_features.keys()
# fresh variables representing the selected features namefresh_var
fresh_var = "_" + uuid.uuid4().hex
if not opt_features_ls:
log.warning("Nothing to check")
json.dump(data, out_stream)
out_stream.write("\n")
return
elif len(
opt_features_ls
) == 1: # zip problem raised by smt if list of one element is used for z3.PbEq
solver.add(z3.Bool(opt_features_ls[0] + fresh_var))
else:
# only one selected
solver.add(
z3.PbEq([(z3.Bool(i + fresh_var), 1) for i in opt_features_ls], 1))
log.info(
"Adding constraint limiting time context based on the optional features to check"
)
for i in opt_features_ls:
ls = []
for k in optional_features[i]:
ls.append(z3.Int(time_context) >= k[0])
ls.append(z3.Int(time_context) <= k[1])
solver.add(z3.Implies(z3.Bool(i + fresh_var), z3.And(ls)))
solver.push()
if features_as_boolean:
z3_features = [z3.Bool(j) for j in features]
else:
z3_features = [z3.Int(j) for j in features]
log.info("Search for dead features")
solver.add(
z3.ForAll(
z3_features + [z3.Int(j) for j in attributes.keys()] +
[z3.Int(j) for j in contexts if j != time_context],
z3.Implies(
z3.And([
z3.Implies(
z3.Bool(i + fresh_var),
z3.Bool(i) if features_as_boolean else
z3.Int(i).__eq__(z3.IntVal(1)))
for i in opt_features_ls
]), z3.Not(z3.And(formulas)))))
log.debug(unicode(solver))
while True:
log.info("Computing")
result = solver.check()
if result == z3.sat:
model = solver.model()
for i in opt_features_ls:
if model[z3.Bool(i + fresh_var)] == z3.BoolVal(True):
found_feature = i
break
assert found_feature
found_context = model[z3.Int(time_context)].as_long()
# remove check for false optional
log.debug("Dead feature for time {}: {}".format(
found_context, found_feature))
if found_feature in data["dead_features"]:
data["dead_features"][found_feature].append(found_context)
else:
data["dead_features"][found_feature] = [found_context]
# add constraint for next iteration
solver.add(
z3.Not(
z3.And(
z3.Bool(found_feature + fresh_var),
z3.Int(time_context).__eq__(
z3.IntVal(found_context)))))
elif result == z3.unsat:
log.debug("Formula found unsat. No more dead features.")
break
else:
log.critical(
"SMT solver can not solve the forall formula (result unknown)."
)
log.critical("Exiting")
sys.exit(1)
solver.pop()
log.info("Search for false positive features")
solver.add(
z3.ForAll(
z3_features + [z3.Int(j) for j in attributes.keys()] +
[z3.Int(j) for j in contexts if j != time_context],
z3.Implies(
z3.And([
z3.Implies(
z3.Bool(i + fresh_var),
z3.Not(z3.Bool(i)) if features_as_boolean else
z3.Int(i).__eq__(z3.IntVal(0)))
for i in opt_features_ls
]), z3.Not(z3.And(formulas)))))
log.info("Remove also the checks for the {} features found dead".format(
len(data["dead_features"])))
for i in data["dead_features"]:
for j in data["dead_features"][i]:
solver.add(
z3.Not(
z3.And(z3.Bool(i + fresh_var),
z3.Int(time_context).__eq__(z3.IntVal(j)))))
#log.debug(unicode(solver))
while True:
log.info("Computing")
result = solver.check()
if result == z3.sat:
model = solver.model()
for i in opt_features_ls:
if model[z3.Bool(i + fresh_var)] == z3.BoolVal(True):
found_feature = i
break
assert found_feature
found_context = model[z3.Int(time_context)].as_long()
log.debug("False positive feature for time {}: {}".format(
found_context, found_feature))
if found_feature in data["false_optionals"]:
data["false_optionals"][found_feature].append(found_context)
else:
data["false_optionals"][found_feature] = [found_context]
# add constraint for next iteration
solver.add(
z3.Not(
z3.And(
z3.Bool(found_feature + fresh_var),
z3.Int(time_context).__eq__(
z3.IntVal(found_context)))))
elif result == z3.unsat:
log.debug("Formula found unsat. No more false positives.")
break
else:
log.critical(
"SMT solver can not solve the forall formula (result unknown)."
)
log.critical("Exiting")
sys.exit(1)
log.info("Printing output")
json.dump(data, out_stream)
out_stream.write("\n")
def exactlyOne(problem, varList):
# constrains at exactly one of the vars in the list to be true
problem.add(z3.PbEq([(v, 1) for v in varList], 1))
def to_z3(self, ctx):
args = list(map(lambda v: (ctx.z3var(v), 1), self._vars))
return z3.PbEq(args, self._n)
def solve(puzzle: Puzzle,
forced_rects: Set[Rect] = frozenset(),
clue_constraints: str = 'hard',
cover_constraints: str = 'exact',
corner_constraints: str = 'hard',
reflex_three_corners: bool = False) -> Iterator[List[Rect]]:
rect_to_var: Dict[Rect, z3.Bool] = {}
# Each cell is covered by exactly one rect.
cell_to_rects: Dict[Point, z3.Bool] = {c: list() for c in puzzle.cells}
# Each clue is satisfied by exactly one rect (of the right shape).
clue_to_rects: Dict[Point,
z3.Bool] = {c: list()
for c in puzzle.clues.keys()}
# Maps cells to rects having a there, for tracking four-corner violations.
# The values may be empty (but most won't be).
ul_to_rects: Dict[Point, z3.Bool] = {c: list() for c in puzzle.cells}
ur_to_rects: Dict[Point, z3.Bool] = {c: list() for c in puzzle.cells}
ll_to_rects: Dict[Point, z3.Bool] = {c: list() for c in puzzle.cells}
lr_to_rects: Dict[Point, z3.Bool] = {c: list() for c in puzzle.cells}
for r1 in range(puzzle.rmax):
for c1 in range(puzzle.cmax):
for r2 in range(r1, puzzle.rmax):
for c2 in range(c1, puzzle.cmax):
width, height = c2 - c1 + 1, r2 - r1 + 1 # inclusive
rect = Rect(r1, c1, height, width)
rect_cells = {
Point(r, c)
for r in range(r1, r2 + 1) for c in range(c1, c2 + 1)
}
# Depending on where the violation was, we may be able to
# break the r2 loop early for both of these checks.
if not rect_cells <= puzzle.cells:
if rect in forced_rects:
raise RuntimeError(
'forced rect {} contains holes {}'.format(
rect, rect_cells - puzzle.cells))
break
rect_clues = rect_cells & puzzle.clues.keys()
if len(rect_clues) > 1:
if rect in forced_rects:
raise RuntimeError(
'forced rect {} contains multiple clues at {}'.
format(rect, rect_clues))
break
if len(rect_clues) == 0:
if rect in forced_rects:
raise RuntimeError(
'forced rect {} contains no clues'.format(
rect))
continue # expanding the rect may add a clue
clue_cell = rect_clues.pop()
clue = puzzle.clues[clue_cell]
expected_clue = Clue.PLUS if width == height else Clue.VERT if width < height else Clue.HORIZ
if clue != expected_clue and clue_constraints == 'hard':
if rect in forced_rects:
raise RuntimeError(
'forced rect {} contains a {}, but is shaped for a {}'
.format(rect, clue, expected_clue))
continue
var = z3.Bool('{},{},{},{}'.format(r1, c1, height, width))
rect_to_var[rect] = var
for c in rect_cells:
cell_to_rects[c].append(var)
clue_to_rects[clue_cell].append(var)
ul_to_rects[Point(r1, c1)].append(var)
ur_to_rects[Point(r1, c2)].append(var)
ll_to_rects[Point(r2, c1)].append(var)
lr_to_rects[Point(r2, c2)].append(var)
missing_forced_rects = forced_rects - rect_to_var.keys()
if missing_forced_rects:
# We could add a command-line flag to disable pruning to get a
# better error message here.
raise RuntimeError(
'forced rects {} were pruned'.format(missing_forced_rects))
for cell, rects in cell_to_rects.items():
if not rects:
print('cell', cell, 'has no covering rects')
for clue_cell, rects in clue_to_rects.items():
if not rects:
print('clue', puzzle.clues[clue_cell], 'in', clue_cell,
'has no candidate rects')
solver = z3.Optimize()
for c in puzzle.cells:
if c in clue_to_rects and clue_constraints == 'hard':
solver.add(z3.PbEq([(r, 1) for r in clue_to_rects[c]], 1))
elif cover_constraints == 'exact':
solver.add(z3.PbEq([(r, 1) for r in cell_to_rects[c]], 1))
elif cover_constraints == 'subset':
solver.add(z3.PbLe([(r, 1) for r in cell_to_rects[c]], 1))
solver.add_soft(z3.PbGe([(r, 1) for r in cell_to_rects[c]], 1), 1,
'cover')
elif cover_constraints == 'superset':
solver.add_soft(z3.PbLe([(r, 1) for r in cell_to_rects[c]], 1), 1,
'cover')
solver.add(z3.PbGe([(r, 1) for r in cell_to_rects[c]], 1))
elif cover_constraints == 'incomparable':
solver.add_soft(z3.PbEq([(r, 1) for r in cell_to_rects[c]], 1), 1,
'cover')
else:
raise AssertionError('bad cover_constraints: ' + cover_constraints)
if corner_constraints != 'ignore': # skip the loop if we wouldn't add anyway
for c in puzzle.cells:
for r1 in lr_to_rects.get(c, []):
for r2 in ll_to_rects.get(Point(c.r, c.c + 1), []):
for r3 in ur_to_rects.get(Point(c.r + 1, c.c), []):
for r4 in ul_to_rects.get(Point(c.r + 1, c.c + 1), []):
if corner_constraints == 'hard':
solver.add(
z3.PbLe([(r1, 1), (r2, 1), (r3, 1),
(r4, 1)], 3))
elif corner_constraints == 'soft':
solver.add_soft(
z3.PbLe([(r1, 1), (r2, 1), (r3, 1),
(r4, 1)], 3), 1, 'corner')
else:
raise AssertionError(
'bad corner_constraints: ' +
corner_constraints)
if reflex_three_corners:
holes = [
Point(r, c) for r in range(puzzle.rmax)
for c in range(puzzle.cmax) if Point(r, c) not in puzzle.cells
]
for c in holes:
for r2 in ll_to_rects.get(Point(c.r, c.c + 1), []):
for r3 in ur_to_rects.get(Point(c.r + 1, c.c), []):
for r4 in ul_to_rects.get(Point(c.r + 1, c.c + 1), []):
if corner_constraints == 'hard':
solver.add(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2))
elif corner_constraints == 'soft':
solver.add_soft(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2), 1,
'corner')
else:
raise AssertionError(
'bad corner_constraints: ' +
corner_constraints)
for r2 in lr_to_rects.get(Point(c.r, c.c - 1), []):
for r3 in ur_to_rects.get(Point(c.r + 1, c.c - 1), []):
for r4 in ul_to_rects.get(Point(c.r + 1, c.c), []):
if corner_constraints == 'hard':
solver.add(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2))
elif corner_constraints == 'soft':
solver.add_soft(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2), 1,
'corner')
else:
raise AssertionError(
'bad corner_constraints: ' +
corner_constraints)
for r2 in lr_to_rects.get(Point(c.r - 1, c.c), []):
for r3 in ll_to_rects.get(Point(c.r - 1, c.c + 1), []):
for r4 in ul_to_rects.get(Point(c.r, c.c + 1), []):
if corner_constraints == 'hard':
solver.add(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2))
elif corner_constraints == 'soft':
solver.add_soft(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2), 1,
'corner')
else:
raise AssertionError(
'bad corner_constraints: ' +
corner_constraints)
for r2 in lr_to_rects.get(Point(c.r - 1, c.c - 1), []):
for r3 in ll_to_rects.get(Point(c.r - 1, c.c), []):
for r4 in ur_to_rects.get(Point(c.r, c.c - 1), []):
if corner_constraints == 'hard':
solver.add(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2))
elif corner_constraints == 'soft':
solver.add_soft(
z3.PbLe([(r2, 1), (r3, 1), (r4, 1)], 2), 1,
'corner')
else:
raise AssertionError(
'bad corner_constraints: ' +
corner_constraints)
if forced_rects:
solver.add(z3.And(list(rect_to_var[r] for r in forced_rects)))
while solver.check() == z3.sat:
model = solver.model()
soln: List[Rect] = []
blockers = []
for d in model.decls():
if z3.is_true(model[d]):
soln.append(str_to_rect(d.name()))
# Build a constraint that prevents this model from being returned again.
# https://stackoverflow.com/a/11869410/3614835
blockers.append(d() != model[d])
soln.sort()
yield soln
solver.add(z3.Or(blockers))
def _loop_cons(self):
# Every corner must have either no edges or exactly two edges
for point, c in self.iter_corners():
vars = tuple([(v, 1) for v in c.values()])
yield z3.PbEq(vars, 0) | z3.PbEq(vars, 2)
def __init__(self, bool_expressions: Sequence[expr.BooleanExpression], weights: Sequence[float], value: float):
super().__init__(expr.WeightedSum(bool_expressions, weights), expr.NumericValue(value))
self.z3_expr = z3.PbEq([(e.get_z3(), w) for (e, w) in zip(bool_expressions, weights)], value)