class Y2021D24(object):
_re_inp = re.compile(r'inp ([wxyz])')
_re_add = re.compile(r'add ([wxyz]) ([wxyz]|-?\d+)')
_re_mul = re.compile(r'mul ([wxyz]) ([wxyz]|-?\d+)')
_re_div = re.compile(r'div ([wxyz]) ([wxyz]|-?\d+)')
_re_mod = re.compile(r'mod ([wxyz]) ([wxyz]|-?\d+)')
_re_eql = re.compile(r'eql ([wxyz]) ([wxyz]|-?\d+)')
def __init__(self, file_name):
self.solver = Optimize()
inputs = [Int(f'model_{i}') for i in range(14)]
self.solver.add([i >= 1 for i in inputs])
self.solver.add([i <= 9 for i in inputs])
# Please don't ask me to explain this. There's a common pattern in the input code that treats z like a number
# of base 26 and the operations are either right shift or left shift on that number +- some value.
self.solver.add(inputs[0] + 6 - 6 == inputs[13])
self.solver.add(inputs[1] + 11 - 6 == inputs[12])
self.solver.add(inputs[2] + 5 - 13 == inputs[11])
self.solver.add(inputs[3] + 6 - 8 == inputs[8])
self.solver.add(inputs[4] + 8 - 1 == inputs[5])
self.solver.add(inputs[6] + 9 - 16 == inputs[7])
self.solver.add(inputs[9] + 13 - 16 == inputs[10])
my_sum = IntVal(0)
for index in range(len(inputs)):
my_sum = (my_sum * 10) + inputs[index]
self.value = Int('value')
self.solver.add(my_sum == self.value)
def part1(self):
self.solver.push()
self.solver.maximize(self.value)
self.solver.check()
result = self.solver.model()[self.value]
self.solver.pop()
print("Part 1:", result)
def part2(self):
self.solver.push()
self.solver.minimize(self.value)
self.solver.check()
result = self.solver.model()[self.value]
self.solver.pop()
print("Part 2:", result)
def _solve(
solver: z3.Optimize, channels: List[Channel], devices: List[Device]
) -> Tuple[Problem, z3.Model]:
problem = _problem(solver, freqs=[c.frequency for c in channels], devices=devices)
if solver.check() != z3.sat:
# TODO: consider getting an unsat core
raise ValueError(f"No valid assignment possible, add more devices")
# find the minimal number of devices that cover all frequencies
# it is faster to do this iteratively than to offload these to
# smt constraints. do this in reverse so we end up assigning
# the lowest numbered devices
for r in problem.ranges[::-1]:
# to control the device placements adjust the order they're eliminated from
# the solution. for example, this will prefer devices that have a smaller
# minimum sample rate over devices with a larger one:
# for r, _ in zip(problem.ranges, problem.devices), key=lambda x: -x[1].min_sample_rate
solver.push()
solver.add(r == 0)
if solver.check() != z3.sat:
solver.pop()
break
devices_required = z3.Sum([z3.If(r > 0, 1, 0) for r in problem.ranges])
# minimize the sum of frequency ranges
solver.minimize(z3.Sum(*problem.ranges))
# and the frequency, just to produce deterministic results
solver.minimize(z3.Sum(*problem.lower_freq))
assert solver.check() == z3.sat
model = solver.model()
print(f"Devices required: {model.eval(devices_required)}", file=sys.stderr)
return problem, model
def main(args):
# print(args)
seed = int(args[0])
random.seed(seed)
# X is a three dimensional grid containing (t, x, y)
X = [[[Bool("x_%s_%s_%s" % (k, i, j)) for j in range(GRID_SZ)]
for i in range(GRID_SZ)] for k in range(HOPS + 1)]
s = Optimize()
# Initial Constraints
s.add(X[0][0][0])
s.add([Not(cell) for row in X[0] for cell in row][1:])
# Final constraints
s.add(X[HOPS][GRID_SZ - 1][GRID_SZ - 1])
s.add([Not(cell) for row in X[HOPS] for cell in row][:-1])
#Sanity Constraints
for grid in X:
for i in range(len(grid)):
for j in range(len(grid)):
for p in range(len(grid)):
for q in range(len(grid)):
if not (i == p and j == q):
s.add(Not(And(grid[i][j], grid[p][q])))
#Motion primitives
for t in range(HOPS):
for x in range(GRID_SZ):
for y in range(GRID_SZ):
temp = Or(X[t][x][y])
if (x + 1 < GRID_SZ):
temp = Or(temp, X[t][x + 1][y])
if (y + 1 < GRID_SZ):
temp = Or(temp, X[t][x][y + 1])
if (x - 1 >= 0):
temp = Or(temp, X[t][x - 1][y])
if (y - 1 >= 0):
temp = Or(temp, X[t][x][y - 1])
s.add(simplify(Implies(X[t + 1][x][y], temp)))
# Cost constraints
for t in range(HOPS):
for x in range(GRID_SZ):
for y in range(GRID_SZ):
s.add_soft(Not(X[t][x][y]),
distance(x, y, GRID_SZ - 1, GRID_SZ - 1))
hop = 0
if s.check() == sat:
m = s.model()
else:
print("No.of hops too low...")
exit(1)
obs1 = Obstacle(0, 3, GRID_SZ)
robot_plan = []
obs_plan = []
# for a in s.assertions():
# print(a)
while (hop < HOPS):
robot_pos = (0, 0) if hop == 0 else get_robot_pos(m, hop)
obs_pos = obs1.next_move()
s.add(X[hop][robot_pos[0]][robot_pos[1]])
# print("hop is ", hop)
# print("robot at ", robot_pos)
# print("obs at ", obs_pos)
if robot_pos == obs_pos:
print("COLLISION!!!")
print(robot_plan)
print(obs_plan)
exit()
robot_plan.append(robot_pos)
obs_plan.append(obs_pos)
#next position of the robot
next_robot_pos = get_robot_pos(m, hop + 1)
s.push()
# print("intersection points")
# print(intersection_points(robot_pos, obs_pos))
# count = 0
next_overlap = next_intersection_points(next_robot_pos, obs_pos)
for (x, y) in next_overlap:
# consider only the intersection with the next step in the plan
s.add(Not(X[hop + 1][x][y]))
if len(next_overlap) > 0: # we need to find a new path
if (s.check() == unsat):
print("stay there")
else:
m = s.model()
# print("Plan for hop = " + str(hop+1))
# print(get_plan(m))
hop += 1
else:
# we don't need to worry about the path
hop += 1
s.pop()
robot_pos = get_robot_pos(m, hop)
obs_pos = obs1.next_move()
# print("hop is ", hop)
# print("robot at ", robot_pos)
# print("obs at ", obs_pos)
robot_plan.append(robot_pos)
obs_plan.append(obs_pos)
if path_valid(robot_plan, obs_plan):
print("PATH IS VALID!!!")
else:
print("PATH IS INVALID!!!")
print("ROBOT MOVEMENT:")
print(robot_plan)
print("OBSTACLE MOVEMENT:")
print(obs_plan)
class Oracle(ABC):
"""
An oracle is a dict from state_ids to values (not neccessarily probabilities since o.w. the eq system does not always have a solution).
This is an abstract base class.
Concrete sub-classes must overwrite `initialize`.
Attributes:
state_graph (StateGraph): the associated state graph
default_value (Fraction): The default value is the oracle value returned if the given state_id is not a key of the oracle
statistics (Statistics): access to the global statistics
settings (Settings): all settings
solver (Solver): a solver for the equation system
oracle_states (Set[StateId]): states in this oracle
oracle (Dict[StateId, z3.ExprRef]): the oracle's internal value dict
"""
def __init__(self, state_graph: StateGraph, default_value: Fraction,
statistics: Statistics, settings: Settings,
model_type: PrismModelType):
self.state_graph = state_graph
self.statistics = statistics
self.settings = settings
self.model_type = model_type
if default_value < 0:
raise ValueError("Oracle values must be greater or equal to 0")
self.default_value = RealVal(default_value)
self.solver = Solver()
self.solver_mdp = Optimize()
# The way we refine the Oracle depends on the model type
if model_type == PrismModelType.DTMC:
self.refine_oracle = self.refine_oracle_mc
elif model_type == PrismModelType.MDP:
self.refine_oracle = self.refine_oracle_mdp
else:
raise Exception("Oracle: Unsupported model type")
self.oracle_states: Set[StateId] = set()
self.oracle: Dict[StateId, z3.ExprRef] = dict()
# self.save_oracle_on_disk()
def _ensure_value_in_oracle(self, state_id: StateId):
"""
Used to override standard behaviour. Takes a state id, ensures that self.oracle contains this value.
:param state_id:
:return:
"""
pass
def get_oracle_value(self, state_id: StateId) -> z3.ExprRef:
if state_id not in self.oracle:
self._ensure_value_in_oracle(state_id)
return self.oracle.get(state_id, self.default_value)
def refine_oracle_mc(self, visited_states: Set[StateId]) -> Set[StateId]:
self.statistics.inc_refine_oracle_counter()
# First ensure progress
if visited_states <= self.oracle_states:
# Ensure progress by adding all non-target successors of states in oracle_states to the set
self.oracle_states = self.oracle_states.union({
succ_id
for state_id in self.oracle_states for succ_id, prob in
self.state_graph.get_filtered_successors(state_id)
if succ_id != -1
})
else:
self.oracle_states = self.oracle_states.union(visited_states)
# TODO: A lot of optimization potential
self.solver.push()
# We need a variable for every oracle state
variables = {
state_id: Real("x_%s" % state_id)
for state_id in self.oracle_states
}
# Set up EQ - System
for state_id in self.oracle_states:
self.solver.add(variables[state_id] == Sum([
RealVal(1) *
prob if succ_id == -1 else # Case succ_id target state
(
variables[succ_id] * prob if succ_id in
self.oracle_states else # Case succ_id oracle state
self.get_oracle_value(succ_id) *
prob) # Case sycc_id no target and no oracle state
for succ_id, prob in self.state_graph.get_filtered_successors(
state_id)
]))
self.solver.add(variables[state_id] >= RealVal(0))
#print(self.solver.assertions())
if self.solver.check() == sat:
m = self.solver.model()
# update oracle
for state_id in self.oracle_states:
self.oracle[state_id] = m[variables[state_id]]
logger.info("Refined oracle.")
#logger.info(self.oracle)
self.solver.pop()
return self.oracle_states
else:
# The oracle solver is unsat. In this case, we solve the LP.
self.solver.pop()
self.statistics.refine_oracle_counter = self.statistics.refine_oracle_counter - 1
return self.refine_oracle_mdp(visited_states)
def refine_oracle_mdp(self, visited_states: Set[StateId]) -> Set[StateId]:
self.statistics.inc_refine_oracle_counter()
# First ensure progress
if visited_states <= self.oracle_states:
# Ensure progress by adding all non-target successors of states in oracle_states to the set (for every action)
self.oracle_states = self.oracle_states.union({
succ[0]
for state_id in self.oracle_states for choice in
self.state_graph.get_successors_filtered(state_id).choices
for succ in choice.distribution if succ[0] != -1
})
else:
self.oracle_states = self.oracle_states.union(visited_states)
# TODO: A lot of optimization potential
self.solver_mdp.push()
# We need a variable for every oracle state
variables = {
state_id: Real("x_%s" % state_id)
for state_id in self.oracle_states
}
# Set up EQ - System
for state_id in self.oracle_states:
for choice in self.state_graph.get_successors_filtered(
state_id).choices:
self.solver_mdp.add(variables[state_id] >= Sum([
RealVal(1) *
prob if succ_id == -1 else # Case succ_id target state
(
variables[succ_id] * prob if succ_id in
self.oracle_states else # Case succ_id oracle state
self.get_oracle_value(succ_id) *
prob) # Case sycc_id no target and no oracle state
for succ_id, prob in choice.distribution
]))
self.solver_mdp.add(variables[state_id] >= RealVal(0))
# Minimize value for initial state
self.solver_mdp.minimize(
variables[self.state_graph.get_initial_state_id()])
if self.solver_mdp.check() == sat:
m = self.solver_mdp.model()
# update oracle
for state_id in self.oracle_states:
self.oracle[state_id] = m[variables[state_id]]
logger.info("Refined oracle.")
# logger.info(self.oracle)
self.solver_mdp.pop()
return self.oracle_states
else:
logger.error("Oracle solver unsat")
raise RuntimeError("Oracle solver inconsistent.")
@abstractmethod
def initialize(self):
"""
Stub to be overwritten by concrete oracles.
:return:
"""
pass
def save_oracle_on_disk(self):
"""
Save this oracle to disk using `save_oracle_dict` from `pric3.oracles.file_oracle`.
"""
from pric3.oracles.file_oracle import save_oracle_dict
save_oracle_dict(self.state_graph, self.oracle)
def _get_prism_program(self):
return self.state_graph.input_program.prism_program
class StateProbabilityGenerator:
def __init__(self, state_graph, statistics, settings, model_type):
self.statistics = statistics
self.state_graph = state_graph
self.model_type = model_type
logger.debug("Initialize oracle...")
self._initialize_oracle(settings)
logger.debug("Initialize obligation cache...")
self._obligation_cache = ObligationCache()
logger.debug("Initialize optimization solver...")
# Initialize solver for optimization queries
self.opt_solver = Optimize()
self._realval_zero = RealVal(0)
self._realval_one = RealVal(1)
self.obligation_queue_class = settings.get_obligation_queue_class()
def _initialize_oracle(self, settings):
self.statistics.start_initialize_oracle_timer()
args = [self.state_graph,settings.default_oracle_value,self.statistics,settings, self.model_type]
if settings.oracle_type == "simulation":
self.oracle = SimulationOracle(*args)
elif settings.oracle_type == "perfect":
self.oracle = ExactOracle(*args)
elif settings.oracle_type == "modelchecking":
self.oracle = ModelCheckingOracle(*args)
elif settings.oracle_type == "solveeqspartly_exact" or settings.oracle_type == "solveeqspartly_inexact":
self.oracle = SolveEQSPartlyOracle(*args)
elif settings.oracle_type == "file":
self.oracle = FileOracle(*args)
else:
raise RuntimeError("Unclear which oracle to use.")
self.oracle.initialize()
self.statistics.stop_initialize_oracle_timer()
def refine_oracle(self, visited_states):
res = self.oracle.refine_oracle(visited_states)
self.reset_cache()
return res
def reset_cache(self):
logger.debug("Reset obligation cache ...")
self._obligation_cache.reset_cache()
def finalize_statistics(self):
self.statistics.set_number_oracle_states(len(self.oracle.oracle_states))
def run(self, state_id, chosen_command, delta, states_with_fixed_probabilities = set()):
"""
:param state_id:
:param delta:
:return: (1) True iff it is possible to find probabilities for the successors of the given state_id and delta.
(2) If True, then it returns a dict form succ_ids to probabilities. This dict does not contain goal states.
"""
# TODO consider changing to None if not possible, and dict otherwise.
self.statistics.inc_get_probability_counter()
self.statistics.start_get_probability_timer()
# First check whether we have cached the corresponding obligation
res = self._obligation_cache.get_cached(state_id, chosen_command, delta)
if res != False:
self.statistics.stop_get_probability_timer()
return (True, res)
# If not, we have to ask the SMT-Solver
succ_dist = self.state_graph.get_successors_filtered(state_id).by_command_index(chosen_command)
succ_dist_without_target_states = [(state_id, prob)
for (state_id, prob) in succ_dist
if state_id != -1]
# Check if there is at least one non-target state. Otherwise, repairing is not possible (smt solver would return unsat if we continued, so checking this is an optimization).
if len(succ_dist_without_target_states) == 0:
self.statistics.stop_get_probability_timer()
return (False, None)
self.opt_solver.push()
vars = {}
# We need a variable for each successor
for (succ_id, prob) in succ_dist:
if succ_id != -1:
vars[succ_id] = Real("x_%s" % succ_id)
# all results must of be probabilities
self.opt_solver.add(vars[succ_id] >= self._realval_zero)
self.opt_solver.add(vars[succ_id] <= self._realval_one)
# \Phi(F)[s] = delta constraint
# TODO: Type of porb is pycarl.gmp.gmp.Rational. Z3 magically deals with this
self.opt_solver.add(
Sum([
(vars[succ_id] if succ_id != -1 else RealVal(1)) * prob
# Note: Keep in mind that you need to check whether succ is a target state
for (succ_id, prob) in succ_dist
]) == delta)
for (succ_id, prob) in succ_dist:
if succ_id in states_with_fixed_probabilities:
self.opt_solver.add(vars[succ_id] == self.obligation_queue_class.smallest_probability_for_state[succ_id])
# If we have more than one non-target successor, we have to optimize
if len(succ_dist_without_target_states) > 1:
# first check whether all oracle values are 0 (note that we do not have to do this if there is only one succ without target)
if len(succ_dist_without_target_states) > 1 and sum([self.oracle.get_oracle_value(state_id).as_fraction() for state_id, prob in
succ_dist_without_target_states]) == 0:
# In this case, we require that the probability mass is distributed equally
for i in range(0, len(succ_dist_without_target_states) - 1):
self.opt_solver.add(
vars[succ_dist_without_target_states[i][0]] == vars[succ_dist_without_target_states[i + 1][0]])
else:
# First Try to solve the eq system
# TODO: Do not use opt_solver for this
if self._get_probabilities_by_solving_eq_system(succ_dist_without_target_states, vars):
self.statistics.inc_solved_eq_system_instead_of_optimization_counter()
m = self.opt_solver.model()
result = {
succ_id: m[vars[succ_id]]
for (succ_id, prob) in succ_dist_without_target_states
}
# Because get_probabilities_by_solving_eq_system pushes
# TODO: This is ugly
# TODO: Compare solve-eq-system-time with optimization-problem-time
self.opt_solver.pop()
self.opt_solver.pop()
self._obligation_cache.cache(state_id, chosen_command, delta, result)
self.statistics.stop_get_probability_timer()
return (True, result)
else:
self.statistics.inc_had_to_solve_optimization_problem_counter()
# for each non-target-succ, we need n opt-var
opt_vars = {}
# For every non-target successor, we need an optimization variable
for (succ_id, prob) in succ_dist_without_target_states:
opt_vars[succ_id] = Real("opt_var_%s" % succ_id)
# Now assert that opt_var_i = |var_i \ (var_1 + ... + var_n) - oracle(s_i) \ ( oracle(s_1) + ... + oracle(s_n ) |
# for every opt_var_i
for (succ_id, prob) in succ_dist_without_target_states:
# opt_var is the absolute value of the ratio
self.opt_solver.add(
If(((vars[succ_id] * Sum([
self.oracle.get_oracle_value(succ_id_2) for
(succ_id_2, prob) in succ_dist_without_target_states
])) - ((self.oracle.get_oracle_value(succ_id) * Sum([
vars[succ_id_2] for
(succ_id_2, prob) in succ_dist_without_target_states
])))) < 0, opt_vars[succ_id] ==
(((self.oracle.get_oracle_value(succ_id) * Sum([
vars[succ_id_2] for
(succ_id_2, prob) in succ_dist_without_target_states
]))) - (vars[succ_id] * Sum([
self.oracle.get_oracle_value(succ_id_2) for
(succ_id_2, prob) in succ_dist_without_target_states
]))), opt_vars[succ_id] == ((vars[succ_id] * Sum([
self.oracle.get_oracle_value(succ_id_2) for
(succ_id_2, prob) in succ_dist_without_target_states
])) - ((self.oracle.get_oracle_value(succ_id) * Sum([
vars[succ_id_2] for
(succ_id_2, prob) in succ_dist_without_target_states
]))))))
# minimize sum of opt-vars
opt = self.opt_solver.minimize(
Sum([
opt_vars[succ_id]
for (succ_id, prob) in succ_dist_without_target_states
]))
if self.opt_solver.check() == sat:
# We found probabilities or the successors
m = self.opt_solver.model()
result = {
succ_id: m[vars[succ_id]]
for (succ_id, prob) in succ_dist_without_target_states
}
self.opt_solver.pop()
self._obligation_cache.cache(state_id, chosen_command, delta, result)
self.statistics.stop_get_probability_timer()
return (True, result)
else:
# There are no such probabilities
self.opt_solver.pop()
self.statistics.stop_get_probability_timer()
return (False, None)
def _get_probabilities_by_solving_eq_system(self, succ_dist_without_target_states, vars):
self.opt_solver.push()
#TODO is this correct?
lhs_sum = Sum([
self.oracle.get_oracle_value(succ_id_2) for
(succ_id_2, _) in succ_dist_without_target_states
])
rhs_sum = Sum([
vars[succ_id_2] for
(succ_id_2, _) in succ_dist_without_target_states
])
def _multiply(left,right):
args = (Ast * 2)()
args[0] = left.as_ast()
args[1] = right.as_ast()
return ArithRef(Z3_mk_mul(left.ctx.ref(), 2, args), left.ctx)
for (succ_id, prob) in succ_dist_without_target_states:
# opt_var is the absolute value of the ratio
lhs = _multiply(vars[succ_id], lhs_sum)
rhs = _multiply(self.oracle.get_oracle_value(succ_id), rhs_sum)
equality = lhs == rhs
self.opt_solver.add(equality)
if self.opt_solver.check() == sat:
return True
else:
self.opt_solver.pop()
return False