def compose_abs_transition_bdd():
global cached_abs_transition, procd_blocks
# check cache
if cached_abs_transition is None:
log.DBG_MSG("Rebuilding abstract transition relation")
for b in preds.abs_blocks:
procd_blocks[b] = False
c = bdd.true()
else:
c = cached_abs_transition
latches = [x.lit for x in iterate_latches_and_error()]
latches_bdd = bdd.get_cube(get_all_latches_as_bdds())
latch_funs = [get_bdd_for_aig_lit(x.next) for x in
iterate_latches_and_error()]
for b in preds.abs_blocks:
if b not in procd_blocks or not procd_blocks[b]:
procd_blocks[b] = True
temp = bdd.make_eq(bdd.BDD(get_primed_variable(b)),
preds.block_to_bdd[b])
c &= temp.compose(latches, latch_funs)
# cache c
cached_abs_transition = c
return c.and_abstract(compose_abs_eq_bdd(), latches_bdd)
def extract_output_funcs(strategy, care_set=None):
""" Calculate BDDs for output functions given non-deterministic winning
strategy.
"""
if care_set is None:
care_set = bdd.true()
output_models = dict()
all_outputs = get_controllable_inputs_bdds()
for c in get_controllable_inputs_bdds():
others = set(set(all_outputs) - set([c]))
if others:
others_cube = bdd.get_cube(others)
c_arena = strategy.exist_abstract(others_cube)
else:
c_arena = strategy
# pairs (x,u) in which c can be true
can_be_true = c_arena.cofactor(c)
# pairs (x,u) in which c can be false
can_be_false = c_arena.cofactor(~c)
must_be_true = (~can_be_false) & can_be_true
must_be_false = (~can_be_true) & can_be_false
local_care_set = care_set & (must_be_true | must_be_false)
# Restrict operation:
# on care_set: must_be_true.restrict(care_set) <-> must_be_true
c_model = min([must_be_true.safe_restrict(local_care_set),
(~must_be_false).safe_restrict(local_care_set)],
key=bdd.dag_size)
output_models[c] = c_model
log.DBG_MSG("Size of function for " + str(c.get_index()) + " = " +
str(c_model.dag_size()))
strategy &= bdd.make_eq(c, c_model)
return output_models
def over_post_bdd_abs(src_states_bdd, env_strat=None):
# make sure the block_funs are current
update_block_funs()
# take the step forward and get rid of latches
conc_src = gamma(src_states_bdd)
if env_strat is not None:
conc_strat = gamma(env_strat)
else:
conc_strat = bdd.true()
# to do this, we use an over-simplified transition relation, EXu,Xc
simple_trans = bdd.true()
for b in preds.abs_blocks:
trans_b = bdd.make_eq(bdd.BDD(b), block_funs[b])
simple_trans &= trans_b.exist_abstract(
bdd.get_cube(get_controllable_inputs_bdds()))
simple_trans &= conc_strat & conc_src
return simple_trans.exist_abstract(
bdd.get_cube(get_all_latches_as_bdds() +
get_uncontrollable_inputs_bdds()))
def single_post_bdd(src_states_bdd, sys_strat=None):
""" Over-approximated version of concrete post which can be done even
without the transition relation """
strat = bdd.true()
if sys_strat is not None:
strat &= sys_strat
# to do this, we use an over-simplified transition relation, EXu,Xc
b = bdd.true()
for x in iterate_latches_and_error():
temp = bdd.make_eq(bdd.BDD(get_primed_variable(x.lit)),
get_bdd_for_aig_lit(x.next))
b &= temp.and_abstract(strat,
bdd.get_cube(get_controllable_inputs_bdds()))
if restrict_like_crazy:
b = b.restrict(src_states_bdd)
b &= src_states_bdd
b = b.exist_abstract(
bdd.get_cube(get_all_latches_as_bdds() +
get_uncontrollable_inputs_bdds()))
return unprime_latches_in_bdd(b)
def to_bdd(self):
b = bdd.true()
for c in self.clauses:
nu_clause = bdd.false()
for l in c:
nu_var = bdd.BDD(abs(l))
if l < 0:
nu_var = ~nu_var
nu_clause |= nu_var
b &= nu_clause
return b
def compose_transition_bdd():
global cached_transition
# check cache
if cached_transition:
return cached_transition
b = bdd.true()
for x in iterate_latches_and_error():
b &= bdd.make_eq(bdd.BDD(get_primed_variable(x.lit)),
get_bdd_for_aig_lit(x.next))
cached_transition = b
log.BDD_DMP(b, "Composed and cached the concrete transition relation")
return b
def single_pre_bdd(dst_states_bdd, strat=None):
if strat is None:
strat = bdd.true()
latches = [x.lit for x in iterate_latches_and_error()]
latch_funs = [get_bdd_for_aig_lit(x.next) for x in
iterate_latches_and_error()]
if restrict_like_crazy:
latch_funs = [x.restrict(~dst_states_bdd) for x in latch_funs]
# take a transition step backwards
p_bdd = dst_states_bdd.compose(latches, latch_funs)
# use the given strategy
p_bdd &= strat
p_bdd = p_bdd.exist_abstract(
bdd.get_cube(get_uncontrollable_inputs_bdds() +
get_controllable_inputs_bdds()))
return p_bdd
def compose_abs_eq_bdd():
global cached_abs_eq, abs_eq_procd_blocks
# check cache
if cached_abs_eq is None:
log.DBG_MSG("Rebuilding abs_eq")
for b in preds.abs_blocks:
abs_eq_procd_blocks[b] = False
c = bdd.true()
else:
c = cached_abs_eq
for b in preds.abs_blocks:
if b not in procd_blocks or not procd_blocks[b]:
c &= bdd.make_eq(bdd.BDD(b), preds.block_to_bdd[b])
# cache c
cached_abs_eq = c
return c
def walk(a_bdd):
global bdd_gate_cache
"""
Walk given BDD node (recursively). If given input BDD requires
intermediate AND gates for its representation, the function adds them.
Literal representing given input BDD is `not` added to the spec.
"""
if a_bdd in bdd_gate_cache:
return bdd_gate_cache[a_bdd]
if a_bdd.is_constant():
res = int(a_bdd == bdd.true()) # in aiger 0/1 = False/True
return res
# get an index of variable,
# all variables used in bdds also introduced in aiger,
# except fake error latch literal,
# but fake error latch will not be used in output functions (at least we
# don't need this..)
a_lit = a_bdd.get_index()
assert (a_lit != error_fake_latch.lit), ("using error latch in the " +
"definition of output " +
"function is not allowed")
t_bdd = a_bdd.then_child()
e_bdd = a_bdd.else_child()
t_lit = walk(t_bdd)
e_lit = walk(e_bdd)
# ite(a_bdd, then_bdd, else_bdd)
# = a*then + !a*else
# = !(!(a*then) * !(!a*else))
# -> in general case we need 3 more ANDs
a_t_lit = aig.get_optimized_and_lit(a_lit, t_lit)
na_e_lit = aig.get_optimized_and_lit(aig.negate_lit(a_lit), e_lit)
n_a_t_lit = aig.negate_lit(a_t_lit)
n_na_e_lit = aig.negate_lit(na_e_lit)
ite_lit = aig.get_optimized_and_lit(n_a_t_lit, n_na_e_lit)
res = aig.negate_lit(ite_lit)
if a_bdd.is_complement():
res = aig.negate_lit(res)
# cache result
bdd_gate_cache[a_bdd] = res
return res
def update_block_funs():
global cached_block_funs, block_funs
latches = [x.lit for x in iterate_latches_and_error()]
latch_funs = [get_bdd_for_aig_lit(x.next) for x in
iterate_latches_and_error()]
# check cache
if cached_block_funs is None:
log.DBG_MSG("Rebuilding block_funs")
block_funs = dict()
for b in preds.abs_blocks:
block_funs[b] = gamma(preds.block_to_bdd[b]).compose(latches,
latch_funs)
else:
for b in preds.abs_blocks:
if b not in block_funs:
block_funs[b] = gamma(preds.block_to_bdd[b])
block_funs[b] = block_funs[b].compose(latches,
latch_funs)
# set cache
cached_block_funs = bdd.true()
def single_pre_env_bdd(dst_states_bdd, env_strat=None, get_strat=False):
if env_strat is not None:
strat = env_strat
else:
strat = bdd.true()
latches = [x.lit for x in iterate_latches_and_error()]
latch_funs = [get_bdd_for_aig_lit(x.next) for x in
iterate_latches_and_error()]
if restrict_like_crazy:
latch_funs = [x.restrict(~dst_states_bdd) for x in latch_funs]
# take a transition step backwards
p_bdd = dst_states_bdd.compose(latches, latch_funs)
# use the given strategy
p_bdd &= strat
# there is an uncontrollable action such that for all contro...
temp_bdd = p_bdd.univ_abstract(
bdd.get_cube(get_controllable_inputs_bdds()))
p_bdd = temp_bdd.exist_abstract(
bdd.get_cube(get_uncontrollable_inputs_bdds()))
if get_strat:
return temp_bdd
else:
return p_bdd
def abs_synthesis(compute_win_region=False):
global use_abs
# declare winner
def declare_winner(controllable, conc_lose):
log.LOG_MSG("Nr. of predicates: " + str(len(preds.abs_blocks)))
log.LOG_ACCUM()
if controllable:
log.LOG_MSG("The spec is realizable.")
if compute_win_region:
# make sure we reached the fixpoint
log.DBG_MSG("Get winning region")
return (~fp(bdd.BDD(error_fake_latch.lit) | conc_lose,
fun=lambda x: x | pre_env_bdd(x)), [])
else:
return (~conc_lose, [])
log.LOG_MSG("The spec is unrealizable.")
return (None, [])
# make sure that we have something to abstract
if aig.num_latches() == 0:
log.WRN_MSG("No latches in spec. Defaulting to regular synthesis.")
use_abs = False
return synthesize()
# update loss steps
local_loss_steps = (aig.num_latches() + 1) // loss_steps
log.DBG_MSG("Loss steps = " + str(local_loss_steps))
# registered quants
steps = 0
log.register_sum("ref_cnt", "Nr. of refinements: ")
log.register_sum("abs_time", "Time spent abstracting: ")
log.register_sum("uabs_time", "Time spent computing under-app of fp: ")
log.register_sum("oabs_time", "Time spent exhausting info of over-app: ")
log.register_average("unsafe_bdd_size",
"Average unsafe iterate bdd size: ")
# create the abstract game
initial_abstraction()
error_bdd = alpha_under(bdd.BDD(error_fake_latch.lit))
# add some latches
if ini_latch:
make_vis = (aig.num_latches() + 1) // ini_latch
log.DBG_MSG("Making visible " + str(make_vis) + " latches")
for i in range(make_vis):
preds.loc_red()
# first over-approx of the reachable region
reachable_bdd = bdd.true()
# The REAL algo
while True:
log.start_clock()
if use_trans:
transition_bdd = compose_abs_transition_bdd()
log.BDD_DMP(transition_bdd, "transition relation")
init_state_bdd = compose_abs_init_state_bdd()
log.BDD_DMP(init_state_bdd, "initial state set")
log.BDD_DMP(error_bdd, "unsafe state set")
log.stop_clock("abs_time")
# STEP 1: check if under-approx is losing
log.DBG_MSG("Computing over approx of FP")
log.start_clock()
under_fp = fp(error_bdd,
fun=lambda x: (reachable_bdd &
(x | pre_env_bdd_uabs(x))))
log.stop_clock("uabs_time")
if (init_state_bdd & under_fp) != bdd.false():
return declare_winner(False)
# STEP 2: exhaust information from the abstract game, i.e.
# update the reachability information we have
log.start_clock()
prev_reach = bdd.false()
reach = reachable_bdd
while prev_reach != reach:
prev_reach = reach
# STEP 2.1: check if the over-approx is winning
log.DBG_MSG("Computing over approx of FP")
over_fp = fp(under_fp,
fun=lambda x: (reach &
(x | pre_env_bdd_abs(x))))
if (over_fp & init_state_bdd) == bdd.false():
log.DBG_MSG("FP of the over-approx losing region not initial")
return declare_winner(True, gamma(under_fp))
# if there is no early exit we compute a strategy for Env
env_strats = pre_env_bdd_abs(over_fp, get_strat=True)
log.DBG_MSG("Computing over approx of Reach")
reach = fp(init_state_bdd,
fun=lambda x: (reach & (x | post_bdd_abs(x,
env_strats))))
log.stop_clock("oabs_time")
# STEP 3: refine or declare controllable
log.DBG_MSG("Concretizing the strategy of Env")
conc_env_strats = gamma(env_strats)
conc_reach = gamma(reach)
conc_under_fp = gamma(under_fp)
log.DBG_MSG("Taking one step of UPRE in the concrete game")
conc_step = single_pre_env_bdd(conc_under_fp,
env_strat=conc_env_strats)
conc_step &= conc_reach
if bdd.make_impl(conc_step, conc_under_fp) == bdd.true():
log.DBG_MSG("The concrete step revealed we are at the FP")
return declare_winner(True, conc_under_fp)
else:
# drop latches every number of steps
reset = False
if (steps != 0 and steps % local_loss_steps == 0):
log.DBG_MSG("Dropping all visible latches!")
reset = preds.drop_latches()
# add new predicates and reset caches if necessary
nu_losing_region = conc_step | conc_under_fp
reset |= preds.add_fixed_pred("reach", conc_reach)
reset |= preds.add_fixed_pred("unsafe", nu_losing_region)
# find interesting set of latches
log.DBG_MSG("Localization reduction step.")
reset |= preds.loc_red(not_imply=nu_losing_region)
log.DBG_MSG("# of predicates = " + str(len(preds.abs_blocks)))
if reset:
reset_caches()
# update error bdd
log.push_accumulated("unsafe_bdd_size",
nu_losing_region.dag_size())
error_bdd = alpha_under(nu_losing_region)
# update reachable area
reachable_bdd = alpha_over(conc_reach)
steps += 1
log.push_accumulated("ref_cnt", 1)
def compose_init_state_bdd():
b = bdd.true()
for x in iterate_latches_and_error():
b &= ~bdd.BDD(x.lit)
return b
def main(aiger_file_name, out_file):
aig.parse_into_spec(aiger_file_name)
log.DBG_MSG("AIG spec file parsed")
log.LOG_MSG("Nr. of latches: " + str(aig.num_latches()))
log.DBG_MSG("Latches: " + str([x.lit for x in
iterate_latches_and_error()]))
log.DBG_MSG("U. Inputs: " + str([x.lit for x in
aig.iterate_uncontrollable_inputs()]))
log.DBG_MSG("C. Inputs: " + str([x.lit for x in
aig.iterate_controllable_inputs()]))
# realizability and preliminary synthesis
if use_abs:
(win_region, reach_over) = abs_synthesis(out_file is not None)
else:
(win_region, reach_over) = synthesize()
if out_file and win_region:
log.LOG_MSG("Win region bdd node count = " +
str(win_region.dag_size()))
strategy = single_pre_sys_bdd(win_region, get_strat=True)
log.LOG_MSG("Strategy bdd node count = " +
str(strategy.dag_size()))
func_by_var = extract_output_funcs(strategy, win_region)
# attempt to minimize the winning region
for r in reach_over:
for (c_bdd, func_bdd) in func_by_var.items():
func_by_var[c_bdd] = func_bdd.safe_restrict(r)
log.DBG_MSG("Min'd version size " +
str(func_by_var[c_bdd].dag_size()))
# attempt to minimize the winning region
if min_win:
bdd.disable_reorder()
strategy = bdd.true()
for (c_bdd, func_bdd) in func_by_var.items():
strategy &= bdd.make_eq(c_bdd, func_bdd)
win_region = fp(compose_init_state_bdd(),
fun=lambda x: x | post_bdd(x, strategy))
for (c_bdd, func_bdd) in func_by_var.items():
func_by_var[c_bdd] = func_bdd.safe_restrict(win_region)
log.DBG_MSG("Min'd version size " +
str(func_by_var[c_bdd].dag_size()))
# model check?
if model_check:
strategy = bdd.true()
for (c_bdd, func_bdd) in func_by_var.items():
strategy &= bdd.make_eq(c_bdd, func_bdd)
assert (fp(bdd.BDD(error_fake_latch.lit),
fun=lambda x: x | single_pre_bdd(x, strategy)) &
compose_init_state_bdd()) == bdd.false()
# print out the strategy
total_dag = 0
for (c_bdd, func_bdd) in func_by_var.items():
total_dag += func_bdd.dag_size()
model_to_aiger(c_bdd, func_bdd)
log.LOG_MSG("Sum of func dag sizes = " + str(total_dag))
log.LOG_MSG("# of added gates = " + str(len(bdd_gate_cache)))
aig.write_spec(out_file)
return True
elif win_region:
return True
else:
return False
def main(aiger_file_name, out_file):
aig.parse_into_spec(aiger_file_name)
log.DBG_MSG("AIG spec file parsed")
log.LOG_MSG("Nr. of latches: " + str(aig.num_latches()))
log.DBG_MSG("Latches: " + str([x.lit
for x in iterate_latches_and_error()]))
log.DBG_MSG("U. Inputs: " +
str([x.lit for x in aig.iterate_uncontrollable_inputs()]))
log.DBG_MSG("C. Inputs: " +
str([x.lit for x in aig.iterate_controllable_inputs()]))
# realizability and preliminary synthesis
if use_abs:
(win_region, reach_over) = abs_synthesis(out_file is not None)
else:
(win_region, reach_over) = synthesize()
if out_file and win_region:
log.LOG_MSG("Win region bdd node count = " +
str(win_region.dag_size()))
strategy = single_pre_sys_bdd(win_region, get_strat=True)
log.LOG_MSG("Strategy bdd node count = " + str(strategy.dag_size()))
func_by_var = extract_output_funcs(strategy, win_region)
# attempt to minimize the winning region
for r in reach_over:
for (c_bdd, func_bdd) in func_by_var.items():
func_by_var[c_bdd] = func_bdd.safe_restrict(r)
log.DBG_MSG("Min'd version size " +
str(func_by_var[c_bdd].dag_size()))
# attempt to minimize the winning region
if min_win:
bdd.disable_reorder()
strategy = bdd.true()
for (c_bdd, func_bdd) in func_by_var.items():
strategy &= bdd.make_eq(c_bdd, func_bdd)
win_region = fp(compose_init_state_bdd(),
fun=lambda x: x | post_bdd(x, strategy))
for (c_bdd, func_bdd) in func_by_var.items():
func_by_var[c_bdd] = func_bdd.safe_restrict(win_region)
log.DBG_MSG("Min'd version size " +
str(func_by_var[c_bdd].dag_size()))
# model check?
if model_check:
strategy = bdd.true()
for (c_bdd, func_bdd) in func_by_var.items():
strategy &= bdd.make_eq(c_bdd, func_bdd)
assert (fp(bdd.BDD(error_fake_latch.lit),
fun=lambda x: x | single_pre_bdd(x, strategy))
& compose_init_state_bdd()) == bdd.false()
# print out the strategy
total_dag = 0
for (c_bdd, func_bdd) in func_by_var.items():
total_dag += func_bdd.dag_size()
model_to_aiger(c_bdd, func_bdd)
log.LOG_MSG("Sum of func dag sizes = " + str(total_dag))
log.LOG_MSG("# of added gates = " + str(len(bdd_gate_cache)))
aig.write_spec(out_file)
return True
elif win_region:
return True
else:
return False