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twa_graph: fix purge_unreachable_states on alternating automata

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The algorithm had two problems: it was removing only useless
destination from universal destination (instead of removing the entire
edge), and it was not properly iterating over the entire reachable
automaton.

* spot/twa/twagraph.cc: Fix it.
* spot/twa/twagraph.hh: Adjust documentation.
* tests/core/alternating.test: Add more tests.
* tests/python/twagraph.py: Adjust.
* NEWS: Mention the bug.
This commit is contained in:
Alexandre Duret-Lutz 2017-03-28 23:34:41 +02:00
parent 73bb562bf5
commit 6623af67e6
5 changed files with 250 additions and 44 deletions
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3
NEWS
View file

@ -12,6 +12,9 @@ New in spot 2.3.2.dev (not yet released)
the output is "terminal" because dtwa_complement() failed to reset
that property.
- spot::twa_graph::purge_unreachable_states() was misbehaving on
alternating automata.
New in spot 2.3.2 (2017-03-15)
Tools:

113
spot/twa/twagraph.cc
View file

@ -245,6 +245,8 @@ namespace spot
std::vector<unsigned> order;
order.reserve(num_states);
bool purge_unreachable_needed = false;
if (is_existential())
{
std::vector<std::pair<unsigned, unsigned>> todo; // state, edge
@ -307,12 +309,15 @@ namespace spot
const unsigned*& end = std::get<3>(todo.back());
if (tid == 0U && begin == end)
{
unsigned src = std::get<0>(todo.back());
todo.pop_back();
// Last transition from a state?
if ((int)src >= 0 && (todo.empty()
|| src != std::get<0>(todo.back())))
order.emplace_back(src);
if (todo.empty())
break;
unsigned src = std::get<0>(todo.back());
if ((int)src >= 0)
order.emplace_back(src);
else
continue;
}
unsigned dst = *begin++;
@ -338,23 +343,33 @@ namespace spot
}
}
// Process states in topological order
// At this point, all reachable states with successors are marked
// as useful.
for (;;)
{
bool univ_edge_erased = false;
// Process states in topological order to mark those without
// successors as useless.
for (auto s: order)
{
auto t = g_.out_iteraser(s);
bool useless = true;
while (t)
{
bool usefuldst = false;
// An edge is useful if all its
// destinations are useful.
bool usefuledge = true;
for (unsigned d: univ_dests(t->dst))
if (useful[d])
if (!useful[d])
{
usefuldst = true;
usefuledge = false;
break;
}
// Erase any edge to a useless state.
if (!usefuldst)
// Erase any useless edge
if (!usefuledge)
{
if (is_univ_dest(t->dst))
univ_edge_erased = true;
t.erase();
continue;
}
@ -366,25 +381,38 @@ namespace spot
if (useless)
useful[s] = 0;
}
// If we have erased any universal destination, it is possible
// that we have have created some new dead states, so we
// actually need to redo the whole thing again until there is
// no more universal edge to remove. Also we might have
// created some unreachable states, so we will simply call
// purge_unreachable_states() later to clean this.
if (!univ_edge_erased)
break;
else
purge_unreachable_needed = true;
}
// Make sure at least one initial destination is useful (even if
// it has been marked as useless by the previous loop because it
// has no successor).
bool usefulinit = false;
// Is the initial state actually useful? If not, make this an
// empty automaton by resetting the graph.
bool usefulinit = true;
for (unsigned d: univ_dests(init_number_))
if (useful[d])
if (!useful[d])
{
usefulinit = true;
usefulinit = false;
break;
}
if (!usefulinit)
for (unsigned d: univ_dests(init_number_))
{
useful[d] = true;
break;
g_ = graph_t();
init_number_ = new_state();
prop_deterministic(true);
prop_stutter_invariant(true);
prop_weak(true);
return;
}
// Now renumber each used state.
// Renumber each used state.
unsigned current = 0;
for (unsigned s = 0; s < num_states; ++s)
if (useful[s])
@ -394,6 +422,9 @@ namespace spot
if (current == num_states)
return; // No useless state.
defrag_states(std::move(useful), current);
if (purge_unreachable_needed)
purge_unreachable_states();
}
void twa_graph::defrag_states(std::vector<unsigned>&& newst,
@ -401,14 +432,46 @@ namespace spot
{
if (!is_existential())
{
// Running defrag_states() on alternating automata is tricky,
// because we want to
// #1 rename the regular states
// #2 rename the states in universal destinations
// #3 get rid of the unused universal destinations
// #4 merge identical universal destinations
//
// graph::degrag_states() actually does only #1. It it could
// do #2, but that would prevent use from doing #3 and #4. It
// cannot do #3 and #4 because the graph object does not know
// what an initial state is, and our initial state might be
// universal.
//
// As a consequence this code preforms #2, #3, and #4 before
// calling graph::degrag_states() to finish with #1. We clear
// the "dests vector" of the current automaton, recreate all
// the new destination groups using a univ_dest_mapper to
// simplify an unify them, and extend newst with some new
// entries that will point the those new universal destination
// so that graph::defrag_states() does not have to deal with
// universal destination in any way.
auto& g = get_graph();
auto& dests = g.dests_vector();
// Clear the destination vector, saving the old one.
std::vector<unsigned> old_dests;
std::swap(dests, old_dests);
std::vector<unsigned> seen(old_dests.size(), -1U);
// dests will be updated as a side effect of declaring new
// destination groups to uniq.
internal::univ_dest_mapper<twa_graph::graph_t> uniq(g);
// The newst entry associated to each of the old destination
// group.
std::vector<unsigned> seen(old_dests.size(), -1U);
// Rename a state if it denotes a universal destination. This
// function has to be applied to the destination of each edge,
// as well as to the initial state. The need to work on the
// initial state is the reason it cannot be implemented in
// graph::defrag_states().
auto fixup = [&](unsigned& in_dst)
{
unsigned dst = in_dst;
@ -416,8 +479,9 @@ namespace spot
return;
dst = ~dst;
unsigned& nd = seen[dst];
if (nd == -1U)
if (nd == -1U) // An unprocessed destination group
{
// store all renamed destination states in tmp
std::vector<unsigned> tmp;
auto begin = old_dests.data() + dst + 1;
auto end = begin + old_dests[dst];
@ -430,10 +494,17 @@ namespace spot
}
if (tmp.empty())
{
// All destinations of this group were marked for
// removal. Mark this universal transition for
// removal as well. Is this really what we expect?
nd = -1U;
}
else
{
// register this new destination group, add et two
// newst, and use the index in newst to relabel
// the state so that graph::degrag_states() will
// eventually update it to the correct value.
nd = newst.size();
newst.emplace_back(uniq.new_univ_dests(tmp.begin(),
tmp.end()));

14
spot/twa/twagraph.hh
View file

@ -541,18 +541,26 @@ namespace spot
/// states without successors, unreachable states, and states
/// that only have dead successors.
///
/// This function runs in linear time on non-alternating automata,
/// but its current implementation can be quadratic when removing
/// dead states from alternating automata. (In the latter case, a
/// universal edge has to be remove when any of its destination is
/// dead, but this might cause the other destinations to become
/// dead or unreachable themselves.)
///
/// \see purge_unreachable_states
void purge_dead_states();
/// \brief Remove all unreachable states.
///
/// A state is unreachable if it cannot be reached from the initial state.
/// A state is unreachable if it cannot be reached from the
/// initial state.
///
/// Use this function if you have declared more states than you
/// actually need in the automaton.
/// actually need in the automaton. It runs in linear time.
///
/// purge_dead_states() will remove more states than
/// purge_unreachable_states().
/// purge_unreachable_states(), but it is more costly.
///
/// \see purge_dead_states
void purge_unreachable_states();

125
tests/core/alternating.test
View file

@ -276,6 +276,27 @@ autfilt -q --intersect=ex1 ex3
cat >ex4<<EOF
HOA: v1
States: 5
Start: 0&2
AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: univ-branch trans-labels explicit-labels trans-acc
properties: deterministic
--BODY--
State: 0
[0] 0
[!0] 0&2
State: 1
[t] 1&4
State: 2
[!0] 2 {0}
[0] 3
State: 3
[t] 3
State: 4
--END--
HOA: v1
States: 5
Start: 0&2&4
AP: 1 "a"
acc-name: co-Buchi
@ -299,6 +320,24 @@ EOF
cat >expect4<<EOF
HOA: v1
States: 3
Start: 0&1
AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: univ-branch trans-labels explicit-labels trans-acc complete
properties: deterministic
--BODY--
State: 0
[0] 0
[!0] 0&1
State: 1
[!0] 1 {0}
[0] 2
State: 2
[t] 2
--END--
HOA: v1
States: 4
Start: 0&1&3
AP: 1 "a"
@ -319,10 +358,42 @@ State: 3
--END--
EOF
cat >expect4d<<EOF
HOA: v1
States: 3
Start: 0&1
AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: univ-branch trans-labels explicit-labels trans-acc complete
properties: deterministic
--BODY--
State: 0
[0] 0
[!0] 0&1
State: 1
[!0] 1 {0}
[0] 2
State: 2
[t] 2
--END--
HOA: v1
States: 1
Start: 0
AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: trans-labels explicit-labels state-acc deterministic
properties: stutter-invariant weak
--BODY--
State: 0
--END--
EOF
run 0 autfilt --remove-unreachable-states ex4 > out4
diff expect4 out4
run 0 autfilt --remove-dead-states ex4 > out4
diff ex2 out4
diff expect4d out4
cat >ex5<<EOF
@ -336,6 +407,33 @@ Acceptance: 1 Fin(0)
State: 0
State: 1
--END--
HOA: v1
States: 3
Start: 0
AP: 1 "a"
Acceptance: 0 t
--BODY--
State: 0
[0] 1&2
[!0] 1
State: 1
[!0] 1
State: 2
--END--
HOA: v1
States: 4
Start: 0&1
AP: 1 "a"
Acceptance: 0 t
--BODY--
State: 0
[0] 1&2
State: 1
[!0] 1&0&3
State: 2
State: 3
[t] 3
--END--
EOF
run 0 autfilt --remove-dead-states ex5 > out5
@ -347,6 +445,31 @@ AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: trans-labels explicit-labels state-acc deterministic
properties: stutter-invariant weak
--BODY--
State: 0
--END--
HOA: v1
States: 2
Start: 0
AP: 1 "a"
acc-name: all
Acceptance: 0 t
properties: trans-labels explicit-labels state-acc deterministic
--BODY--
State: 0
[!0] 1
State: 1
[!0] 1
--END--
HOA: v1
States: 1
Start: 0
AP: 1 "a"
acc-name: all
Acceptance: 0 t
properties: trans-labels explicit-labels state-acc deterministic
properties: stutter-invariant weak
--BODY--
State: 0
--END--

1
tests/python/twagraph.py
View file

@ -87,4 +87,5 @@ assert aut.edge_data(1).cond == bddtrue
aut.release_iter(it)
aut.purge_dead_states()
i = aut.get_init_state()
assert aut.state_is_accepting(i) == False