zlktree: add a paritization based on zielonka trees
* spot/twaalgos/zlktree.hh, spot/twaalgos/zlktree.cc (zielonka_tree_transform): New function. * tests/python/_zlktree.ipynb: Test it on three examples.
This commit is contained in:
Alexandre Duret-Lutz
parent
c924c63255
commit
8c5bb6c2eb
3 changed files with 877 additions and 11 deletions
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@ -20,13 +20,15 @@
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#include "config.h"
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#include <iostream>
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#include <spot/twaalgos/zlktree.hh>
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#include <spot/twaalgos/sccinfo.hh>
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#include <deque>
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#include "spot/priv/bddalloc.hh"
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namespace spot
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{
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zielonka_tree::zielonka_tree(acc_cond& cond)
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zielonka_tree::zielonka_tree(const acc_cond& cond)
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{
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acc_cond::acc_code& code = cond.get_acceptance();
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const acc_cond::acc_code& code = cond.get_acceptance();
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auto used = code.used_sets();
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unsigned c = used.count();
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unsigned max = used.max_set();
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@ -225,4 +227,124 @@ namespace spot
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}
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return {branch, lvl};
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}
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namespace
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{
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// A state in the zielonka_tree_transform output corresponds to a
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// state in the input associated to a branch of the tree.
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typedef std::pair<unsigned, unsigned> zlk_state;
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struct zlk_state_hash
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{
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size_t
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operator()(const zlk_state& s) const noexcept
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{
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return wang32_hash(s.first ^ wang32_hash(s.second));
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}
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};
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}
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twa_graph_ptr
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zielonka_tree_transform(const const_twa_graph_ptr& a)
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{
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auto res = make_twa_graph(a->get_dict());
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res->copy_ap_of(a);
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zielonka_tree zlk(a->get_acceptance());
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// Preserve determinism, weakness, and stutter-invariance
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res->prop_copy(a, { false, true, true, true, true, true });
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auto orig_states = new std::vector<unsigned>();
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auto branches = new std::vector<unsigned>();
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unsigned ns = a->num_states();
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orig_states->reserve(ns); // likely more are needed.
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res->set_named_prop("original-states", orig_states);
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res->set_named_prop("degen-levels", branches);
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// Associate each zlk_state to its number.
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typedef std::unordered_map<zlk_state, unsigned, zlk_state_hash> zs2num_map;
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zs2num_map zs2num;
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// Queue of states to be processed.
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std::deque<zlk_state> todo;
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auto new_state = [&](zlk_state zs)
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{
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if (auto i = zs2num.find(zs); i != zs2num.end())
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return i->second;
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unsigned ns = res->new_state();
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zs2num[zs] = ns;
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todo.emplace_back(zs);
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unsigned orig = zs.first;
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assert(ns == orig_states->size());
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orig_states->emplace_back(orig);
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branches->emplace_back(zs.second);
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return ns;
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};
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zlk_state s(a->get_init_state_number(), zlk.first_branch());
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new_state(s);
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unsigned max_color = 0;
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while (!todo.empty())
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{
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s = todo.front();
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todo.pop_front();
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int src = zs2num[s];
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unsigned branch = s.second;
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for (auto& i: a->out(s.first))
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{
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auto [newbranch, prio] = zlk.step(branch, i.acc);
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zlk_state d(i.dst, newbranch);
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unsigned dst = new_state(d);
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max_color = std::max(max_color, prio);
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res->new_edge(src, dst, i.cond, {prio});
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}
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}
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res->set_acceptance(max_color + 1,
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acc_cond::acc_code::parity_min(!zlk.is_even(),
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max_color + 1));
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// compose original-states with the any previously existing one.
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// We do that now, because for the bottommost copy below, it's better
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// if we compose everything.
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if (auto old_orig_states =
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a->get_named_prop<std::vector<unsigned>>("original-states"))
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for (auto& s: *orig_states)
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s = (*old_orig_states)[s];
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// Now we will iterate over the SCCs in topological order to
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// remember the "bottommost" SCCs that contain each original
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// state. If an original state is duplicated in a higher SCC,
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// it can be shunted away. Amen.
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scc_info si_res(res, scc_info_options::TRACK_STATES);
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unsigned res_scc_count = si_res.scc_count();
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unsigned maxorig = *std::max_element(orig_states->begin(),
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orig_states->end());
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std::vector<unsigned> bottommost_occurence(maxorig + 1);
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{
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unsigned n = res_scc_count;
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do
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for (unsigned s: si_res.states_of(--n))
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bottommost_occurence[(*orig_states)[s]] = s;
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while (n);
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}
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unsigned res_ns = res->num_states();
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std::vector<unsigned> retarget(res_ns);
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for (unsigned n = 0; n < res_ns; ++n)
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{
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unsigned other = bottommost_occurence[(*orig_states)[n]];
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retarget[n] =
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(si_res.scc_of(n) != si_res.scc_of(other)) ? other : n;
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}
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for (auto& e: res->edges())
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e.dst = retarget[e.dst];
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res->set_init_state(retarget[res->get_init_state_number()]);
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res->purge_unreachable_states();
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return res;
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}
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}
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@ -37,7 +37,7 @@ namespace spot
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{
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public:
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/// \brief Build a Zielonka tree from the acceptance condition.
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zielonka_tree(acc_cond& cond);
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zielonka_tree(const acc_cond& cond);
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/// \brief The number of branches in the Zielonka tree.
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///
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@ -129,4 +129,17 @@ namespace spot
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bool has_streett_shape_ = true;
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};
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/// \ingroup twa_acc_transform
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/// \brief Paritize an automaton using Zielonka tree.
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///
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/// This corresponds to the application of Section 3 of
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/// \cite casares.21.icalp
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///
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/// The resulting automaton has a parity acceptance that is either
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/// "min odd" or "min even", depending on the original acceptance.
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/// It may uses up to n+1 colors if the input automaton has n
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/// colors. Finally, it is colored, i.e., each output transition
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/// has exactly one color.
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SPOT_API
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twa_graph_ptr zielonka_tree_transform(const const_twa_graph_ptr& aut);
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}
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@ -191,7 +191,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb0897c00> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe7807fa80> >"
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]
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},
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"metadata": {},
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@ -755,7 +755,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb10dd300> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe7807fab0> >"
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]
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},
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"metadata": {},
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@ -1111,7 +1111,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb083c900> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301e70> >"
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]
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},
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"metadata": {},
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@ -1247,7 +1247,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a46f0> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301e10> >"
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]
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},
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"metadata": {},
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@ -1358,7 +1358,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a48a0> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301840> >"
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]
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},
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"metadata": {},
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@ -1421,7 +1421,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a43f0> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301300> >"
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]
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},
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"metadata": {},
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@ -1484,7 +1484,7 @@
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"</svg>\n"
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],
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"text/plain": [
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a43c0> >"
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"<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a305780> >"
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]
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},
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"metadata": {},
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@ -1511,10 +1511,741 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 19,
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"id": "interesting-seller",
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"metadata": {},
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"outputs": [],
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"source": [
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"a = spot.automaton(\"\"\"HOA: v1 name: \"(FGp0 & ((XFp0 & F!p1) | F(Gp1 &\n",
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"XG!p0))) | G(F!p0 & (XFp0 | F!p1) & F(Gp1 | G!p0))\" States: 14 Start:\n",
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"0 AP: 2 \"p1\" \"p0\" Acceptance: 6 (Fin(0) & Fin(1)) | ((Fin(4)|Fin(5)) &\n",
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"(Inf(2)&Inf(3))) properties: trans-labels explicit-labels trans-acc\n",
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"complete properties: deterministic --BODY-- State: 0 [!0] 1 [0] 2\n",
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"State: 1 [!0&!1] 1 {0 1 2 3 5} [0&!1] 3 [!0&1] 4 [0&1] 5 State: 2\n",
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"[0&!1] 2 {1} [!0&1] 4 [!0&!1] 6 [0&1] 7 State: 3 [0&!1] 3 {1 3} [!0&1]\n",
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"4 [!0&!1] 6 {0 1 2 3 5} [0&1] 8 State: 4 [!0&!1] 4 {1 2 3 5} [!0&1] 4\n",
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"{2 4 5} [0&!1] 5 {1 3} [0&1] 5 {4} State: 5 [!0&1] 4 {2 4 5} [0&!1] 5\n",
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"{1 3} [0&1] 8 {2 4} [!0&!1] 9 {1 2 3 5} State: 6 [0&!1] 3 {1 3} [!0&1]\n",
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"4 [0&1] 5 [!0&!1] 10 State: 7 [!0&1] 4 [0&!1] 7 {1 3} [!0&!1] 11 [0&1]\n",
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"12 {0 4} State: 8 [!0&1] 4 {2 4 5} [0&1] 5 {4} [0&!1] 8 {1 3} [!0&!1]\n",
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"11 {1 3 5} State: 9 [!0&1] 4 {2 4 5} [0&!1] 5 {1 3} [0&1] 5 {4}\n",
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"[!0&!1] 11 {1 3 5} State: 10 [!0&1] 4 [0&1] 8 [!0&!1] 10 {0 1 2 3 5}\n",
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"[0&!1] 13 {1 2 3} State: 11 [!0&1] 4 {2 4 5} [0&!1] 8 {1 2 3} [0&1] 8\n",
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"{2 4} [!0&!1] 11 {1 2 3 5} State: 12 [!0&1] 4 [0&1] 7 {0 2 4} [!0&!1]\n",
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"9 [0&!1] 12 {1 3} State: 13 [!0&1] 4 [0&1] 5 [!0&!1] 10 {0 1 3 5}\n",
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"[0&!1] 13 {1 3} --END--\"\"\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "informative-mainland",
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"metadata": {},
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"outputs": [],
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"source": [
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"b = spot.zielonka_tree_transform(a)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "angry-comedy",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"33"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"b.num_states()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "contained-combat",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"a.equivalent_to(b)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "paperback-handle",
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"metadata": {},
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"outputs": [
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{
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}
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"source": [
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"HOA: v1\n",
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"States: 2\n",
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"Start: 0\n",
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"AP: 2 \"p1\" \"p0\"\n",
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"properties: trans-labels explicit-labels trans-acc complete\n",
|
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"properties: deterministic stutter-invariant\n",
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"--BODY--\n",
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"--END--\n",
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{
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"execution_count": 24,
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"id": "tired-webcam",
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"source": [
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"e = spot.translate('!(GFa -> (GFb & GF(!b & !Xb)))', 'gen', 'det')\n",
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},
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{
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"execution_count": 27,
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"id": "complimentary-person",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"True"
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]
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},
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"metadata": {},
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}
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],
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"source": [
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"e.equivalent_to(f)"
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "determined-bankruptcy",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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|
|
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|||
Loading…
Add table
Add a link
Reference in a new issue