doc: show more metadata about automata

* src/twa/bdddict.hh (varnum): New method.
* doc/org/tut21.org: Show more metadata.

doc/org/tut21.org

@@ -48,10 +48,16 @@ We now write some C++ to load this automaton [[file:tut20.org][as we did before]
 iterating over it states and edges.
 
 The only tricky part is to print the edge labels.  Since they are
-BDDs, printing them directly would just show the number of BDD
-variables involved.  Using =bdd_print_formula= and passing it the BDD
-dictionary associated to the automaton is the way to print the edge
-labels.
+BDDs, printing them directly would just show the identifiers of BDDs
+involved.  Using =bdd_print_formula= and passing it the BDD dictionary
+associated to the automaton is one way to print the edge labels.
+
+Each automaton stores a vector the atomic propositions it uses.  You
+can iterate on that vector using the =ap()= member function.  If you
+want to convert an atomic proposition (represented by a =formula=)
+into a BDD, use the =bdd_dict::varnum()= method to obtain the
+corresponding BDD variable number, and then use for instance
+=bdd_ithvar()= to convert this BDD variable number into an actual BDD.
 
 #+BEGIN_SRC C++ :results verbatim :exports both
   #include <string>
@@ -83,15 +89,30 @@ labels.
 
   void custom_print(std::ostream& out, spot::twa_graph_ptr& aut)
   {
+    // We need the dictionary to print the BDD that labels the edge
+    const auto& dict = aut->get_dict();
+
     // Print some meta-data
     out << "Acceptance: " << aut->get_acceptance() << '\n';
     out << "Number of sets: " << aut->num_sets() << '\n';
     out << "Number of states: " << aut->num_states() << '\n';
     out << "Number of edges: " << aut->num_edges() << '\n';
     out << "Initial state: " << aut->get_init_state_number() << '\n';
-
-    // We need the dictionary to print the BDD that labels the edge
-    const auto& dict = aut->get_dict();
+    out << "Atomic propositions:";
+    for (spot::formula ap: aut->ap())
+        out << ' ' << ap << " (=" << dict->varnum(ap) << ')';
+    out << '\n';
+    // For these methods, true means "it's sure", false means "I don't
+    // know".  These properties correspond to bits stored in the
+    // automaton, so they can be queried in constant time, and they are
+    // only set whenever they can be determined at a cheap cost.
+    out << "Deterministic: "
+        << (aut->is_deterministic() ? "yes\n" : "maybe\n");
+    out << "StateBasedAcc: "
+        << (aut->has_state_based_acc() ? "yes\n" : "maybe\n");
+    out << "Stutter Invariant: "
+        << (aut->is_stutter_invariant() ? "yes\n" :
+            aut->is_stutter_sensitive() ? "no\n" : "maybe\n");
 
     // States are numbered from 0 to n-1
     unsigned n = aut->num_states();
@@ -121,6 +142,10 @@ Number of sets: 2
 Number of states: 4
 Number of edges: 10
 Initial state: 0
+Atomic propositions: a (=0) b (=1) c (=2)
+Deterministic: maybe
+StateBasedAcc: maybe
+Stutter Invariant: yes
 State 0:
   edge(0 -> 1)
     label = a

src/twa/bdddict.hh

@@ -123,6 +123,15 @@ namespace spot
     }
     /// @}
 
+    // \brief return the BDD variable associated to a registered
+    // proposition.
+    //
+    // Throws std::out_of_range if the \a is not a known proposition.
+    int varnum(formula f)
+    {
+      return var_map.at(f);
+    }
+
     /// \brief Register an acceptance variable.
     ///
     /// Return (and maybe allocate) a BDD variable designating an