to_parity: only call reduce_parity() when prefix_parity is enabled

Calling reduce_parity() in to_parity() is confusing, because then
running to_parity() on one SCC does not necessarily produce the same
output as running to_parity() on the entire automaton.  However it is
necessary for the implementation of parity_prefix.  As a compromise,
disable reduce_parity() when parity_prefix is disabled, this way we
can use that to demonstrate how the algorithm works.

* spot/twaalgos/toparity.hh, spot/twaalgos/toparity.cc: Do not
call reduce_parity() when parity_prefix is disabled.
* tests/python/toparity.py: Adjust.

spot/twaalgos/toparity.cc

@@ -1679,13 +1679,25 @@ run()
         res_->set_init_state(initial_state_res->second);
     else
         res_->new_state();
-    res_->set_acceptance(
-        acc_cond::acc_code::parity_max(is_odd, SPOT_MAX_ACCSETS));
     if (options.pretty_print)
         res_->set_named_prop("state-names", names);
-    reduce_parity_here(res_);
+
     res_->purge_unreachable_states();
-    // res_->merge_states();
+    // If parity_prefix is used, we use all available colors by
+    // default: The IAR/CAR are using lower indices, and the prefix is
+    // using the upper indices.  So we use reduce_parity() to clear
+    // the mess.   If parity_prefix is not used,
+    unsigned max_color = SPOT_MAX_ACCSETS;
+    if (!options.parity_prefix)
+      {
+        acc_cond::mark_t all = {};
+        for (auto& e: res_->edges())
+          all |= e.acc;
+        max_color = all.max_set();
+      }
+    res_->set_acceptance(acc_cond::acc_code::parity_max(is_odd, max_color));
+    if (options.parity_prefix)
+      reduce_parity_here(res_);
     return res_;
 }
 

spot/twaalgos/toparity.hh

@@ -31,11 +31,11 @@ namespace spot
     /// several elements in a record, it tries to find an order such
     /// that the new permutation already exists.
     bool search_ex = true;
-    /// If \a use_last is true and \a search_ex are true, we use the
+    /// If \c use_last is true and \a search_ex are true, we use the
     /// most recent state when we find multiple existing state
     /// compatible with the current move.
     bool use_last = true;
-    /// If \a force_order is true, we force to use an order when CAR or IAR is
+    /// If \c force_order is true, we force to use an order when CAR or IAR is
     /// applied. Given a state s and a set E ({0}, {0 1}, {2} for example) we
     /// construct an order on colors. With the given example, we ask to have
     /// a permutation that start with [0 …], [0 1 …] or [2 …] in
@@ -51,15 +51,25 @@ namespace spot
     /// If \c scc_acc_clean is true, to_parity() will ignore colors
     /// no occoring in an SCC while processing this SCC.
     bool acc_clean = true;
-    /// If \a parity_equiv is true, to_parity() will check if there
+    /// If \c parity_equiv is true, to_parity() will check if there
     /// exists a permutations of colors such that the acceptance
     /// condition is a parity condition.
     bool parity_equiv = true;
-    /// If \a parity_prefix is true, to_parity() will remove the prefix of
-    /// the acceptance condition that correspond to parity, works on the
-    // remaining and adds marks to process the prefix.
+    /// If \c parity_prefix is true, to_parity() will use a special
+    /// handling for acceptance conditions of the form `Inf(m0) |
+    /// (Fin(m1) & (Inf(m2) | (… β)))` that start as a parity
+    /// condition (modulo a renumbering of `m0`, `m1`, `m2`, ...) but where
+    /// `β` can be an arbitrary formula.  In this case, the paritization
+    /// algorithm is really applied only to `β`, and the marks of the
+    /// prefix are appended after a suitable renumbering.
+    ///
+    /// For technical reasons, activating this option (and this is the
+    /// default) causes reduce_parity() to be called at the end to
+    /// minimize the number of colors used.  It is therefore
+    /// recommended to disable this option when one wants to follow
+    /// the output CAR/IAR constructions.
     bool parity_prefix = true;
-    /// If \a rabin_to_buchi is true, to_parity() tries to convert a Rabin or
+    /// If \c rabin_to_buchi is true, to_parity() tries to convert a Rabin or
     /// Streett condition to Büchi or co-Büchi with
     /// rabin_to_buchi_if_realizable().
     bool rabin_to_buchi = true;
@@ -70,7 +80,7 @@ namespace spot
     /// in order to move more colors (and increase the number of
     /// compatible states) when we apply LAR.
     bool propagate_col = true;
-    /// If \a pretty_print is true, states of the output automaton are
+    /// If \c pretty_print is true, states of the output automaton are
     /// named to help debugging.
     bool pretty_print = false;
   };

tests/python/toparity.py

@@ -106,6 +106,10 @@ def test(aut, expected_num_states=[], full=True):
                             propagate_col = opt.propagate_col,
                             pretty_print = opt.pretty_print,
                             )
+        p1st, p1ed, p1se = p1.num_states(), p1.num_edges(), p1.num_sets()
+        if opt.parity_prefix is False:
+            # Reduce the number of colors to help are_equivalent
+            spot.reduce_parity_here(p1)
         assert spot.are_equivalent(aut, p1)
         if expected_num is not None:
                 assert p1.num_states() == expected_num
@@ -113,9 +117,9 @@ def test(aut, expected_num_states=[], full=True):
             # Make sure passing opt is the same as setting
             # each argument individually
             p2 = spot.to_parity(aut, opt)
-            assert p2.num_states() == p1.num_states()
-            assert p2.num_edges() == p1.num_edges()
-            assert p2.num_sets() == p1.num_sets()
+            assert p2.num_states() == p1st
+            assert p2.num_edges() == p1ed
+            assert p2.num_sets() == p1se
 
 test(spot.automaton("""HOA: v1
 name: "(FGp0 & ((XFp0 & F!p1) | F(Gp1 & XG!p0))) | G(F!p0 & (XFp0 | F!p1) &