diff --git a/src/dstarparse/dra2ba.cc b/src/dstarparse/dra2ba.cc
index a90356440..08364e12f 100644
--- a/src/dstarparse/dra2ba.cc
+++ b/src/dstarparse/dra2ba.cc
@@ -238,6 +238,7 @@ namespace spot
       {
 	bdd_dict* bd = a->aut->get_dict();
 	bd->register_all_variables_of(a->aut, out_);
+	out_->set_bprop(tgba_digraph::StateBasedAcc);
 
 	// Invent a new acceptance set for the degeneralized automaton.
 	int accvar =
diff --git a/src/dstarparse/nra2nba.cc b/src/dstarparse/nra2nba.cc
index 3df34ad28..7c539a850 100644
--- a/src/dstarparse/nra2nba.cc
+++ b/src/dstarparse/nra2nba.cc
@@ -52,6 +52,8 @@ namespace spot
 	int accvar =
 	  bd->register_acceptance_variable(ltl::constant::true_instance(),
 					   out_);
+	out_->set_bprop(tgba_digraph::StateBasedAcc);
+
 	acc_ = bdd_ithvar(accvar);
 	out_->set_acceptance_conditions(acc_);
 	out_->new_states(num_states_ * (d_->accpair_count + 1));
diff --git a/src/neverparse/neverclaimparse.yy b/src/neverparse/neverclaimparse.yy
index d5ec008b8..9cec1a443 100644
--- a/src/neverparse/neverclaimparse.yy
+++ b/src/neverparse/neverclaimparse.yy
@@ -309,6 +309,8 @@ namespace spot
     bdd acc = bdd_ithvar(dict->register_acceptance_variable(t, result));
     result->set_acceptance_conditions(acc);
 
+    result->set_bprop(tgba_digraph::SBA);
+
     neverclaimyy::parser parser(error_list, env, result, namer, fcache);
     parser.set_debug_level(debug);
     parser.parse();
diff --git a/src/taalgos/tgba2ta.cc b/src/taalgos/tgba2ta.cc
index 0cc1fdaef..1b970c6d1 100644
--- a/src/taalgos/tgba2ta.cc
+++ b/src/taalgos/tgba2ta.cc
@@ -29,7 +29,6 @@
 #include "ltlast/atomic_prop.hh"
 #include "ltlast/constant.hh"
 #include "tgba/formula2bdd.hh"
-#include "tgba/sba.hh"
 #include "misc/bddop.hh"
 #include <cassert>
 #include "ltlvisit/tostring.hh"
diff --git a/src/tgba/Makefile.am b/src/tgba/Makefile.am
index 15fbba016..e60c205a0 100644
--- a/src/tgba/Makefile.am
+++ b/src/tgba/Makefile.am
@@ -30,7 +30,6 @@ tgba_HEADERS = \
   bddprint.hh \
   formula2bdd.hh \
   futurecondcol.hh \
-  sba.hh \
   state.hh \
   succiter.hh \
   taatgba.hh \
diff --git a/src/tgba/sba.hh b/src/tgba/sba.hh
deleted file mode 100644
index b2166c41c..000000000
--- a/src/tgba/sba.hh
+++ /dev/null
@@ -1,43 +0,0 @@
-// Copyright (C) 2012 Laboratoire de Recherche et Développement
-// de l'Epita (LRDE).
-//
-// This file is part of Spot, a model checking library.
-//
-// Spot is free software; you can redistribute it and/or modify it
-// under the terms of the GNU General Public License as published by
-// the Free Software Foundation; either version 3 of the License, or
-// (at your option) any later version.
-//
-// Spot is distributed in the hope that it will be useful, but WITHOUT
-// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
-// License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-
-#ifndef SPOT_TGBA_SBA_HH
-# define SPOT_TGBA_SBA_HH
-
-#include "tgba.hh"
-
-namespace spot
-{
-  /// \ingroup tgba_essentials
-  /// \brief A State-based Generalized Büchi Automaton.
-  ///
-  /// An SBA is a TGBA in which the outgoing transitions of
-  /// a state are either all accepting (in which case the
-  /// source state is said "accepting"(, or all non-accepting.
-  class sba: public tgba
-  {
-  public:
-    /// \brief is \a s an accepting state?
-    ///
-    /// If a state is accepting all its outgoing transitions are
-    /// accepting.
-    virtual bool state_is_accepting(const spot::state* s) const = 0;
-  };
-}
-
-#endif // SPOT_TGBA_SBA_HH
diff --git a/src/tgba/tgbagraph.hh b/src/tgba/tgbagraph.hh
index 986d0a497..1e026b297 100644
--- a/src/tgba/tgbagraph.hh
+++ b/src/tgba/tgbagraph.hh
@@ -314,6 +314,11 @@ namespace spot
 	}
       all_acceptance_conditions_ =
 	compute_all_acceptance_conditions(neg_acceptance_conditions_);
+
+      if (number_of_acceptance_conditions() == 1)
+	set_bprop(tgba_digraph::SingleAccSet);
+      else
+	clear_bprop(tgba_digraph::SingleAccSet);
     }
 
     unsigned new_state()
diff --git a/src/tgbaalgos/dotty.cc b/src/tgbaalgos/dotty.cc
index 8bb4f3b00..7cd9b1770 100644
--- a/src/tgbaalgos/dotty.cc
+++ b/src/tgbaalgos/dotty.cc
@@ -21,8 +21,7 @@
 // along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 #include <ostream>
-#include "tgba/tgba.hh"
-#include "tgba/sba.hh"
+#include "tgba/tgbagraph.hh"
 #include "dotty.hh"
 #include "dottydec.hh"
 #include "tgba/bddprint.hh"
@@ -42,7 +41,7 @@ namespace spot
 		dotty_decorator* dd)
 	: tgba_reachable_iterator_breadth_first(a), os_(os),
 	  mark_accepting_states_(mark_accepting_states), dd_(dd),
-	  sba_(dynamic_cast<const sba*>(a))
+	  sba_(dynamic_cast<const tgba_digraph*>(a))
       {
       }
 
@@ -120,7 +119,7 @@ namespace spot
       std::ostream& os_;
       bool mark_accepting_states_;
       dotty_decorator* dd_;
-      const sba* sba_;
+      const tgba_digraph* sba_;
     };
   }
 
diff --git a/src/tgbaalgos/lbtt.cc b/src/tgbaalgos/lbtt.cc
index 607ad2ce0..3a4ce30ef 100644
--- a/src/tgbaalgos/lbtt.cc
+++ b/src/tgbaalgos/lbtt.cc
@@ -244,6 +244,7 @@ namespace spot
       auto aut = std::unique_ptr<tgba_digraph>(new tgba_digraph(dict));
       acc_mapper_int acc_b(aut.get(), num_acc, envacc);
       aut->new_states(num_states);
+      aut->set_bprop(tgba_digraph::StateBasedAcc);
 
       for (unsigned n = 0; n < num_states; ++n)
 	{
diff --git a/src/tgbaalgos/minimize.cc b/src/tgbaalgos/minimize.cc
index 1b4836b14..99b3f9c83 100644
--- a/src/tgbaalgos/minimize.cc
+++ b/src/tgbaalgos/minimize.cc
@@ -143,7 +143,6 @@ namespace spot
     bdd allacc = bddfalse;
     if (!final->empty())
       {
-	res->set_bprop(tgba_digraph::SingleAccSet);
 	int accvar =
 	  dict->register_acceptance_variable(ltl::constant::true_instance(),
 					     res);
diff --git a/src/tgbaalgos/neverclaim.cc b/src/tgbaalgos/neverclaim.cc
index ecc6dfce2..3a81338f7 100644
--- a/src/tgbaalgos/neverclaim.cc
+++ b/src/tgbaalgos/neverclaim.cc
@@ -23,7 +23,7 @@
 #include <ostream>
 #include <sstream>
 #include "bdd.h"
-#include "tgba/sba.hh"
+#include "tgba/tgbagraph.hh"
 #include "neverclaim.hh"
 #include "tgba/bddprint.hh"
 #include "reachiter.hh"
@@ -42,8 +42,9 @@ namespace spot
 	: tgba_reachable_iterator_breadth_first(a),
 	  os_(os), f_(f), accept_all_(-1), fi_needed_(false),
 	  comments_(comments), all_acc_conds_(a->all_acceptance_conditions()),
-	  sba_(dynamic_cast<const sba*>(a))
+	  sba_(dynamic_cast<const tgba_digraph*>(a))
       {
+	assert(!sba_ || sba_->get_bprop(tgba_digraph::StateBasedAcc));
       }
 
       void
@@ -193,7 +194,7 @@ namespace spot
       state* init_;
       bool comments_;
       bdd all_acc_conds_;
-      const sba* sba_;
+      const tgba_digraph* sba_;
     };
   } // anonymous
 
diff --git a/src/tgbaalgos/sccfilter.cc b/src/tgbaalgos/sccfilter.cc
index 4c9c63f99..5aed42152 100644
--- a/src/tgbaalgos/sccfilter.cc
+++ b/src/tgbaalgos/sccfilter.cc
@@ -499,7 +499,11 @@ namespace spot
   tgba_digraph*
   scc_filter_states(const tgba_digraph* aut, scc_info* given_si)
   {
-    return scc_filter_apply<state_filter<>>(aut, given_si);
+    bool sb = aut->get_bprop(tgba_digraph::StateBasedAcc);
+    auto res = scc_filter_apply<state_filter<>>(aut, given_si);
+    if (sb)
+      res->set_bprop(tgba_digraph::StateBasedAcc);
+    return res;
   }
 
   tgba_digraph*
diff --git a/src/tgbaalgos/simulation.cc b/src/tgbaalgos/simulation.cc
index d8053c496..2d8418717 100644
--- a/src/tgbaalgos/simulation.cc
+++ b/src/tgbaalgos/simulation.cc
@@ -550,6 +550,8 @@ namespace spot
 	tgba_digraph* res = new tgba_digraph(d);
 	d->register_all_variables_of(a_, res);
 	res->set_acceptance_conditions(all_acceptance_conditions_);
+	if (Sba)
+	  res->set_bprop(tgba_digraph::StateBasedAcc);
 
 	bdd sup_all_acc = bdd_support(all_acceptance_conditions_);
 	// Non atomic propositions variables (= acc and class)
diff --git a/src/tgbatest/ltl2tgba.cc b/src/tgbatest/ltl2tgba.cc
index c8df4f274..8ee42b88f 100644
--- a/src/tgbatest/ltl2tgba.cc
+++ b/src/tgbatest/ltl2tgba.cc
@@ -1089,10 +1089,13 @@ main(int argc, char** argv)
 		  {
 		    if (daut->type == spot::Rabin)
 		      {
+			spot::tgba_digraph* res;
 			if (dra2dba)
-			  to_free = a = spot::dstar_to_tgba(daut);
+			  res = spot::dstar_to_tgba(daut);
 			else
-			  to_free = a = spot::nra_to_nba(daut);
+			  res = spot::nra_to_nba(daut);
+			to_free = a = res;
+			assert(res->get_bprop(spot::tgba_digraph::SBA));
 			assume_sba = true;
 		      }
 		    else
diff --git a/wrap/python/spot.i b/wrap/python/spot.i
index 6750052e3..69d38cc31 100644
--- a/wrap/python/spot.i
+++ b/wrap/python/spot.i
@@ -77,7 +77,6 @@ namespace std {
 #include "tgba/state.hh"
 #include "tgba/succiter.hh"
 #include "tgba/tgba.hh"
-#include "tgba/sba.hh"
 #include "tgba/taatgba.hh"
 #include "tgba/tgbaproduct.hh"
 #include "tgba/tgbatba.hh"
@@ -218,7 +217,6 @@ using namespace spot;
 %include "tgba/state.hh"
 %include "tgba/succiter.hh"
 %include "tgba/tgba.hh"
-%include "tgba/sba.hh"
 %include "tgba/taatgba.hh"
 %include "tgba/tgbaproduct.hh"
 %include "tgba/tgbatba.hh"