diff --git a/src/kripke/kripkegraph.hh b/src/kripke/kripkegraph.hh
index d145848fd..122d88bd6 100644
--- a/src/kripke/kripkegraph.hh
+++ b/src/kripke/kripkegraph.hh
@@ -180,12 +180,11 @@ namespace spot
       return init_number_;
     }
 
-    // FIXME: The return type ought to be const.
-    virtual kripke_graph_state* get_init_state() const
+    virtual const kripke_graph_state* get_init_state() const
     {
       if (num_states() == 0)
 	const_cast<graph_t&>(g_).new_state();
-      return const_cast<kripke_graph_state*>(state_from_number(init_number_));
+      return state_from_number(init_number_);
     }
 
     /// \brief Allow to get an iterator on the state we passed in
diff --git a/src/ta/ta.cc b/src/ta/ta.cc
index 17c62aff9..c8c825eb5 100644
--- a/src/ta/ta.cc
+++ b/src/ta/ta.cc
@@ -56,7 +56,7 @@ namespace spot
     s.emplace_front(index);
   }
 
-  std::list<state*>&
+  std::list<const state*>&
   scc_stack_ta::rem()
   {
     return top().rem;
diff --git a/src/ta/ta.hh b/src/ta/ta.hh
index f2b8bdc04..e64ac465e 100644
--- a/src/ta/ta.hh
+++ b/src/ta/ta.hh
@@ -90,9 +90,10 @@ namespace spot
     }
 
     typedef std::set<state*, state_ptr_less_than> states_set_t;
+    typedef std::set<const state*, state_ptr_less_than> const_states_set_t;
 
     /// \brief Get the initial states set of the automaton.
-    virtual const states_set_t
+    virtual const_states_set_t
     get_initial_states_set() const = 0;
 
     /// \brief Get the artificial initial state set of the automaton.
@@ -102,7 +103,7 @@ namespace spot
     /// artificial initial state have one transition to each real initial state,
     /// and this transition is labeled by the corresponding initial condition.
     /// (For more details, see the paper cited above)
-    virtual spot::state*
+    virtual const spot::state*
     get_artificial_initial_state() const
     {
       return nullptr;
@@ -205,17 +206,14 @@ namespace spot
     virtual bool next() = 0;
     virtual bool done() const = 0;
 
-    virtual state*
-    dst() const = 0;
+    virtual const state* dst() const = 0;
 
     /// \brief Get the changeset on the transition leading to current successor.
     ///
     /// This is a boolean function of atomic propositions.
-    virtual bdd
-    cond() const = 0;
+    virtual bdd cond() const = 0;
 
-    acc_cond::mark_t
-    acc() const = 0;
+    acc_cond::mark_t acc() const = 0;
 
   };
 
@@ -238,7 +236,7 @@ namespace spot
       /// transitions which connect the states of the connected component.
       acc_cond::mark_t condition;
 
-      std::list<state*> rem;
+      std::list<const state*> rem;
     };
 
     /// Stack a new SCC with index \a index.
@@ -262,7 +260,7 @@ namespace spot
     size() const;
 
     /// The \c rem member of the top SCC.
-    std::list<state*>&
+    std::list<const state*>&
     rem();
 
     /// Is the stack empty?
diff --git a/src/ta/taexplicit.cc b/src/ta/taexplicit.cc
index d70194145..796181746 100644
--- a/src/ta/taexplicit.cc
+++ b/src/ta/taexplicit.cc
@@ -71,7 +71,7 @@ namespace spot
     return !transitions_ || i_ == transitions_->end();
   }
 
-  state*
+  const state*
   ta_explicit_succ_iterator::dst() const
   {
     trace
@@ -81,8 +81,7 @@ namespace spot
     trace
       << "***ta_explicit_succ_iterator::dst() (*i_)->condition =***"
           << (*i_)->condition << std::endl;
-    state_ta_explicit* s = (*i_)->dest;
-    return s;
+    return (*i_)->dest;
   }
 
   bdd
@@ -273,7 +272,7 @@ namespace spot
     if (trans)
       for (it_trans = trans->begin(); it_trans != trans->end();)
         {
-          state_ta_explicit* dest = (*it_trans)->dest;
+          auto dest = (*it_trans)->dest;
           bool is_stuttering_transition = (get_tgba_condition()
               == (dest)->get_tgba_condition());
           bool dest_is_livelock_accepting =
@@ -316,14 +315,11 @@ namespace spot
   state_ta_explicit::free_transitions()
   {
     state_ta_explicit::transitions* trans = transitions_;
-    state_ta_explicit::transitions::iterator it_trans;
     // We don't destroy the transitions in the state's destructor because
     // they are not cloned.
     if (trans)
-      for (it_trans = trans->begin(); it_trans != trans->end(); ++it_trans)
-        {
-          delete *it_trans;
-        }
+      for (auto& t: *trans)
+	delete t;
     delete trans;
 
     std::unordered_map<int, transitions*, std::hash<int> >::iterator i =
@@ -353,7 +349,7 @@ namespace spot
     acc().set_generalized_buchi();
     if (artificial_initial_state)
       {
-        state_ta_explicit* is = add_state(artificial_initial_state);
+        auto is = add_state(artificial_initial_state);
         assert(is == artificial_initial_state);
 	(void)is;
       }
@@ -364,7 +360,8 @@ namespace spot
     ta::states_set_t::iterator it;
     for (it = states_set_.begin(); it != states_set_.end(); ++it)
       {
-        state_ta_explicit* s = down_cast<state_ta_explicit*>(*it);
+        auto* s = const_cast<state_ta_explicit*>
+	  (down_cast<const state_ta_explicit*>(*it));
 
         s->free_transitions();
         s->get_tgba_state()->destroy();
@@ -379,7 +376,7 @@ namespace spot
     std::pair<ta::states_set_t::iterator, bool> add_state_to_ta =
         states_set_.insert(s);
 
-    return static_cast<state_ta_explicit*>(*add_state_to_ta.first);
+    return down_cast<state_ta_explicit*>(*add_state_to_ta.first);
   }
 
   void
@@ -389,21 +386,21 @@ namespace spot
     s->set_initial_state(true);
     if (condition == bddfalse)
       condition = get_state_condition(s);
-    std::pair<ta::states_set_t::iterator, bool> add_state =
-        initial_states_set_.insert(s);
+    auto add_state = initial_states_set_.insert(s);
     if (get_artificial_initial_state())
       if (add_state.second)
 	{
-	  state_ta_explicit* i =
+	  auto i =
 	    down_cast<state_ta_explicit*>(get_artificial_initial_state());
 	  create_transition(i, condition, 0U, s);
 	}
   }
 
   void
-  ta_explicit::delete_stuttering_and_hole_successors(spot::state* s)
+  ta_explicit::delete_stuttering_and_hole_successors(const spot::state* s)
   {
-    state_ta_explicit * state = down_cast<state_ta_explicit*>(s);
+    auto state =
+      const_cast<state_ta_explicit*>(down_cast<const state_ta_explicit*>(s));
     assert(state);
     state->delete_stuttering_and_hole_successors();
     if (state->is_initial_state())
@@ -414,7 +411,8 @@ namespace spot
   void
   ta_explicit::create_transition(state_ta_explicit* source, bdd condition,
 				 acc_cond::mark_t acceptance_conditions,
-				 state_ta_explicit* dest, bool add_at_beginning)
+				 const state_ta_explicit* dest,
+				 bool add_at_beginning)
   {
     state_ta_explicit::transition* t = new state_ta_explicit::transition;
     t->dest = dest;
@@ -424,7 +422,7 @@ namespace spot
 
   }
 
-  const ta::states_set_t
+  ta::const_states_set_t
   ta_explicit::get_initial_states_set() const
   {
     return initial_states_set_;
diff --git a/src/ta/taexplicit.hh b/src/ta/taexplicit.hh
index 98cb0d6b6..38a222660 100644
--- a/src/ta/taexplicit.hh
+++ b/src/ta/taexplicit.hh
@@ -56,7 +56,7 @@ namespace spot
     void
     create_transition(state_ta_explicit* source, bdd condition,
 		      acc_cond::mark_t acceptance_conditions,
-		      state_ta_explicit* dest,
+		      const state_ta_explicit* dest,
 		      bool add_at_beginning = false);
 
     void
@@ -64,7 +64,7 @@ namespace spot
     // ta interface
     virtual
     ~ta_explicit();
-    virtual const states_set_t
+    virtual const_states_set_t
     get_initial_states_set() const;
 
     virtual ta_succ_iterator*
@@ -108,7 +108,7 @@ namespace spot
     }
 
     virtual void
-    delete_stuttering_and_hole_successors(spot::state* s);
+    delete_stuttering_and_hole_successors(const spot::state* s);
 
     ta::states_set_t
     get_states_set()
@@ -124,7 +124,7 @@ namespace spot
     const_twa_ptr tgba_;
     state_ta_explicit* artificial_initial_state_;
     ta::states_set_t states_set_;
-    ta::states_set_t initial_states_set_;
+    ta::const_states_set_t initial_states_set_;
   };
 
   /// states used by spot::ta_explicit.
@@ -139,7 +139,7 @@ namespace spot
     {
       bdd condition;
       acc_cond::mark_t acceptance_conditions;
-      state_ta_explicit* dest;
+      const state_ta_explicit* dest;
     };
 
     typedef std::list<transition*> transitions;
@@ -238,13 +238,10 @@ namespace spot
     virtual bool next();
     virtual bool done() const;
 
-    virtual state*
-    dst() const;
-    virtual bdd
-    cond() const;
+    virtual const state* dst() const;
+    virtual bdd cond() const;
 
-    virtual acc_cond::mark_t
-    acc() const;
+    virtual acc_cond::mark_t acc() const;
 
   private:
     state_ta_explicit::transitions* transitions_;
diff --git a/src/ta/taproduct.cc b/src/ta/taproduct.cc
index 60e90b0a9..dac0dd17a 100644
--- a/src/ta/taproduct.cc
+++ b/src/ta/taproduct.cc
@@ -259,26 +259,25 @@ namespace spot
     dict_->unregister_all_my_variables(this);
   }
 
-  const ta::states_set_t
+  ta::const_states_set_t
   ta_product::get_initial_states_set() const
   {
     //build initial states set
 
-    ta::states_set_t ta_init_states_set;
-    ta::states_set_t::const_iterator it;
+    ta::const_states_set_t ta_init_states_set;
+    ta::const_states_set_t::const_iterator it;
 
-    ta::states_set_t initial_states_set;
-    state* kripke_init_state = kripke_->get_init_state();
-    bdd kripke_init_state_condition = kripke_->state_condition(
-        kripke_init_state);
+    ta::const_states_set_t initial_states_set;
+    const state* kripke_init = kripke_->get_init_state();
+    bdd kripke_init_condition = kripke_->state_condition(kripke_init);
 
-    spot::state* artificial_initial_state =
+    const spot::state* artificial_initial_state =
       ta_->get_artificial_initial_state();
 
     if (artificial_initial_state)
       {
         ta_succ_iterator* ta_init_it_ = ta_->succ_iter(
-            artificial_initial_state, kripke_init_state_condition);
+            artificial_initial_state, kripke_init_condition);
         for (ta_init_it_->first(); !ta_init_it_->done(); ta_init_it_->next())
           {
             ta_init_states_set.insert(ta_init_it_->dst());
@@ -291,21 +290,13 @@ namespace spot
         ta_init_states_set = ta_->get_initial_states_set();
       }
 
-    for (it = ta_init_states_set.begin(); it != ta_init_states_set.end(); ++it)
-      {
+    for (auto s: ta_init_states_set)
+      if (artificial_initial_state ||
+	  (kripke_init_condition == ta_->get_state_condition(s)))
+	initial_states_set.insert(new state_ta_product(s,
+						       kripke_init->clone()));
 
-        if (artificial_initial_state ||
-	    (kripke_init_state_condition == ta_->get_state_condition(*it)))
-          {
-            state_ta_product* stp = new state_ta_product((*it),
-                kripke_init_state->clone());
-
-            initial_states_set.insert(stp);
-          }
-
-      }
-
-    kripke_init_state->destroy();
+    kripke_init->destroy();
     return initial_states_set;
   }
 
@@ -369,8 +360,8 @@ namespace spot
     const state_ta_product* stp = down_cast<const state_ta_product*> (s);
     assert(stp);
 
-    state* ta_s = stp->get_ta_state();
-    state* kr_s = stp->get_kripke_state();
+    const state* ta_s = stp->get_ta_state();
+    const state* kr_s = stp->get_kripke_state();
 
     return (ta_->is_initial_state(ta_s))
         && ((kripke_->get_init_state())->compare(kr_s) == 0)
@@ -393,7 +384,7 @@ namespace spot
   {
     const state_ta_product* stp = down_cast<const state_ta_product*> (s);
     assert(stp);
-    state* ta_s = stp->get_ta_state();
+    const state* ta_s = stp->get_ta_state();
     return ta_->get_state_condition(ta_s);
   }
 
diff --git a/src/ta/taproduct.hh b/src/ta/taproduct.hh
index 96ab85219..0db9c070d 100644
--- a/src/ta/taproduct.hh
+++ b/src/ta/taproduct.hh
@@ -36,7 +36,7 @@ namespace spot
     /// \brief Constructor
     /// \param ta_state The state from the ta automaton.
     /// \param kripke_state The state from Kripke structure.
-    state_ta_product(state* ta_state, state* kripke_state) :
+    state_ta_product(const state* ta_state, const state* kripke_state) :
       ta_state_(ta_state), kripke_state_(kripke_state)
     {
     }
@@ -47,13 +47,13 @@ namespace spot
     virtual
     ~state_ta_product();
 
-    state*
+    const state*
     get_ta_state() const
     {
       return ta_state_;
     }
 
-    state*
+    const state*
     get_kripke_state() const
     {
       return kripke_state_;
@@ -67,8 +67,8 @@ namespace spot
     clone() const;
 
   private:
-    state* ta_state_; ///< State from the ta automaton.
-    state* kripke_state_; ///< State from the kripke structure.
+    const state* ta_state_; ///< State from the ta automaton.
+    const state* kripke_state_; ///< State from the kripke structure.
   };
 
   /// \brief Iterate over the successors of a product computed on the fly.
@@ -117,12 +117,12 @@ namespace spot
     const kripke* kripke_;
     ta_succ_iterator* ta_succ_it_;
     twa_succ_iterator* kripke_succ_it_;
-    state_ta_product* current_state_;
+    const state_ta_product* current_state_;
     bdd current_condition_;
     acc_cond::mark_t current_acceptance_conditions_;
     bool is_stuttering_transition_;
     bdd kripke_source_condition;
-    state * kripke_current_dest_state;
+    const state* kripke_current_dest_state;
 
   };
 
@@ -141,7 +141,7 @@ namespace spot
     virtual
     ~ta_product();
 
-    virtual const std::set<state*, state_ptr_less_than>
+    virtual ta::const_states_set_t
     get_initial_states_set() const;
 
     virtual ta_succ_iterator_product*
diff --git a/src/ta/tgtaproduct.cc b/src/ta/tgtaproduct.cc
index 16bfca601..8a444c405 100644
--- a/src/ta/tgtaproduct.cc
+++ b/src/ta/tgtaproduct.cc
@@ -49,7 +49,7 @@ namespace spot
   {
   }
 
-  state*
+  const state*
   tgta_product::get_init_state() const
   {
     fixed_size_pool* p = const_cast<fixed_size_pool*> (&pool_);
@@ -79,7 +79,7 @@ namespace spot
     : source_(s), tgta_(t), kripke_(k), pool_(pool)
   {
 
-    state * tgta_init_state = tgta_->get_init_state();
+    const state* tgta_init_state = tgta_->get_init_state();
     if ((s->right())->compare(tgta_init_state) == 0)
       source_ = nullptr;
 
diff --git a/src/ta/tgtaproduct.hh b/src/ta/tgtaproduct.hh
index 182233171..3429a6594 100644
--- a/src/ta/tgtaproduct.hh
+++ b/src/ta/tgtaproduct.hh
@@ -35,8 +35,7 @@ namespace spot
     tgta_product(const const_kripke_ptr& left,
 		 const const_tgta_ptr& right);
 
-    virtual state*
-    get_init_state() const;
+    virtual const state* get_init_state() const;
 
     virtual twa_succ_iterator*
     succ_iter(const state* local_state) const;
@@ -97,6 +96,6 @@ namespace spot
     bdd current_condition_;
     acc_cond::mark_t current_acceptance_conditions_;
     bdd kripke_source_condition;
-    state* kripke_current_dest_state;
+    const state* kripke_current_dest_state;
   };
 }
diff --git a/src/taalgos/dot.cc b/src/taalgos/dot.cc
index ed5bc8124..65237b1a3 100644
--- a/src/taalgos/dot.cc
+++ b/src/taalgos/dot.cc
@@ -146,9 +146,7 @@ namespace spot
 
         artificial_initial_state_ = t_automata_->get_artificial_initial_state();
 
-        ta::states_set_t init_states_set;
-
-        ta::states_set_t::const_iterator it;
+        ta::const_states_set_t init_states_set;
 
         if (artificial_initial_state_)
 	  {
@@ -159,10 +157,9 @@ namespace spot
 	  {
 	    int n = 0;
 	    init_states_set = t_automata_->get_initial_states_set();
-	    for (it = init_states_set.begin();
-		 it != init_states_set.end(); ++it)
+	    for (auto s: init_states_set)
 	      {
-		bdd init_condition = t_automata_->get_state_condition(*it);
+		bdd init_condition = t_automata_->get_state_condition(s);
 		std::string label = bdd_format_formula(t_automata_->get_dict(),
 						       init_condition);
 		++n;
@@ -223,7 +220,7 @@ namespace spot
 
     private:
       std::ostream& os_;
-      spot::state* artificial_initial_state_;
+      const spot::state* artificial_initial_state_;
 
       bool opt_horizontal_ = true;
       bool opt_circles_ = false;
diff --git a/src/taalgos/emptinessta.cc b/src/taalgos/emptinessta.cc
index 08ba135ac..11d8b97c1 100644
--- a/src/taalgos/emptinessta.cc
+++ b/src/taalgos/emptinessta.cc
@@ -88,11 +88,11 @@ namespace spot
     // Setup depth-first search from initial states.
     auto& ta_ = a_->get_ta();
     auto& kripke_ = a_->get_kripke();
-    state* kripke_init_state = kripke_->get_init_state();
+    auto kripke_init_state = kripke_->get_init_state();
     bdd kripke_init_state_condition = kripke_->state_condition(
         kripke_init_state);
 
-    spot::state* artificial_initial_state = ta_->get_artificial_initial_state();
+    auto artificial_initial_state = ta_->get_artificial_initial_state();
 
     ta_succ_iterator* ta_init_it_ = ta_->succ_iter(artificial_initial_state,
         kripke_init_state_condition);
@@ -124,8 +124,7 @@ namespace spot
 
         while (!todo.empty())
           {
-
-            state* curr = todo.top().first;
+            auto curr = todo.top().first;
 
             // We are looking at the next successor in SUCC.
             ta_succ_iterator_product* succ = todo.top().second;
@@ -249,7 +248,7 @@ namespace spot
             // top of ROOT that have an index greater to the one of
             // the SSCC of S2 (called the "threshold").
             int threshold = std::abs(p.first->second);
-            std::list<state*> rem;
+            std::list<const state*> rem;
             bool acc = false;
 
             trace << "***PASS 1: CYCLE***\n";
@@ -393,21 +392,17 @@ namespace spot
     std::stack<pair_state_iter> todo;
 
     // * init: the set of the depth-first search initial states
-    std::queue<spot::state*> ta_init_it_;
+    std::queue<const spot::state*> ta_init_it_;
 
-    const ta::states_set_t init_states_set = a_->get_initial_states_set();
-    ta::states_set_t::const_iterator it;
-    for (it = init_states_set.begin(); it != init_states_set.end(); ++it)
-      {
-        state* init_state = (*it);
-        ta_init_it_.push(init_state);
-      }
+    auto init_states_set = a_->get_initial_states_set();
+    for (auto init_state: init_states_set)
+      ta_init_it_.push(init_state);
 
     while (!ta_init_it_.empty())
       {
         // Setup depth-first search from initial states.
           {
-            state* init = ta_init_it_.front();
+            auto init = ta_init_it_.front();
             ta_init_it_.pop();
 
 	    if (!h.emplace(init, num + 1).second)
@@ -426,8 +421,7 @@ namespace spot
 
         while (!todo.empty())
           {
-
-            state* curr = todo.top().first;
+            auto curr = todo.top().first;
 
             // We are looking at the next successor in SUCC.
             ta_succ_iterator_product* succ = todo.top().second;
@@ -517,16 +511,12 @@ namespace spot
 
             //self loop state
             if (!curr->compare(i->first))
-              {
-                state* self_loop_state = curr;
-
-                if (t->is_livelock_accepting_state(self_loop_state))
-                  {
-                    clear(h, todo, ta_init_it_);
-                    trace << "PASS 2: SUCCESS\n";
-                    return true;
-                  }
-              }
+	      if (t->is_livelock_accepting_state(curr))
+		{
+		  clear(h, todo, ta_init_it_);
+		  trace << "PASS 2: SUCCESS\n";
+		  return true;
+		}
 
             // Now this is the most interesting case.  We have reached a
             // state S1 which is already part of a non-dead SSCC.  Any such
@@ -540,7 +530,7 @@ namespace spot
             // top of ROOT that have an index greater to the one of
             // the SSCC of S2 (called the "threshold").
             int threshold = i->second;
-            std::list<state*> rem;
+            std::list<const state*> rem;
             bool acc = false;
 
             while (threshold < sscc.top().index)
@@ -578,7 +568,7 @@ namespace spot
 
   void
   ta_check::clear(hash_type& h, std::stack<pair_state_iter> todo,
-      std::queue<spot::state*> init_states)
+      std::queue<const spot::state*> init_states)
   {
 
     set_states(states() + h.size());
diff --git a/src/taalgos/emptinessta.hh b/src/taalgos/emptinessta.hh
index db451f1e2..cd2e4e63b 100644
--- a/src/taalgos/emptinessta.hh
+++ b/src/taalgos/emptinessta.hh
@@ -33,7 +33,8 @@ namespace spot
 
   namespace
   {
-    typedef std::pair<spot::state*, ta_succ_iterator_product*> pair_state_iter;
+    typedef std::pair<const spot::state*,
+		      ta_succ_iterator_product*> pair_state_iter;
   }
 
   /// \addtogroup ta_emptiness_check Emptiness-checks
@@ -127,7 +128,7 @@ namespace spot
   protected:
     void
     clear(hash_type& h, std::stack<pair_state_iter> todo, std::queue<
-        spot::state*> init_set);
+        const spot::state*> init_set);
 
     void
     clear(hash_type& h, std::stack<pair_state_iter> todo,
diff --git a/src/taalgos/minimize.cc b/src/taalgos/minimize.cc
index c0bdf0d5c..cd5daf939 100644
--- a/src/taalgos/minimize.cc
+++ b/src/taalgos/minimize.cc
@@ -230,8 +230,7 @@ namespace spot
 
       std::set<const state*>::iterator it;
 
-      spot::state* artificial_initial_state =
-	ta_->get_artificial_initial_state();
+      auto artificial_initial_state = ta_->get_artificial_initial_state();
 
       for (it = states_set.begin(); it != states_set.end(); ++it)
 	{
diff --git a/src/taalgos/reachiter.cc b/src/taalgos/reachiter.cc
index 86ecd1056..1ec9b72ee 100644
--- a/src/taalgos/reachiter.cc
+++ b/src/taalgos/reachiter.cc
@@ -50,12 +50,10 @@ namespace spot
     int n = 0;
     start();
 
-   spot::state* artificial_initial_state =
-        t_automata_->get_artificial_initial_state();
+    const spot::state* artificial_initial_state =
+      t_automata_->get_artificial_initial_state();
 
-    ta::states_set_t init_states_set;
-
-    ta::states_set_t::const_iterator it;
+    ta::const_states_set_t init_states_set;
 
     if (artificial_initial_state)
       {
@@ -66,13 +64,11 @@ namespace spot
         init_states_set = t_automata_->get_initial_states_set();
       }
 
-    for (it = init_states_set.begin(); it != init_states_set.end(); ++it)
+    for (auto init_state: init_states_set)
       {
-        state* init_state = (*it);
         if (want_state(init_state))
           add_state(init_state);
         seen[init_state] = ++n;
-
       }
 
     const state* t;
diff --git a/src/taalgos/tgba2ta.cc b/src/taalgos/tgba2ta.cc
index eb629a1eb..bf6bc6557 100644
--- a/src/taalgos/tgba2ta.cc
+++ b/src/taalgos/tgba2ta.cc
@@ -42,7 +42,7 @@ namespace spot
 
   namespace
   {
-    typedef std::pair<spot::state*, twa_succ_iterator*> pair_state_iter;
+    typedef std::pair<const spot::state*, twa_succ_iterator*> pair_state_iter;
 
     static void
     transform_to_single_pass_automaton
@@ -52,7 +52,7 @@ namespace spot
 
       if (artificial_livelock_acc_state)
 	{
-	  state_ta_explicit* artificial_livelock_acc_state_added =
+	  auto artificial_livelock_acc_state_added =
             testing_automata->add_state(artificial_livelock_acc_state);
 
 	  // unique artificial_livelock_acc_state
@@ -71,7 +71,8 @@ namespace spot
 
       for (it = states_set.begin(); it != states_set.end(); ++it)
 	{
-	  state_ta_explicit* source = static_cast<state_ta_explicit*> (*it);
+	  auto source = const_cast<state_ta_explicit*>
+	    (static_cast<const state_ta_explicit*>(*it));
 
 	  transitions_to_livelock_states->clear();
 
@@ -81,10 +82,10 @@ namespace spot
 	  if (trans)
 	    for (it_trans = trans->begin(); it_trans != trans->end();)
 	      {
-		state_ta_explicit* dest = (*it_trans)->dest;
+		auto dest = const_cast<state_ta_explicit*>((*it_trans)->dest);
 
 		state_ta_explicit::transitions* dest_trans =
-                  (dest)->get_transitions();
+		  dest->get_transitions();
 		bool dest_trans_empty = !dest_trans || dest_trans->empty();
 
 		//select transitions where a destination is a livelock state
@@ -175,9 +176,9 @@ namespace spot
       std::stack<pair_state_iter> todo;
 
       // * init: the set of the depth-first search initial states
-      std::stack<state*> init_set;
+      std::stack<const state*> init_set;
 
-      for (state* s: testing_aut->get_initial_states_set())
+      for (auto s: testing_aut->get_initial_states_set())
 	init_set.push(s);
 
       while (!init_set.empty())
@@ -185,8 +186,7 @@ namespace spot
 	  // Setup depth-first search from initial states.
 
 	  {
-	    state_ta_explicit* init =
-	      down_cast<state_ta_explicit*> (init_set.top());
+	    auto init = down_cast<const state_ta_explicit*> (init_set.top());
 	    init_set.pop();
 
 	    if (!h.emplace(init, num + 1).second)
@@ -206,7 +206,7 @@ namespace spot
 
 	  while (!todo.empty())
 	    {
-	      state* curr = todo.top().first;
+	      auto curr = todo.top().first;
 
 	      auto i = h.find(curr);
 	      // If we have reached a dead component, ignore it.
@@ -254,8 +254,9 @@ namespace spot
 			      trace << "*** sscc.size() > 1: states: ***"
 				    << testing_aut->format_state(j)
 				    << '\n';
-			      state_ta_explicit* livelock_accepting_state =
-				down_cast<state_ta_explicit*>(j);
+			      auto livelock_accepting_state =
+				const_cast<state_ta_explicit*>
+				(down_cast<const state_ta_explicit*>(j));
 
 			      livelock_accepting_state->
 				set_livelock_accepting_state(true);
@@ -285,7 +286,7 @@ namespace spot
 		}
 
 	      // Fetch the values destination state we are interested in...
-	      state* dest = succ->dst();
+	      auto dest = succ->dst();
 
 	      auto acc_cond = succ->acc();
 	      // ... and point the iterator to the next successor, for
@@ -332,8 +333,8 @@ namespace spot
 
 	      if (!curr->compare(id->first))
 		{
-		  state_ta_explicit * self_loop_state =
-		    down_cast<state_ta_explicit*> (curr);
+		  auto self_loop_state = const_cast<state_ta_explicit*>
+		    (down_cast<const state_ta_explicit*>(curr));
 		  assert(self_loop_state);
 
 		  if (testing_aut->is_accepting_state(self_loop_state)
@@ -365,7 +366,7 @@ namespace spot
 	      // top of ROOT that have an index greater to the one of
 	      // the SSCC of S2 (called the "threshold").
 	      int threshold = id->second;
-	      std::list<state*> rem;
+	      std::list<const state*> rem;
 	      bool acc = false;
 
 	      while (threshold < sscc.top().index)
@@ -412,7 +413,7 @@ namespace spot
       const_twa_ptr tgba_ = ta->get_tgba();
 
       // build Initial states set:
-      state* tgba_init_state = tgba_->get_init_state();
+      auto tgba_init_state = tgba_->get_init_state();
 
       bdd tgba_condition = tgba_->support_conditions(tgba_init_state);
 
@@ -546,7 +547,7 @@ namespace spot
   {
     ta_explicit_ptr ta;
 
-    state* tgba_init_state = tgba_->get_init_state();
+    auto tgba_init_state = tgba_->get_init_state();
     if (artificial_initial_state_mode)
       {
         state_ta_explicit* artificial_init_state =
@@ -597,7 +598,7 @@ namespace spot
   tgta_explicit_ptr
   tgba_to_tgta(const const_twa_ptr& tgba_, bdd atomic_propositions_set_)
   {
-    state* tgba_init_state = tgba_->get_init_state();
+    auto tgba_init_state = tgba_->get_init_state();
     auto artificial_init_state = new state_ta_explicit(tgba_init_state->clone(),
 						       bddfalse, true);
     tgba_init_state->destroy();
diff --git a/src/twa/twa.hh b/src/twa/twa.hh
index 0407fa4c6..87f2165bc 100644
--- a/src/twa/twa.hh
+++ b/src/twa/twa.hh
@@ -385,7 +385,7 @@ namespace spot
     ///
     /// The returned state should be destroyed (see state::destroy)
     /// by the caller after it is no longer used.
-    virtual state* dst() const = 0;
+    virtual const state* dst() const = 0;
     /// \brief Get the condition on the transition leading to this successor.
     ///
     /// This is a boolean function of atomic propositions.
@@ -531,7 +531,7 @@ namespace spot
     /// The state has been allocated with \c new.  It is the
     /// responsability of the caller to \c destroy it when no
     /// longer needed.
-    virtual state* get_init_state() const = 0;
+    virtual const state* get_init_state() const = 0;
 
     /// \brief Get an iterator over the successors of \a local_state.
     ///
diff --git a/src/twa/twagraph.hh b/src/twa/twagraph.hh
index 2b216c582..3ce5129ef 100644
--- a/src/twa/twagraph.hh
+++ b/src/twa/twagraph.hh
@@ -143,11 +143,10 @@ namespace spot
       return !p_;
     }
 
-    virtual twa_graph_state* dst() const
+    virtual const twa_graph_state* dst() const
     {
       assert(!done());
-      return const_cast<twa_graph_state*>
-	(&g_->state_data(g_->edge_storage(p_).dst));
+      return &g_->state_data(g_->edge_storage(p_).dst);
     }
 
     virtual bdd cond() const
@@ -266,12 +265,11 @@ namespace spot
       return init_number_;
     }
 
-    // FIXME: The return type ought to be const.
-    virtual twa_graph_state* get_init_state() const
+    virtual const twa_graph_state* get_init_state() const
     {
       if (num_states() == 0)
 	const_cast<graph_t&>(g_).new_state();
-      return const_cast<twa_graph_state*>(state_from_number(init_number_));
+      return state_from_number(init_number_);
     }
 
     virtual twa_succ_iterator*
diff --git a/src/twa/twaproduct.cc b/src/twa/twaproduct.cc
index 983aa6e7b..b9ba03b4e 100644
--- a/src/twa/twaproduct.cc
+++ b/src/twa/twaproduct.cc
@@ -130,7 +130,7 @@ namespace spot
 	return !right_ || right_->done();
       }
 
-      state_product* dst() const
+      const state_product* dst() const
       {
 	return new(pool_->allocate()) state_product(left_->dst(),
 						    right_->dst(),
@@ -330,7 +330,7 @@ namespace spot
       }
   }
 
-  state*
+  const state*
   twa_product::get_init_state() const
   {
     fixed_size_pool* p = const_cast<fixed_size_pool*>(&pool_);
@@ -434,7 +434,7 @@ namespace spot
       std::swap(left_init_, right_init_);
   }
 
-  state*
+  const state*
   twa_product_init::get_init_state() const
   {
     fixed_size_pool* p = const_cast<fixed_size_pool*>(&pool_);
diff --git a/src/twa/twaproduct.hh b/src/twa/twaproduct.hh
index 72855f2cd..1e0316eea 100644
--- a/src/twa/twaproduct.hh
+++ b/src/twa/twaproduct.hh
@@ -42,20 +42,22 @@ namespace spot
     /// \param pool The pool from which the state was allocated.
     /// These states are acquired by spot::state_product, and will
     /// be destroyed on destruction.
-    state_product(state* left, state* right, fixed_size_pool* pool)
+    state_product(const state* left,
+		  const state* right,
+		  fixed_size_pool* pool)
       :	left_(left), right_(right), count_(1), pool_(pool)
     {
     }
 
     virtual void destroy() const;
 
-    state*
+    const state*
     left() const
     {
       return left_;
     }
 
-    state*
+    const state*
     right() const
     {
       return right_;
@@ -66,8 +68,8 @@ namespace spot
     virtual state_product* clone() const;
 
   private:
-    state* left_;		///< State from the left automaton.
-    state* right_;		///< State from the right automaton.
+    const state* left_;		///< State from the left automaton.
+    const state* right_;	///< State from the right automaton.
     mutable unsigned count_;
     fixed_size_pool* pool_;
 
@@ -88,7 +90,7 @@ namespace spot
 
     virtual ~twa_product();
 
-    virtual state* get_init_state() const;
+    virtual const state* get_init_state() const;
 
     virtual twa_succ_iterator*
     succ_iter(const state* state) const;
@@ -124,7 +126,7 @@ namespace spot
   public:
     twa_product_init(const const_twa_ptr& left, const const_twa_ptr& right,
 		      const state* left_init, const state* right_init);
-    virtual state* get_init_state() const;
+    virtual const state* get_init_state() const;
   protected:
     const state* left_init_;
     const state* right_init_;
diff --git a/src/twaalgos/compsusp.cc b/src/twaalgos/compsusp.cc
index 9d3d51b72..b2e460276 100644
--- a/src/twaalgos/compsusp.cc
+++ b/src/twaalgos/compsusp.cc
@@ -178,7 +178,7 @@ namespace spot
       pair_queue todo;
 
       state_pair p(left->get_init_state(), nullptr);
-      state* ris = right->get_init_state();
+      const state* ris = right->get_init_state();
       p.second = ris;
       unsigned i = res->new_state();
       seen[p] = i;
diff --git a/src/twaalgos/gtec/gtec.cc b/src/twaalgos/gtec/gtec.cc
index 743356430..0537a9d5b 100644
--- a/src/twaalgos/gtec/gtec.cc
+++ b/src/twaalgos/gtec/gtec.cc
@@ -108,7 +108,7 @@ namespace spot
 	    {
 	      inc_transitions();
 
-	      state* s = i->dst();
+	      const state* s = i->dst();
 	      auto j = ecs_->h.find(s);
 	      assert(j != ecs_->h.end());
 	      s->destroy();
@@ -158,7 +158,7 @@ namespace spot
 
     // Setup depth-first search from the initial state.
     {
-      state* init = ecs_->aut->get_init_state();
+      const state* init = ecs_->aut->get_init_state();
       ecs_->h[init] = 1;
       ecs_->root.push(1);
       arc.push(0U);
diff --git a/src/twaalgos/ltl2tgba_fm.cc b/src/twaalgos/ltl2tgba_fm.cc
index 54691b654..63678e24c 100644
--- a/src/twaalgos/ltl2tgba_fm.cc
+++ b/src/twaalgos/ltl2tgba_fm.cc
@@ -1235,7 +1235,7 @@ namespace spot
 	      for (auto i: aut->succ(st))
 		{
 		  bdd label = i->cond();
-		  state* s = i->dst();
+		  const state* s = i->dst();
 		  formula dest =
 		    namer->get_name(aut->state_number(s));
 
@@ -1280,7 +1280,7 @@ namespace spot
 	      for (auto i: aut->succ(st))
 		{
 		  bdd label = i->cond();
-		  state* s = i->dst();
+		  const state* s = i->dst();
 		  formula dest = namer->get_name(aut->state_number(s));
 
 		  missing -= label;
diff --git a/src/twaalgos/reachiter.cc b/src/twaalgos/reachiter.cc
index d32d3185d..a8111e6b4 100644
--- a/src/twaalgos/reachiter.cc
+++ b/src/twaalgos/reachiter.cc
@@ -50,7 +50,7 @@ namespace spot
   {
     int n = 0;
     start();
-    state* i = aut_->get_init_state();
+    const state* i = aut_->get_init_state();
     if (want_state(i))
       add_state(i);
     seen[i] = ++n;
@@ -188,7 +188,7 @@ namespace spot
   {
     int n = 1;
     start();
-    state* i = aut_->get_init_state();
+    const state* i = aut_->get_init_state();
     if (want_state(i))
       push(i, n);
     seen[i] = n++;
diff --git a/src/twaalgos/stutter.cc b/src/twaalgos/stutter.cc
index 3d0f010dc..dfc469b9f 100644
--- a/src/twaalgos/stutter.cc
+++ b/src/twaalgos/stutter.cc
@@ -43,7 +43,7 @@ namespace spot
     class state_tgbasl: public state
     {
     public:
-      state_tgbasl(state* s, bdd cond) : s_(s), cond_(cond)
+      state_tgbasl(const state* s, bdd cond) : s_(s), cond_(cond)
       {
       }
 
@@ -77,7 +77,7 @@ namespace spot
         return new state_tgbasl(*this);
       }
 
-      state*
+      const state*
       real_state() const
       {
         return s_;
@@ -90,7 +90,7 @@ namespace spot
       }
 
     private:
-      state* s_;
+      const state* s_;
       bdd cond_;
     };
 
@@ -220,7 +220,7 @@ namespace spot
 	get_dict()->unregister_all_my_variables(this);
       }
 
-      virtual state* get_init_state() const override
+      virtual const state* get_init_state() const override
       {
 	return new state_tgbasl(a_->get_init_state(), bddfalse);
       }