diff --git a/NEWS b/NEWS
index cc58fede5..23f721805 100644
--- a/NEWS
+++ b/NEWS
@@ -1,6 +1,13 @@
 New in spot 2.9.0.dev (not yet released)
 
-  Nothing yet.
+  Library:
+
+  - product_xor() and product_xnor() are two new versions of the
+    synchronized product.  The only work with operands that are
+    deterministic automata, and build automata whose language are
+    respectively the symmetric difference of the operands, and the
+    complement of that.
+
 
 New in spot 2.9 (2020-04-30)
 
@@ -19,7 +26,7 @@ New in spot 2.9 (2020-04-30)
     spot-rejected-word: "!a; !a; cycle{a}"
 
   - autfilt learned the --partial-degeneralize option, to remove
-    conjunctions of Inf, or disjunction of Fin that appears in
+    conjunctions of Inf, or disjunctions of Fin that appears in
     arbitrary conditions.
 
   - ltlfilt and autfilt learned a --nth=RANGE (a.k.a. -N) option to
diff --git a/spot/twaalgos/product.cc b/spot/twaalgos/product.cc
index 84efbcf32..7fb70ddd6 100644
--- a/spot/twaalgos/product.cc
+++ b/spot/twaalgos/product.cc
@@ -22,6 +22,7 @@
 #include <spot/twa/twagraph.hh>
 #include <spot/twaalgos/complete.hh>
 #include <spot/twaalgos/sccinfo.hh>
+#include <spot/twaalgos/isdet.hh>
 #include <deque>
 #include <unordered_map>
 #include <spot/misc/hash.hh>
@@ -41,7 +42,6 @@ namespace spot
       }
     };
 
-
     template<typename T>
     static
     void product_main(const const_twa_graph_ptr& left,
@@ -100,12 +100,15 @@ namespace spot
         }
     }
 
+    enum acc_op { and_acc, or_acc, xor_acc, xnor_acc };
+
+
     static
     twa_graph_ptr product_aux(const const_twa_graph_ptr& left,
                               const const_twa_graph_ptr& right,
                               unsigned left_state,
                               unsigned right_state,
-                              bool and_acc,
+                              acc_op aop,
                               const output_aborter* aborter)
     {
       if (SPOT_UNLIKELY(!(left->is_existential() && right->is_existential())))
@@ -122,164 +125,271 @@ namespace spot
       bool leftweak = left->prop_weak().is_true();
       bool rightweak = right->prop_weak().is_true();
       // We have optimization to the standard product in case one
-      // of the arguments is weak.  However these optimizations
-      // are pointless if the said arguments are "t" or "f".
-      if ((leftweak || rightweak)
-          && (left->num_sets() > 0) && (right->num_sets() > 0))
+      // of the arguments is weak.
+      if (leftweak || rightweak)
         {
           // If both automata are weak, we can restrict the result to
-          // Büchi or co-Büchi.  We will favor Büchi unless the two
-          // operands are co-Büchi.
+          // t, f, Büchi or co-Büchi.  We use co-Büchi only when
+          // t and f cannot be used, and both acceptance conditions
+          // are in {t,f,co-Büchi}.
           if (leftweak && rightweak)
             {
             weak_weak:
+              res->prop_weak(true);
               acc_cond::mark_t accmark = {0};
               acc_cond::mark_t rejmark = {};
-              if (left->acc().is_co_buchi() && right->acc().is_co_buchi())
+              auto& lacc = left->acc();
+              auto& racc = right->acc();
+              if ((lacc.is_co_buchi() && (racc.is_co_buchi()
+                                         || racc.num_sets() == 0))
+                  || (lacc.num_sets() == 0 && racc.is_co_buchi()))
                 {
                   res->set_co_buchi();
                   std::swap(accmark, rejmark);
                 }
+              else if ((aop == and_acc && lacc.is_t() && racc.is_t())
+                       || (aop == or_acc && (lacc.is_t() || racc.is_t()))
+                       || (aop == xnor_acc && ((lacc.is_t() && racc.is_t()) ||
+                                               (lacc.is_f() && racc.is_f())))
+                       || (aop == xor_acc && ((lacc.is_t() && racc.is_f()) ||
+                                              (lacc.is_f() && racc.is_t()))))
+                {
+                  res->set_acceptance(0, acc_cond::acc_code::t());
+                  accmark = {};
+                }
+              else if ((aop == and_acc && (lacc.is_f() || racc.is_f()))
+                       || (aop == or_acc && lacc.is_f() && racc.is_f())
+                       || (aop == xor_acc && ((lacc.is_t() && racc.is_t()) ||
+                                              (lacc.is_f() && racc.is_f())))
+                       || (aop == xnor_acc && ((lacc.is_t() && racc.is_f()) ||
+                                               (lacc.is_f() && racc.is_t()))))
+                {
+                  res->set_acceptance(0, acc_cond::acc_code::f());
+                  accmark = {};
+                }
               else
                 {
                   res->set_buchi();
                 }
-              res->prop_weak(true);
-              auto& lacc = left->acc();
-              auto& racc = right->acc();
-              if (and_acc)
-                product_main(left, right, left_state, right_state, res,
-                             [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                             {
-                               if (lacc.accepting(ml) && racc.accepting(mr))
-                                 return accmark;
-                               else
-                                 return rejmark;
-                             }, aborter);
-              else
-                product_main(left, right, left_state, right_state, res,
-                             [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                             {
-                               if (lacc.accepting(ml) || racc.accepting(mr))
-                                 return accmark;
-                               else
-                                 return rejmark;
-                             }, aborter);
+              switch (aop)
+                {
+                case and_acc:
+                  product_main(left, right, left_state, right_state, res,
+                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                               {
+                                 if (lacc.accepting(ml) && racc.accepting(mr))
+                                   return accmark;
+                                 else
+                                   return rejmark;
+                               }, aborter);
+                  break;
+                case or_acc:
+                  product_main(left, right, left_state, right_state, res,
+                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                               {
+                                 if (lacc.accepting(ml) || racc.accepting(mr))
+                                   return accmark;
+                                 else
+                                   return rejmark;
+                               }, aborter);
+                  break;
+                case xor_acc:
+                  product_main(left, right, left_state, right_state, res,
+                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                               {
+                                 if (lacc.accepting(ml) ^ racc.accepting(mr))
+                                   return accmark;
+                                 else
+                                   return rejmark;
+                               }, aborter);
+                  break;
+                case xnor_acc:
+                  product_main(left, right, left_state, right_state, res,
+                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                               {
+                                 if (lacc.accepting(ml) == racc.accepting(mr))
+                                   return accmark;
+                                 else
+                                   return rejmark;
+                               }, aborter);
+                  break;
+                }
             }
           else if (!rightweak)
             {
-              if (and_acc)
+              switch (aop)
                 {
-                  auto rightunsatmark = right->acc().unsat_mark();
-                  if (!rightunsatmark.first)
-                    {
-                      // Left is weak.  Right was not weak, but it is
-                      // always accepting.  We can therefore pretend
-                      // that right is weak.
-                      goto weak_weak;
-                    }
-                  res->copy_acceptance_of(right);
-                  acc_cond::mark_t rejmark = rightunsatmark.second;
-                  auto& lacc = left->acc();
-                  product_main(left, right, left_state, right_state, res,
-                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                               {
-                                 if (lacc.accepting(ml))
-                                   return mr;
-                                 else
-                                   return rejmark;
-                               }, aborter);
-                }
-              else
-                {
-                  auto rightsatmark = right->acc().sat_mark();
-                  if (!rightsatmark.first)
-                    {
-                      // Left is weak.  Right was not weak, but it is
-                      // always rejecting.  We can therefore pretend
-                      // that right is weak.
-                      goto weak_weak;
-                    }
-                  res->copy_acceptance_of(right);
-                  acc_cond::mark_t accmark = rightsatmark.second;
-                  auto& lacc = left->acc();
-                  product_main(left, right, left_state, right_state, res,
-                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                               {
-                                 if (!lacc.accepting(ml))
-                                   return mr;
-                                 else
-                                   return accmark;
-                               }, aborter);
-
+                case and_acc:
+                  {
+                    auto rightunsatmark = right->acc().unsat_mark();
+                    if (!rightunsatmark.first)
+                      {
+                        // Left is weak.  Right was not weak, but it is
+                        // always accepting.  We can therefore pretend
+                        // that right is weak.
+                        goto weak_weak;
+                      }
+                    res->copy_acceptance_of(right);
+                    acc_cond::mark_t rejmark = rightunsatmark.second;
+                    auto& lacc = left->acc();
+                    product_main(left, right, left_state, right_state, res,
+                                 [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                                 {
+                                   if (lacc.accepting(ml))
+                                     return mr;
+                                   else
+                                     return rejmark;
+                                 }, aborter);
+                    break;
+                  }
+                case or_acc:
+                  {
+                    auto rightsatmark = right->acc().sat_mark();
+                    if (!rightsatmark.first)
+                      {
+                        // Left is weak.  Right was not weak, but it is
+                        // always rejecting.  We can therefore pretend
+                        // that right is weak.
+                        goto weak_weak;
+                      }
+                    res->copy_acceptance_of(right);
+                    acc_cond::mark_t accmark = rightsatmark.second;
+                    auto& lacc = left->acc();
+                    product_main(left, right, left_state, right_state, res,
+                                 [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                                 {
+                                   if (!lacc.accepting(ml))
+                                     return mr;
+                                   else
+                                     return accmark;
+                                 }, aborter);
+                    break;
+                  }
+                case xor_acc:
+                case xnor_acc:
+                  {
+                    auto rightsatmark = right->acc().sat_mark();
+                    auto rightunsatmark = right->acc().unsat_mark();
+                    if (!rightunsatmark.first || !rightsatmark.first)
+                      {
+                        // Left is weak.  Right was not weak, but it
+                        // is either always rejecting or always
+                        // accepting.  We can therefore pretend that
+                        // right is weak.
+                        goto weak_weak;
+                      }
+                    goto generalcase;
+                    break;
+                  }
                 }
             }
-          else
+          else // right weak
             {
               assert(!leftweak);
-              if (and_acc)
+              switch (aop)
                 {
-                  auto leftunsatmark = left->acc().unsat_mark();
-                  if (!leftunsatmark.first)
-                    {
-                      // Right is weak.  Left was not weak, but it is
-                      // always accepting.  We can therefore pretend
-                      // that left is weak.
-                      goto weak_weak;
-                    }
-                  res->copy_acceptance_of(left);
-                  acc_cond::mark_t rejmark = leftunsatmark.second;
-                  auto& racc = right->acc();
-                  product_main(left, right, left_state, right_state, res,
-                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                               {
-                                 if (racc.accepting(mr))
-                                   return ml;
-                                 else
-                                   return rejmark;
-                               }, aborter);
-                }
-              else
-                {
-                  auto leftsatmark = left->acc().sat_mark();
-                  if (!leftsatmark.first)
-                    {
-                      // Right is weak.  Left was not weak, but it is
-                      // always rejecting.  We can therefore pretend
-                      // that left is weak.
-                      goto weak_weak;
-                    }
-                  res->copy_acceptance_of(left);
-                  acc_cond::mark_t accmark = leftsatmark.second;
-                  auto& racc = right->acc();
-                  product_main(left, right, left_state, right_state, res,
-                               [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
-                               {
-                                 if (!racc.accepting(mr))
-                                   return ml;
-                                 else
-                                   return accmark;
-                               }, aborter);
+                case and_acc:
+                  {
+                    auto leftunsatmark = left->acc().unsat_mark();
+                    if (!leftunsatmark.first)
+                      {
+                        // Right is weak.  Left was not weak, but it is
+                        // always accepting.  We can therefore pretend
+                        // that left is weak.
+                        goto weak_weak;
+                      }
+                    res->copy_acceptance_of(left);
+                    acc_cond::mark_t rejmark = leftunsatmark.second;
+                    auto& racc = right->acc();
+                    product_main(left, right, left_state, right_state, res,
+                                 [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                                 {
+                                   if (racc.accepting(mr))
+                                     return ml;
+                                   else
+                                     return rejmark;
+                                 }, aborter);
+                    break;
+                  }
+                case or_acc:
+                  {
+                    auto leftsatmark = left->acc().sat_mark();
+                    if (!leftsatmark.first)
+                      {
+                        // Right is weak.  Left was not weak, but it is
+                        // always rejecting.  We can therefore pretend
+                        // that left is weak.
+                        goto weak_weak;
+                      }
+                    res->copy_acceptance_of(left);
+                    acc_cond::mark_t accmark = leftsatmark.second;
+                    auto& racc = right->acc();
+                    product_main(left, right, left_state, right_state, res,
+                                 [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
+                                 {
+                                   if (!racc.accepting(mr))
+                                     return ml;
+                                   else
+                                     return accmark;
+                                 }, aborter);
 
+                    break;
+                  }
+                case xor_acc:
+                case xnor_acc:
+                  {
+                    auto leftsatmark = left->acc().sat_mark();
+                    auto leftunsatmark = left->acc().unsat_mark();
+                    if (!leftunsatmark.first || !leftsatmark.first)
+                      {
+                        // Right is weak.  Left was not weak, but it
+                        // is either always rejecting or always
+                        // accepting.  We can therefore pretend that
+                        // left is weak.
+                        goto weak_weak;
+                      }
+                    goto generalcase;
+                    break;
+                  }
                 }
             }
         }
       else // general case
         {
+        generalcase:
           auto left_num = left->num_sets();
+          auto& left_acc = left->get_acceptance();
           auto right_acc = right->get_acceptance() << left_num;
-          if (and_acc)
-            right_acc &= left->get_acceptance();
-          else
-            right_acc |= left->get_acceptance();
+          switch (aop)
+            {
+            case and_acc:
+              right_acc &= left_acc;
+              break;
+            case or_acc:
+              right_acc |= left_acc;
+              break;
+            case xor_acc:
+              {
+                auto tmp = right_acc.complement() & left_acc;
+                right_acc &= left_acc.complement();
+                right_acc |= tmp;
+                break;
+              }
+            case xnor_acc:
+              {
+                auto tmp = right_acc.complement() & left_acc.complement();
+                right_acc &= left_acc;
+                tmp |= right_acc;
+                std::swap(tmp, right_acc);
+                break;
+              }
+            }
           res->set_acceptance(left_num + right->num_sets(), right_acc);
-
           product_main(left, right, left_state, right_state, res,
                        [&] (acc_cond::mark_t ml, acc_cond::mark_t mr)
                        {
                          return ml | (mr << left_num);
                        }, aborter);
-
         }
 
       if (!res)                 // aborted
@@ -323,7 +433,7 @@ namespace spot
                         unsigned right_state,
                         const output_aborter* aborter)
   {
-    return product_aux(left, right, left_state, right_state, true, aborter);
+    return product_aux(left, right, left_state, right_state, and_acc, aborter);
   }
 
   twa_graph_ptr product(const const_twa_graph_ptr& left,
@@ -341,7 +451,7 @@ namespace spot
                            unsigned right_state)
   {
     return product_aux(complete(left), complete(right),
-                       left_state, right_state, false, nullptr);
+                       left_state, right_state, or_acc, nullptr);
   }
 
   twa_graph_ptr product_or(const const_twa_graph_ptr& left,
@@ -352,6 +462,32 @@ namespace spot
                       right->get_init_state_number());
   }
 
+  twa_graph_ptr product_xor(const const_twa_graph_ptr& left,
+                            const const_twa_graph_ptr& right)
+  {
+    if (SPOT_UNLIKELY(!is_deterministic(left) || !is_deterministic(right)))
+      throw std::runtime_error
+        ("product_xor() only works with deterministic automata");
+
+    return product_aux(complete(left), complete(right),
+                       left->get_init_state_number(),
+                       right->get_init_state_number(),
+                       xor_acc, nullptr);
+  }
+
+  twa_graph_ptr product_xnor(const const_twa_graph_ptr& left,
+                             const const_twa_graph_ptr& right)
+  {
+    if (SPOT_UNLIKELY(!is_deterministic(left) || !is_deterministic(right)))
+      throw std::runtime_error
+        ("product_xnor() only works with deterministic automata");
+
+    return product_aux(complete(left), complete(right),
+                       left->get_init_state_number(),
+                       right->get_init_state_number(),
+                       xnor_acc, nullptr);
+  }
+
 
   namespace
   {
diff --git a/spot/twaalgos/product.hh b/spot/twaalgos/product.hh
index e78b18f7c..49ee9acdf 100644
--- a/spot/twaalgos/product.hh
+++ b/spot/twaalgos/product.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2018, 2019 Laboratoire de Recherche et
+// Copyright (C) 2014-2015, 2018-2020 Laboratoire de Recherche et
 // Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -127,6 +127,45 @@ namespace spot
                            unsigned left_state,
                            unsigned right_state);
 
+  /// \ingroup twa_algorithms
+  /// \brief XOR two deterministic automata using a synchronous product
+  ///
+  /// The two operands must be deterministic.
+  ///
+  /// The resulting automaton will accept the symmetric difference of
+  /// both languages and have an acceptance condition that is the xor
+  /// of the acceptance conditions of the two input automata.  In case
+  /// both operands are weak, the acceptance condition of the result
+  /// is made simpler.
+  ///
+  /// The algorithm also defines a named property called
+  /// "product-states" with type spot::product_states.  This stores
+  /// the pair of original state numbers associated to each state of
+  /// the product.
+  SPOT_API
+  twa_graph_ptr product_xor(const const_twa_graph_ptr& left,
+                            const const_twa_graph_ptr& right);
+
+  /// \ingroup twa_algorithms
+  /// \brief XNOR two automata using a synchronous product
+  ///
+  /// The two operands must be deterministic.
+  ///
+  /// The resulting automaton will accept words that are either in
+  /// both input languages, or not in both languages. (The XNOR gate
+  /// it the logical complement of XOR.  XNOR is also known as logical
+  /// equivalence.)  The output will have an acceptance condition that
+  /// is the XNOR of the acceptance conditions of the two input
+  /// automata.  In case both the operands are weak, the acceptance
+  /// condition of the result is made simpler.
+  ///
+  /// The algorithm also defines a named property called
+  /// "product-states" with type spot::product_states.  This stores
+  /// the pair of original state numbers associated to each state of
+  /// the product.
+  SPOT_API
+  twa_graph_ptr product_xnor(const const_twa_graph_ptr& left,
+                             const const_twa_graph_ptr& right);
 
   /// \ingroup twa_algorithms
   /// \brief Build the product of an automaton with a suspendable
@@ -136,7 +175,7 @@ namespace spot
   /// languages of both input automata.
   ///
   /// This function *assumes* that \a right_susp is a suspendable
-  /// automaton, i.e., it its language L satisfies L = Σ*.L.
+  /// automaton, i.e., its language L satisfies L = Σ*.L.
   /// Therefore the product between the two automata need only be done
   /// with the accepting SCCs of left.
   ///
@@ -155,7 +194,7 @@ namespace spot
   /// both input automata.
   ///
   /// This function *assumes* that \a right_susp is a suspendable
-  /// automaton, i.e., it its language L satisfies L = Σ*.L.
+  /// automaton, i.e., its language L satisfies L = Σ*.L.
   /// Therefore, after left has been completed (this will be done by
   /// product_or_susp) the product between the two automata need only
   /// be done with the SCCs of left that contains some rejecting cycles.
diff --git a/tests/python/_product_weak.ipynb b/tests/python/_product_weak.ipynb
index 093d5d022..5e4a2a4a0 100644
--- a/tests/python/_product_weak.ipynb
+++ b/tests/python/_product_weak.ipynb
@@ -189,7 +189,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7dbc0e99f0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd90c347ba0> >"
       ]
      },
      "metadata": {},
@@ -1410,64 +1410,64 @@
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-       "<text text-anchor=\"start\" x=\"57.8\" y=\"-128.42\" font-family=\"Lato\" font-size=\"14.00\">[Streett&#45;like 1]</text>\n",
+       "<svg width=\"212pt\" height=\"191pt\"\n",
+       " viewBox=\"0.00 0.00 211.59 190.68\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 186.68)\">\n",
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+       "</svg>\n",
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+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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+       "<!-- 0&#45;&gt;2 -->\n",
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+       "<title>0&#45;&gt;2</title>\n",
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+       "<!-- 0&#45;&gt;2 -->\n",
+       "<g id=\"edge5\" class=\"edge\">\n",
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+       "<title>2&#45;&gt;2</title>\n",
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+       "</div>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "left = auts[0]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
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+       "</g>\n",
+       "</svg>\n",
+       "</div><div style='vertical-align:text-top;display:inline-block;'><?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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+       "<!-- 1&#45;&gt;1 -->\n",
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+       "</svg>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "left = auts[1]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
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+       "<!-- 0&#45;&gt;0 -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd90c347cf0> >"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
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+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "left = auts[2]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
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+     "output_type": "display_data"
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+   "source": [
+    "left = auts[3]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
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+   "execution_count": 14,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
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+   "source": [
+    "left = auts[4]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
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+   "execution_count": 15,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
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+       "</div>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "left = auts[5]\n",
+    "display(left)\n",
+    "for right in auts:\n",
+    "    display_inline(right, spot.product_xor(left, right), spot.product_xnor(left, right))"
+   ]
   }
  ],
  "metadata": {
@@ -8098,7 +16662,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.2"
+   "version": "3.8.3rc1"
   }
  },
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diff --git a/tests/python/except.py b/tests/python/except.py
index 926aa864d..f911474e8 100644
--- a/tests/python/except.py
+++ b/tests/python/except.py
@@ -188,3 +188,32 @@ except ValueError as e:
     assert 'any' in s
 else:
     report_missing_exception()
+
+a1 = spot.translate('FGa')
+a2 = spot.translate('Gb')
+assert not spot.is_deterministic(a1)
+assert spot.is_deterministic(a2)
+try:
+    spot.product_xor(a1, a2)
+except RuntimeError as e:
+    assert "product_xor() only works with deterministic automata"
+else:
+    report_missing_exception()
+try:
+    spot.product_xor(a2, a1)
+except RuntimeError as e:
+    assert "product_xor() only works with deterministic automata"
+else:
+    report_missing_exception()
+try:
+    spot.product_xnor(a1, a2)
+except RuntimeError as e:
+    assert "product_xnor() only works with deterministic automata"
+else:
+    report_missing_exception()
+try:
+    spot.product_xnor(a2, a1)
+except RuntimeError as e:
+    assert "product_xnor() only works with deterministic automata"
+else:
+    report_missing_exception()