diff --git a/sxpat/template_manager/template.py b/sxpat/template_manager/template.py
index 1634938c4..03c100d88 100644
--- a/sxpat/template_manager/template.py
+++ b/sxpat/template_manager/template.py
@@ -29,6 +29,9 @@ def z3_abs_diff(a, b):
 # Parameters variables declaration
 {{{{params_declaration}}}}
 
+# Constants variables declaration
+{{{{consts_declaration}}}}
+
 # wires functions declaration for exact circuit
 {{{{exact_wires_declaration}}}}
 
diff --git a/sxpat/template_manager/template_manager.py b/sxpat/template_manager/template_manager.py
index 02f713ef5..e32c3d156 100644
--- a/sxpat/template_manager/template_manager.py
+++ b/sxpat/template_manager/template_manager.py
@@ -213,7 +213,12 @@ def _use_exact_var(self, node_name: str) -> str:
 
         # is constant
         if node_name in self.exact_constants.values():
-            return sxpat_cfg.Z3_GATES_DICTIONARY[self._exact_graph.graph.nodes[node_name][sxpat_cfg.LABEL]]
+            succs = list(self._current_graph.graph.successors(node_name))
+            if len(succs) == 1 and succs[0] in self._current_graph.output_dict.values():
+                output_i = next(node_i for node_i, node_name in self._current_graph.output_dict.items() if node_name == succs[0])
+                return f'{sxpat_cfg.CONSTANT_PREFIX}{output_i}'
+            else:
+                return sxpat_cfg.Z3_GATES_DICTIONARY[self._exact_graph.graph.nodes[node_name][sxpat_cfg.LABEL]]
 
         # is gate
         if node_name in self.exact_gates.values():
@@ -316,6 +321,16 @@ def _update_builder(self, builder: Builder) -> None:
         # error
         builder.update(error=self._encoding.output_variable('error'))
 
+        # consts_declaration  
+        def get_single_predecessor(out_name): return next(self._current_graph.graph.predecessors(out_name))
+        constants = self._current_graph.constant_dict.values()
+        lines = [
+            self._gen_declare_gate(f'{sxpat_cfg.CONSTANT_PREFIX}{output_i}')
+            for output_i, output_name in self.outputs.items()
+            if get_single_predecessor(output_name) in constants
+        ]
+        builder.update(consts_declaration='\n'.join(lines))
+
         # exact_wires_declaration
         builder.update(exact_wires_declaration='\n'.join(
             self._gen_declare_bool_function(f'{sxpat_cfg.EXACT_WIRES_PREFIX}{len(self.inputs) + gate_i}', len(self.inputs))