diff --git a/.gitignore b/.gitignore
index 505680bc9..4329e653d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,3 +8,4 @@ examples/
 
 docs/_build
 docs/doxyxml
+.vs
diff --git a/include/mockturtle/algorithms/cleanup.hpp b/include/mockturtle/algorithms/cleanup.hpp
index 57a7d7c13..f1bf32543 100644
--- a/include/mockturtle/algorithms/cleanup.hpp
+++ b/include/mockturtle/algorithms/cleanup.hpp
@@ -268,7 +268,7 @@ NtkDest cleanup_dangling( NtkSrc const& ntk )
   std::vector<signal<NtkDest>> pis;
   ntk.foreach_pi( [&]( auto ) {
     pis.push_back( dest.create_pi() );
-  } );
+  } ); // record all the primiary inputs of ntk in pis
 
   for ( auto f : cleanup_dangling( ntk, dest, pis.begin(), pis.end() ) )
   {
diff --git a/include/mockturtle/algorithms/simulation.hpp b/include/mockturtle/algorithms/simulation.hpp
index 2c43d88b3..d475002b4 100644
--- a/include/mockturtle/algorithms/simulation.hpp
+++ b/include/mockturtle/algorithms/simulation.hpp
@@ -111,7 +111,7 @@ class default_simulator<kitty::dynamic_truth_table>
 {
 public:
   default_simulator() = delete;
-  default_simulator( unsigned num_vars ) : num_vars( num_vars ) {}
+  default_simulator( unsigned num_vars) : num_vars( num_vars ){}
 
   kitty::dynamic_truth_table compute_constant( bool value ) const
   {
@@ -121,10 +121,11 @@ class default_simulator<kitty::dynamic_truth_table>
 
   kitty::dynamic_truth_table compute_pi( uint32_t index ) const
   {
-    kitty::dynamic_truth_table tt( num_vars );
-    kitty::create_nth_var( tt, index );
-    return tt;
-  }
+        kitty::dynamic_truth_table tt( num_vars );
+        kitty::create_nth_var( tt, index );
+        return tt;
+   }
+   
 
   kitty::dynamic_truth_table compute_not( kitty::dynamic_truth_table const& value ) const
   {
@@ -133,6 +134,8 @@ class default_simulator<kitty::dynamic_truth_table>
 
 private:
   unsigned num_vars;
+  bool isMiter;
+  uint32_t round, split_var;
 };
 
 /*! \brief Simulates truth tables.
@@ -522,7 +525,6 @@ node_map<SimulationType, Ntk> simulate_nodes( Ntk const& ntk, Simulator const& s
     } );
     node_to_value[n] = ntk.compute( n, fanin_values.begin(), fanin_values.end() );
   } );
-
   return node_to_value;
 }
 
diff --git a/include/mockturtle/algorithms/simulation_cec.hpp b/include/mockturtle/algorithms/simulation_cec.hpp
index 2b8cce16c..b2915f4fe 100644
--- a/include/mockturtle/algorithms/simulation_cec.hpp
+++ b/include/mockturtle/algorithms/simulation_cec.hpp
@@ -40,6 +40,8 @@
 #include "miter.hpp"
 #include "simulation.hpp"
 
+#include <bitset> // used for printing
+
 namespace mockturtle
 {
 
@@ -56,6 +58,46 @@ struct simulation_cec_stats
 namespace detail
 {
 
+class cec_simulator
+{
+public:
+    cec_simulator(unsigned num_vars, uint32_t split_var, uint32_t round) : num_vars( num_vars ), split_var(split_var),
+  round(round) {}
+
+    kitty::dynamic_truth_table compute_constant( bool value ) const
+    {
+      kitty::dynamic_truth_table tt( split_var );
+      return value ? ~tt : tt;
+    }
+
+    kitty::dynamic_truth_table compute_pi( uint32_t index ) const
+    {
+      kitty::dynamic_truth_table tt( split_var );
+      if ( index < split_var )
+      {
+        kitty::create_nth_var( tt, index );
+      }
+      else{
+            bool flag = round >> ( index - split_var ) & 1;
+            if ( !flag )
+            {
+            tt = ~tt;
+            }
+        }
+        return tt;
+    }
+
+    kitty::dynamic_truth_table compute_not( kitty::dynamic_truth_table const& value ) const
+    {
+      return ~value;
+    }
+
+private:
+    unsigned int num_vars;
+    uint32_t round, split_var;
+};
+
+
 template<class Ntk>
 class simulation_cec_impl
 {
@@ -74,16 +116,48 @@ class simulation_cec_impl
   bool run()
   {
     /* TODO: write your implementation here */
-    return false;
+    // computing splitting_var and rounds
+    gen_st();
+    // create the pattern with truth table
+
+    for ( auto i = 0; i < _st.rounds; i++ )
+    {
+      std::cout << "[running] round " << i << std::endl;
+      cec_simulator sim( _ntk.num_pis(), _st.split_var, i );
+      const std::vector<kitty::dynamic_truth_table> res = simulate<kitty::dynamic_truth_table>( _ntk, sim );
+
+      for ( auto& po : res )
+      {
+        if ( !kitty::is_const0( po ) )
+        {
+          return false;
+        }
+      }
+      return true;
+    }
   }
-
 private:
   /* you can add additional methods here */
-
-private:
   Ntk& _ntk;
   simulation_cec_stats& _st;
   /* you can add other attributes here */
+
+  void gen_st()
+  {
+    auto n = _ntk.num_pis();
+    if ( n <= 6 )
+    {
+      _st.split_var = n;
+    }
+    else
+    {
+      auto v = _ntk.size();
+      int max_m = std::log2l( std::pow( 2, 29 ) / v - 32 ) + 3;
+      _st.split_var = max_m > n ? n : max_m;
+    }
+
+    _st.rounds = std::pow( 2, n - _st.split_var );
+  }
 };
 
 } // namespace detail
diff --git a/lib/kitty/kitty/constructors.hpp b/lib/kitty/kitty/constructors.hpp
index a60b8c45f..e3b6d02b8 100644
--- a/lib/kitty/kitty/constructors.hpp
+++ b/lib/kitty/kitty/constructors.hpp
@@ -109,7 +109,7 @@ void create_nth_var( TT& tt, uint8_t var_index, bool complement = false )
       tt.mask_bits();
       return;
     }
-  }
+  } // if partial_truth_table
   else
   {
     if ( tt.num_vars() <= 6 )
@@ -123,13 +123,13 @@ void create_nth_var( TT& tt, uint8_t var_index, bool complement = false )
     }
   }
 
-  if ( var_index < 6 )
-  {
+  if ( var_index < 6 ) // if index smaller than six 
+  { // fill in all the bits with the same projection
     std::fill( std::begin( tt._bits ), std::end( tt._bits ), complement ? ~detail::projections[var_index] : detail::projections[var_index] );
   }
-  else
+  else 
   {
-    const auto c = 1 << ( var_index - 6 );
+    const auto c = 1 << ( var_index - 6 ); // var_index 7, c 2
     const auto zero = uint64_t( 0 );
     const auto one = ~zero;
     auto block = uint64_t( 0u );
@@ -150,7 +150,8 @@ void create_nth_var( TT& tt, uint8_t var_index, bool complement = false )
 
 /*! \cond PRIVATE */
 template<uint32_t NumVars>
-void create_nth_var( static_truth_table<NumVars, true>& tt, uint8_t var_index, bool complement = false )
+void create_nth_var( static_truth_table<NumVars, true>& tt, uint8_t var_index, bool complement = false ) 
+// cast to static truth table, can only have up to six varialbes
 {
   /* assign from precomputed table */
   tt._bits = complement ? ~detail::projections[var_index] : detail::projections[var_index];
diff --git a/lib/kitty/kitty/detail/constants.hpp b/lib/kitty/kitty/detail/constants.hpp
index 326044a3c..e5a985ae0 100644
--- a/lib/kitty/kitty/detail/constants.hpp
+++ b/lib/kitty/kitty/detail/constants.hpp
@@ -43,8 +43,8 @@ namespace detail
 {
 
 static constexpr uint64_t projections[] = {
-    UINT64_C( 0xaaaaaaaaaaaaaaaa ),
-    UINT64_C( 0xcccccccccccccccc ),
+    UINT64_C( 0xaaaaaaaaaaaaaaaa ), // 10101010...
+    UINT64_C( 0xcccccccccccccccc ), // 11001100...
     UINT64_C( 0xf0f0f0f0f0f0f0f0 ),
     UINT64_C( 0xff00ff00ff00ff00 ),
     UINT64_C( 0xffff0000ffff0000 ),
diff --git a/lib/kitty/kitty/dynamic_truth_table.hpp b/lib/kitty/kitty/dynamic_truth_table.hpp
index 9963db4bd..05cd985f5 100644
--- a/lib/kitty/kitty/dynamic_truth_table.hpp
+++ b/lib/kitty/kitty/dynamic_truth_table.hpp
@@ -58,7 +58,7 @@ struct dynamic_truth_table
     \param num_vars Number of variables
   */
   explicit dynamic_truth_table( uint32_t num_vars )
-      : _bits( ( num_vars <= 6 ) ? 1u : ( 1u << ( num_vars - 6 ) ) ),
+      : _bits( ( num_vars <= 6 ) ? 1u : ( 1u << ( num_vars - 6 ) ) ),  // initialize length of _bits
         _num_vars( num_vars )
   {
   }