sync state machines with ES6 generators

1.js

// normal JS function

function stateMachine() {
  var state = 1;

  return {
    next: function() {
      switch (state) {
        case 1:
          // handle state 1
          console.log("state " + state + "!");
          state = 2;  // transition to next state
          break;

        case 2:
          // handle state 2
          console.log("state " + state + "!");
          state = 3;  // transition to next state
          break;

        case 3:
          // handle state 3
          console.log("state " + state + "!");
          state = 0;  // transition to next state
          break;

        default:
          // handle state 0
          console.log("already done.");
      }
    }
  };
}

2.js

// ES6 generator

function *stateMachine() {
  // handle state 1
  var state = 1;
  console.log("state " + state + "!");
  state = 2;  // transition to next state

  yield;
  // handle state 2
  console.log("state " + state + "!");
  state = 3;  // transition to next state

  yield;
  // handle state 3
  console.log("state " + state + "!");
  state = 0;  // transition to next state
  
  // handle state 0
  while (true) {
    yield;
    console.log("already done.");
  }
}

3.js

var m = stateMachine();

m.next(); // state 1!
m.next(); // state 2!
m.next(); // state 3!

m.next(); // already done.
m.next(); // already done.

Is there a way to serialize the generator and restore its state?