How can I add jquery ui autocomplete to a dynamically created element?

Function .live() is deprecated now.

Looks like code like this works:

var options = {
    source: ["ActionScript", "AppleScript"],
    minLength: 2
};
var selector = 'input.searchInput';
$(document).on('keydown.autocomplete', selector, function() {
    $(this).autocomplete(options);
});

This works:

$(function() {
  var options = {
    source: [
      "ActionScript",
      "AppleScript",
      "Asp",
      "BASIC",
      "C",
      "C++",
      "Clojure",
      "COBOL",
      "ColdFusion",
      "Erlang",
      "Fortran",
      "Groovy",
      "Haskell",
      "Java",
      "JavaScript",
      "Lisp",
      "Perl",
      "PHP",
      "Python",
      "Ruby",
      "Scala",
      "Scheme"
    ],
    minLength: 2
  };

  $("input.searchInput").live("keydown.autocomplete", function() {
    $(this).autocomplete(options);
  });

  var addInput = function() {
    var inputHTML = " <input name='search' value='' class='searchInput' maxlength='20' />";
    $(inputHTML).appendTo("form#myForm");
    $("input.searchInput:last").focus();
  };

  if (!$("form#myForm").find("input.searchInput").length) {
    addInput();
  }

  $("input#addButton").click(addInput);
});
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.6.2/jquery.min.js"></script>
<script src="//ajax.googleapis.com/ajax/libs/jqueryui/1.8.14/jquery-ui.min.js"></script>
<form id="myForm" name="myForm" method="post">
  <input id="addButton" name="addButton" type="button" value="Add an input" />
</form>