Does jQuery autocomplete work with a dynamic array as source

Question

I am currently trying to create an autocomplete with a source that is stored in a javascript variable but this variable can be updated by another function. So, what I would like

Answer 1

a source that is stored in a javascript variable but this variable can be updated by another function.

That should just work. If both the autocomplete and the updating function reference the same array, you can push new values at any time which will be used as soon as the array is evaluated next time (e.g. on keystroke).

I would like that at each time the user updates the autocomplete field, the source field of autocomplete is generated.

That's a different one. Yes, this needs a callback function to generate the source array dynamically, but that's simple. Have a look at the docs:

$( "#tags" ).autocomplete({
    source: function(request, resolve) {
        // fetch new values with request.term
        resolve(availableTags);
    }
});