You might have actually discovered a bug. Luckily it's just a Notice, which might not have any effect at all.
I will investigate this issue further, as I don't know the cause yet.
Until then please try the following solution:
1. Open up the \wp-content\plugins\ajax-search-pro\includes\views\asp.shortcode.categories_terms.php file, where you should see this line:
$_invisible_terms = array_diff($_needed_terms, $style['selected-showterms']);
2. Change that line to:
$_invisible_terms = @array_diff($_needed_terms, $style['selected-showterms']);
That might help.Best,
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