my $regex = "(";
foreach (@array2) {
  $regex .= $_ . "|";
}
$regex .= ")";
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You're nearly there. The problem with this code is that it produces something like (foo|bar|quox|), and the trailing pipe symbol makes the empty string match. To fix that, use

my $regex = join '|', @array2;
[download]

If you don't want regex meta characters in @array2 to act specially, you should even write

my $regex = join '|', map quotemeta, @array2;
[download]