#!/usr/bin/perl
use warnings;
use strict;

while (<DATA>) {
    print "$. ok\n" if /^foo      # "foo"
                     _            # followed by "underscore"
                     (?:bar|test) # followed by "bar|test" (bar or tes
+t)
                     _            # followed by "underscore"

                     ((?:\w+\.)+) # followed by alhpnum string with
                                  # dot at end (like foo10.1.1.1)

                     \1?          # followed by one or zero occurences
                                  # of same alhpnum string (like
                                  # foo10.1.1.1) followed by dot

                     \w{1,10}     # followed by 1-10 characters,
                                  # containing at least one digit and
                                  # one letter and underscore (e.g.
                                  # TEST_test, TEST_test2,
                                  # TEST1_test2)

                     \.txt$       # ends with .txt
                    /x;
}

__DATA__
foo_bar_foo10.1.1.1.TEST.txt
foo_test_foo10.1.1.1.foo10.1.1.1.TEST_test.txt
[download]

To test the condition "at least one digit and one letter and underscore", I'd probably capture the group and test these conditions independently:

/\d/ && /[[:alpha:]]/ && /_/
[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]