Based on my interpretation of the OPed quasi-spec: 

>perl -wMstrict -le
"my $valid_string = qr{ \A [ACGT]+ \z }xms;
 ;;
 for my $user_subseq (qw(AAA AAC ACA CAA ABC)) {
   validate($user_subseq, $valid_string);
   my $n = 0;
   for my $string (qw(AAAAA  AAACACA  CAACAAA)) {
     $n +=()= $string =~ m{ (?= ($user_subseq)) }xmsg;
     }
   print qq{in all strings, '$user_subseq' = $n};
   }
 ;;
 sub validate {
   my ($user_supplied_string, $valid) = @_;
   return if $user_supplied_string =~ $valid;
   die qq{bad user supplied string '$user_supplied_string'}
   }
"
in all strings, 'AAA' = 5
in all strings, 'AAC' = 2
in all strings, 'ACA' = 3
in all strings, 'CAA' = 2
bad user supplied string 'ABC' at -e line 1.

[download]

Update:

I only need the regular expression...

TheA trick for matching overlapping patterns with a regex is in the capturing group nested within the positive look-ahead assertion of
 (?= ($user_subseq))

In reply to Re: Regex: finding all possible substrings by AnomalousMonk
in thread Regex: finding all possible substrings by ssc11008

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