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  1. or download this
        qr/ (?(DEFINE)
          ( 00 (?1) | 11 (?2) | )               # group 1:  carry = 0
...
        )

        \A(?1)\Z /x;
  2. or download this
        qr/ (?(DEFINE)
          ( 00 (?1) | 11 01 (?1) | 11 10 (?3) | )
...
        )

        \A(?1)\Z /x;
  3. or download this
    my $Regex_Pattern =

    qr/ \A ( 00 | 11 01 | 11 10 ( 00 10 | 11 )* 00 01 )* \Z /x;