Without using the regex, you may traverse through each character one by one, remember the previous character pattern and the pattern count.

You may, but why would you write such a custom, special-case state machine in Perl? This is precisely what regular expressions in scripting languages like Perl are for.

$ echo '........ aaaaaaaasssssss __________ ++++++++++ ---------' |
> perl -pe 's{(.)\1\1\K\1+}{}g'
... aaasss ___ +++ ---
$
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That's unbeatably simple and elegant, don't you think?