What is considered a professionally made knot?
Any strong knot which is tightly tied there is doubt that perhaps it is considered a professional knot.
Double knots: Therefore [strong] double knots are forbidden to be tied or untied unless in a case of pain when made to not last 24 hours.
A bow on top of a single knot: Is considered an amateur knot and is allowed to be tied and untied with intention to undo that day.
May one make a bow on top of a bow?  Yes, it may be done even with intent to never undo.
A single knot made with two ends: Is not considered a knot at all and may thus be tied and untied even if meant to last forever.
A single knot made with one end: Has the same law as a double knot for all matters.
If a professional knot occurred on its own, like strings became tangled and formed a double knot, or a bow over a knot became a double knot, may one open it on Shabbos? 
It may only be undone if
- [By the latter case only if one had intention to undo the bow that day], and
- The current knot not tied tightly, or
- Is tied tightly but is a case that involves pain.
 Admur 651/6; Mishneh Berurah 317/29
 The Chayeh Adam, brought in Mishneh Berurah  as well as in the Ketzos Hashulchan [chapter 123 footnote 11], writes that if one usually ties a bow [over a single knot] and accidentally tied a knot [over the single knot thus forming a double knot] then it has the same law as a knot made with intention to undo that same day. However the Ketzos Hashulchan explains this to mean that only if it was not tied strongly and is thus not a professional knot may it be untied. Alternatively even if tied strongly it may be untied in a scenario of pain. [However this is only referring to a double knot, which is questionable as to whether it is considered professional or not. However by another type of strong knot which is for certain a professional knot then even in a case of pain seemingly untying it would be forbidden, as explained above]. [Vetzaruch Iyun Gadol as according to this explanation of the Ketzos Hashulchan there has been no novelty said in the words of the Chayeh Adam, as it has the same exact law as one who intentionally tied a double knot, of which if strong may not be undone unless in a case of pain and if lose may be undone?]