Can cooking or processing generate more natural sugars? This question excludes all added or synthetic sugars (which I abbreviate to AS), and refers only to only natural sugars intrinsic and inherent in food (which I abbreviate to NS). 

I wish to clarify the following helpful comment in response to my (now closed) question on suggestion for toppings on pancakes and waffles without any added or synthetic sugars, because my grandmother's dentist and physician oppose her consumption of any AS:


  Besides whole fruit, you can also use something like apple sauce. Apple butter and appelstroop are technically apple, but cooked down so that the sugars are concentrated and would likely violate the 'added sugar' exemption. And there are jams that are made with only fruit (eg. Polaner All Fruit), but again, it's concentrated.


Does 'concentrated' here mean that:


cooking and processing generate new sugars, so that the comestible's initial quantity of NS &lt; the comestible's final quantity of NS.
or cooking and processing only condense (ie: increase the density of) the existing NS, so that the total quantity of NS remains the same before and after (but not the total density)?


If the answer is 1, then my grandmother cannot use such products;
but if the answer is 2, then please allow me to pose another question on the healthiness of such products for my grandmother.
The comment you cite obviously means the second explanation. The total quantity of sugars within the apple is not considered to increase in apple sauce making. Its density, however, does increase. And the increase can be substantial, as fruit is mostly water. In fact, "table sugar" is nothing but processed (concentrated) beets or cane. 

It is possible that some production processes will create new sugars, usually by enzymatic splitting of longer carbohydrates. This is where the fructose in high fructose corn syrup comes from. So you can't assume that the second meaning will be true for all cases where you start with a fruit or vegetable. It is just true for traditional applesauce recipes. 

Whether it is possible to make jam "without added sugar" is a very murky question, as "added sugar" is not really definable in this case. 

As for the healthiness of such products, this is both off topic and unanswerable. You should ask your grandmother's doctor. He's the only one who knows what he meant and intended when he prescribed the diet.