The debate about what constitutes a sukaku or not is a debate I like to take part in. (But it is a can of worms, who doesn't like worms
)
I (initially) agree that excluding vanilla sudokus from sukakus is silly because vanilla sudokus are a small set
within Sukakus. in that sense it is vanilla that is the restriction (or variant) to Sukaku and not the opposite.
Here is my definition of vanilla sudokus:
Vanilla sudoku: is a sukaku puzzle where
Only a known set of Naked singles is needed to determine puzzle validity/uniqueness.
Now to the fun part (and the reason why a small part of me favours a restriction):
Can we therefore divide Sukaku puzzles into
2 separate groups; vanilla sudokus and Sukaku puzzles that are non-vanilla sudokus?
The answer should be yes (for that it requires some proper definitions) but currently the answer is no!!
Look at the definition of vanilla sudoku that I provided above: Looking at a cell that has a solved naked single (one candidate in a cell) will look like a solved hidden single (unique candidate per sector). If a vanilla sudoku clue is a naked single then you can substitute that known clue with a hidden singles (through adding that candidate to all other cells in a shared sector then adding other candidates to that cell). With our current definitions; this means that a vanilla puzzle has several equivalent non-vanilla forms (And Yes: each known vanilla puzzle can be transformed into a Pencilmark-only version in that way
)
One way to guarantee that we don't have several versions of essentially the same puzzle appearing is to restrict the definition of non-vanilla further:
Desired non-vanilla: Minimal Sukaku with no hidden singles at the start (Minimal guarantees a single version of the puzzle that has cells with 1 candidate (naked singles), No hidden singles will guarantee that we don't have minimal puzzles appearing in a different form). This may need to extend to hidden doubles and hidden triples that are in more than one sector!
unDesired non-vanilla: All other Sukakus that are not vanilla sudokus nor Desired sukakus.
[Edit: corrected a small mix-up]
tarek