Kuudos is an experiment just for fun. It aims to solve sukoku puzzles in a way that abstracts away as much of the mechanics of the puzzle as possible.
A sudoku puzzle can be thought of as follows. We have a set S of cells (81 in total) and we have a set T of subsets of S all of the same size n (i.e. comprising 9 cells, with 9 subsets representing rows, 9 subsets representing columns, and 9 subsets representing squares). The objective is to label each cell with one of the n symbols (typically 1, 2, ..., 9) such that each of the given subsets of S contains each of the symbols exactly once.
Kuudos represents a sudoku board in a hierarchical structure (but not a tree!). To help us make deductions, we have a node corresponding to each possible intersecion of sets in T (the rows, columns and squares), i.e. the rows, columns and squares themselves, 1x3 or 3x1 blocks inside squares, and single cells. Each node corresponds to a subset of S, and we can give them a partial order by set inclusion. The structure we then store them in is like a Hasse diagram, where every node x is joined to every node y that covers it (i.e. x < y and there is no node z such that x < z < y). The difference to a true Hasse diagram is that there isn't a minimal or maximal node. Each node may have multiple parents (representing sets that contain its set) and multiple children.
Throughout the execution, each node will have a set of numbers that it will contain (a 'yes-set') and a set of numbers that it will certainly not contain (a 'no-set'). Any node's yes-set contains the union of its children's yes-sets, and is the intersection of its parents'. Any node's no-set will be the intersection of its children's no-sets and will be contained in the union of its parents'.
Maintaining this structure allows us to make deductions until no further conclusions can be made, at which point we make a guess (in a single cell that has the smallest number of possible values).
Using this abstract approach means that it takes almost zero effort to adjust to solving 'Samurai sudoku' puzzles and the like.