a reader of the first edition (via my publisher) wrote: I've bought the 1st edition. Is it worth buying the second?
That seems to be a constant for any second edition...
For most buyers of the first edition, probably no. But it all depends on what you are interested in and on what "worth" means for you. Don't worry: sales are not my main source of revenue
As suggested by my previous post, the general framework and theory are unchanged.
Since their first elaboration in "The Hidden Logic of Sudoku" (2007) and their generalisation to any finite Constraint Satisfaction Problem in "Constraint Resolution Theories" (20011), they have been successful to deal with very different types of constraints; so there was no reason to change them.
However, there are many local improvements in the writing. As I intended it to be the final edition, I've been still more cautious than before publishing the first. Of course, all the typos or obscurities found by me or signaled by readers of the first edition have been corrected.
As for the main changes, my previous post was almost complete (more detail is available in the Foreword, available on my website).
There are two main main changes:
- the additions in the Kakuro chapter, with much better examples and (IMO) beautiful examples of g-whips; the first edition gave only the detailed theory of g-labels in Kakuro (which is far from obvious) but lacked an example with g-whips; g-whips are ubiquitous in many puzzles; as (apart from x-wings) they lie in a single sector, they are easy to find. Retrospectively, it was a pity not to have such examples in the first edition.
- the new Slitherlink chapter. Slitherlink is known to be a hard kind of puzzle.
I show that, with a good modeling (basically, a good definition of the CSP-Variables), most of the human-solvable puzzles (based on the hardest ones proposed on the most famous Slitherlink websites) can be solved by short whips, plus a single type of rules (Quasi-Loops of varied lengths) to deal with the global only-one-loop constraint. This is a great success for whips, confirming what was already clear from all the other kinds of puzzles studied in the 1st edition.
I also show how most of the "classical" Slitherlink-specific rules are W-macro-rules, i.e. they can be reduced to sequences of short whips (for most of them, sequences of whips); all the reduction proofs are given; they were obtained semi-automatically, using CSP-Rules as an (assistant) theorem prover - also a new aspect wrt the puzzles studied in the first edition.
One of the constant aspects in my approach is the importance of the proper choice of CSP-Variables and the necessity to have some redundancy between "dual" sets of CSP-Variables.
In Sudoku, it started with my introduction of the Extended Sudoku Board (in HLS1), i.e. of the rc, rn, cn and bn spaces, corresponding respectively to CSP-Variables of types rc (the "natural" ones), rn, cn and bn (the additional ones). They allowed to deal with all the Sudoku symmetries in a uniform way and to automatically extend rules known for the rc-space to their "supersymmetric" counterparts.
In Kakuro, I had to introduce CSP-Variables representing the combinations allowed in each sector.
In Numbrix and Hidato, I had to introduce "dual" CSP-Variables, representing the places a given digit can occupy (dual wrt to the "natural" rc ones, representing the digits that can occupy a given place).
In Slitherlink, given the "natural" (N, H V) CSP-Variables representing the numbers of borders of cells and the horizontal and vertical lines, I had to introduce two additional types of CSP-Variables (P, B) representing the points and cell borders (seen as sets of lines). Some day, I may give an example of a full resolution path in the existing Slitherlink thread.
the same reader of the first edition (via my publisher) wrote: In particular, is there anything new wrt Sudoku?
Globally, nothing fundamentally new.
Sudoku was the first CSP I dealt with, years ago (HLS1 dates back to June 2007). The sections of the book specifically dealing with Sudoku are the result of continuous improvements and extensions over all those years.
The main new thing is the updating of classifications for the hardest puzzles - the main result being that my (now old) T&E(1) and B7B conjectures still hold for 9x9 puzzles.
Notice that, between the two editions, Sudoku solving has been a relatively dormant topic. No new resolution rule has been found. There have been tentatives to define ratings based on the whole resolution path instead of the usual hardest step, but nothing consistent.