[click here to zip down to the schedule of public lectures]
This is the year when I promised to do the seven-year cleanup of TeX and METAFONT (last updated at the beginning of 2014). It took me three weeks to wade through several hundred issues of many different kinds, and five actual bugs were discovered(!). But I'm happy to report that the newly-tuned-up systems don't “break” any of the things that used to work, and the bugs weren't likely to bite. Everyone can therefore upgrade or not, at their convenience.
Even better is the fact that the definitive documentation of the entire TeX project, first published in 1986, has now reached a new peak of perfection, which is being celebrated in the Jubilee Edition of Computers & Typesetting.
VIRUS - VIRES - FIRES - FIRER - FIVER - FEVER
(fortunately my family and I are still healthy)
Don and Jill Knuth, 1961.06.24–2021.06.24. (Wow! We are bursting with gratitude! The heavens seem to have approved, too, by shining a full moon on our celebration.)
I decided to contribute my answers before looking at what Stanley et al had to say. Now, after looking at the other three, I think you might well prefer all of them to mine. But in any case I think these interviews are a great idea, and I wish somebody had asked Euler and Gauss and Babbage and Turing and … the same questions!
The fourth volume of The Art of Computer Programming deals with Combinatorial Algorithms, the area of computer science where good techniques have the most dramatic effects. (I love it the most, because one good idea can often make a program run a million times faster.) It's a huge, fascinating subject, and I published Part 1 (Volume 4A, 883 pages, now in its fifteenth printing) in 2011.
Two-thirds of Part 2 (Volume 4B) are now available in preliminary paperback form as Volume 4, Fascicle 5 (v4f5): “Mathematical Preliminaries Redux; Introduction to Backtracking; Dancing Links”; and Volume 4, Fascicle 6 (v4f6): “Satisfiability”. Here are excerpts from the hype on the back cover of v4f5 (382 pages):
This fascicle, brimming with lively examples, forms the first third of what will eventually become hardcover Volume 4B. It begins with a 27-page tutorial on the major advances in probabilistic methods that have been made during the past 50 years, since those theories are the key to so many modern algorithms. Then it introduces the fundamental principles of efficient backtrack programming, a family of techniques that have been a mainstay of combinatorial computing since the beginning. This introductory material is followed by an extensive exploration of important data structures whose links perform delightful dances.
That section unifies a vast number of combinatorial algorithms by showing that they are special cases of the general XCC problem --- “exact covering with colors.” The firstfruits of the author's decades-old experiments with XCC solving are presented here for the first time, with dozens of applications to a dazzling array of questions that arise in amazingly diverse contexts.
The utility of this approach is illustrated by showing how it resolves and extends a wide variety of fascinating puzzles, old and new. Puzzles provide a great vehicle for understanding basic combinatorial methods and fundamental notions of symmetry. The emphasis here is on how to create new puzzles, rather than how to solve them. A significant number of leading computer scientists and mathematicians have chosen their careers after being inspired by such intellectual challenges. More than 650 exercises are provided, arranged carefully for self-instruction, together with detailed answers---in fact, sometimes also with answers to the answers.
And here is the corresponding hype on the back cover of v4f6 (310 pages, to appear soon in its fifth printing):
This fascicle, brimming with lively examples, introduces and surveys “Satisfiability,” one of the most fundamental problems in all of computer science: Given a Boolean function, can its variables be set to at least one pattern of 0s and 1 that will make the function true?
Satisfiability is far from an abstract exercise in understanding formal systems. Revolutionary methods for solving such problems emerged at the beginning of the twenty-first century, and they've led to game-changing applications in industry. These so-called “SAT solvers” can now routinely find solutions to practical problems that involve millions of variables and were thought until very recently to be hopelessly difficult.
Fascicle 6 presents full details of seven different SAT solvers, ranging from simple algorithms suitable for small problems to state-of-the-art algorithms of industrial strength. Many other significant topics also arise in the course of the discussion, such as bounded model checking, the theory of traces, Las Vegas algorithms, phase changes in random processes, the efficient encoding of problems into conjunctive normal form, and the exploitation of global and local symmetries. More than 500 exercises are provided, arranged carefully for self-instruction, together with detailed answers.
I worked particularly hard while preparing many of the new exercises, attempting to improve on expositions that I found in the literature; and in several noteworthy cases, nobody has yet pointed out any errors. It would be nice to believe that I actually got the details right in my first attempt. But that seems unlikely, because I had hundreds of chances to make mistakes. So I fear that the most probable hypothesis is that nobody has been sufficiently motivated to check these things out carefully as yet.
I still cling to a belief that these details are extremely instructive, and I'm uncomfortable with the prospect of printing a hardcopy edition with so many exercises unvetted. Thus I would like to enter here a plea for some readers to tell me explicitly, “Dear Don, I have read exercise N and its answer very carefully, and I believe that it is 100% correct,” where N is one of the following exercises in Volume 4 Fascicle 5:
Furthermore, I fondly hope that diligent readers will write and say “Dear Don, I have read exercise N and its answer very carefully, and I believe that it is 100% correct,” where N is one of the following exercises in Volume 4 Fascicle 6:
Please don't be alarmed by the highly technical nature of these examples; more than 250 of the other exercises are completely non-scary, indeed quite elementary. But of course I do want to go into high-level details also, for the benefit of advanced readers; and those darker corners of my books are naturally the most difficult to get right. Hence this plea for help.
Remember that you don't have to work the exercise first. You're allowed to peek at the answer; in fact, you're even encouraged to do so. Please send success reports to the usual address for bug reports (firstname.lastname@example.org). Thanks in advance!
By the way, if you want to receive a reward check for discovering an error in TAOCP, your best strategy may well be to scrutinize the answers to the exercises that are listed above.
Meanwhile I continue to work on the final third of Volume 4B, which already has many exciting topics of its own. Those sections are still in very preliminary form, but courageous readers who have nothing better to do might dare to take a peek at the comparatively raw copy in these “prefascicles.” One can look, for instance, at Pre-Fascicle 8a (Hamiltonian Paths and Cycles); Pre-Fascicle 9b (A Potpourri of Puzzles). Thanks to Tom Rokicki, these PostScript files are now searchable!
I seem to get older every day, and people keep asking me to reminisce about the glorious days of yore. If you're interested in checking out some of those videos and other archives, take a look at last year's news page.
Although I must stay home most of the time and work on yet more books that I've promised to complete, I do occasionally get into speaking mode. Nothing is scheduled yet before December, however, in view of the current pandemic.