Customer Reviews

The Art of Computer Programming, Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions

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For those interested in combinatorial thinking, ranging from combinatorial card game puzzles to how to count the number of ways to do something, this is a great re-introduction. In this first part of the long-awaited Volume 4, Knuth tells you why he loves combinatorics and computer algorithms, and why it took him so long to publish volume 4.

Hearing it from Knuth, the fascicle basically reassured me in my personal dance with mathematics and algorithmics: there is no problem if you love these things!

I highly recommended this to few friends who were computer science students, and they really liked it. They could not stop reading it during a party at our home!

Disclaimer: This review is based on the preview version that was made available on Knuth's home page. I believe not much is changed, except that some errors should be corrected.

Nobody should read this book lightly. It continues the decades-long practice of Knuth's series, by furnishing a huge set of exercises in the computational field. Yet ones where the emphasis is not on writing computer programs, though he does have some problems where you are asked to do this. Instead, you have to nut out puzzles in what you might term applied number theory. A key trait of the book, and of the entire series, is that the reduction of an algorithm to source code is a relatively minor aspect.

The book differs from the first 3 volumes in the surfeit of problems. Perhaps in part because decades have elapsed since those volumes came out. During which, Knuth accrued ever more problems that he now gives us.

The focus of this book on Boolean functions can be an eye opener to some readers. You might think, naively, how difficult could the theory of Boolean functions be? Knuth shows that there is a vast level of complexity and conceptual richness lurking in such apparently simple functions. The typical computer science text that mentions Boolean functions might devote some space to examples of these. But it rarely goes deeper than explaining how to optimise, say, ORs of ANDs, where this is used for in turn optimising circuit layouts on a chip. Knuth goes way beyond this.

Granted, those are introductory CS texts, and this is not. But the average computer programmer or chip designer rarely goes beyond those in mathematical depth. And so is unlikely to have seen the material in this book.

I bought this book after a class I had in "Boolean Functions" and I must admit that the content was superb. Many interesting subjects about boolean functions, an extensive range of problems with solutions, and certainly a great deal of "food for thought" for further applications or research. All in all, a highly recommended book, and I am only wondering why volume 4 is not published in its final version (assuming that the rest of fascicles are in the same form). If you are interested in the field, just buy it.