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Edgar G. Daylight

Algorithmic Barriers Falling: P=np?

by Donald E Knuth (Author), Edgar G Daylight (Author), Kurt De Grave (Editor)

4.6 5 ratings

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J. Ernst Oberklammer

Knuth's 11

Reviewed in Germany on August 22, 2015

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"Algorithmic Barriers Falling: P = NP" can be seen as a follow-up to "The Essential Knuth". Again diverse topics in connection with Donald E. Knuth are raised in a long interview, e.g. on "History", "Asymptotics", "Grammars", "TeX & Literate Programming", ..., "P = NP" (these are some of the chapters), mixing bits of history and Knuth's own life and even a few technicalities, - for me the most interesting can be found on page 91, on satisfiability problems. Here the reader gets background information that's not in Pre-Fascicle 6a of "The Art of Computer Programming" ("TAOCP"), a draft of section 7.2.2.2 (SATISFIABILITY), where on page 279, in the answer to excercise 479 (b) [yes: there are 526 exercises!], it is simply stated: "But s(5) = 12 is not optimum, despite the beauty of 7.1.2-(29)! The M_11 = 76321 clauses.... yielding an amazing chain..." (here the 11 gates of the optimum solution are given). ["7.1.2.-(29)" means TAOCP 4A, page 108]. With no more hint than the use of "amazing" that this is something of a breakthrough! But on page 91 Knuth tells E. G. Daylight that "I believed that the best way to evaluate them simultaneously would require 12 gates....The fact that 13 gates weren't necessary was already quite amazing... The SAT solver came up with an 11-gate solution after four hours of computation; I don't think a human being would have been able to come up with it. It represents another breakthrough discovered by a machine". - In a similar fashion, Knuth developes here his opinion concerning P = NP.

In addition the reader will find intersting thoughts and funny anecdotes, e.g. on the "second most hectic time in my life", on a "live turkey", on when biologists began to study Brownian motion, the ideal way to present history, that writing papers abour history is more difficult than writing papers about research, Jeffrey Shallit's great example, which table on page 234 of Iverson's "A Programming Language" "changed" Knuth's life (it hast to do with asymptotics), on the first time that automata theory had taught Knuth something that he wasn't able to discover with ordinary common sense, that in his PhD thesis he resolved a longstanding conjecture in combinatorcics, which book can be seen as "sort of a sequel to "Concrete Mathmatics" (it's "The Concrete Tetrahedron"), that he was elected to the Royal Society as a foreign member, what he thinks is not the "number-one result of the 20th century" (see page 67), etc. etc.

Let me finish with the "six reasons to study the history of a field", according to Knuth:

1. Understanding the process of discovery.
2. Understanding the process of failure.
3. Celebrating the contributions of many cultures.
4. Story telling: the best way to explain.
5. Learning how to cope with life.
6. Besome more familiar with the world.

(Now you just have to go and by a copy of this book and read it immediately! ;-)

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