
Extremal Combinatorics With Applications in Computer Science - furcyd
https://rjlipton.wordpress.com/2020/07/27/a-brilliant-book-on-combinatorics/
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jeffreyrogers
I wish the author would give some motivation for why I should attempt to
understand monotone circuit lower bounds. I can probably follow the math, but
math takes effort to read and I'm not generally willing to make the effort
unless I get some hint as to what the payoff might be.

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xhkkffbf
Two words: 3sat. In other words, answering whether P==NP or not.

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bmc7505
PDF:
[http://bd.unsl.edu.ar/download.php?id=1638](http://bd.unsl.edu.ar/download.php?id=1638)

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daviddaviddavid
As a regular old non-theoretical-CS computer programmer, it amazes me that a
fellow Buffalonian (Dr Ken Regan) pops up on HN and related sites so often for
writings in the headiest areas of CS and chess, etc. Not too many internet
celebrities in this city.

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xenonite
Did someone get why "It cannot be that S has an even number of elements" (in
the first subsection)?

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ColinWright
Because if you just add one element to the set it no longer has the property,
and hence the predicate is not monotone.

In more detail ...

He's talking about properties (or predicates) that are monotone. That means
that if P(S) is true, and T contains S, then P(T) must also be true.

But when P(X) is true if and only if X has an even number of elements, then
P({a,b}) would be true, but P({a,b,c}) will not be true. Then P would not be
monotone.

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xenonite
Great, thank you very much for your explanation! I now get that the sentence
describes a new example predicate that is not connected to the sentence before
(“S includes at least half of the elements of [n]”). This makes sense. Thank
you for your thoughts.

