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# CNF->DNF: exponential blowup?

Posted on 2005-03-18
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I am looking for a small (about 5 atoms/variables) and simple CNF (Conjunctive Normal Form) expression that (obviously?) blows up exponentially when converting to DNF. There should be no equivalent DNF that is small. I know that the CNF I am looking for exists.
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Question by:alberthendriks
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d-glitch earned 2000 total points
ID: 13574438
This paper suggests that one candidate would be the conjunction of parity functions.

See Section 2 -- Functions with Large Blowup

http://eccc.uni-trier.de/eccc-reports/2003/TR03-017/Paper.pdf
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Author Comment

ID: 13574692
It seems more difficult than I thought. Could you (or someone else) write out this CNF? I'm not sure if I could work it all out (maybe with the help of Google but that would take time), but all I really want is one such CNF. (points increased).
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Author Comment

ID: 13582193
Never mind. A conjunction of parity functions is not so difficult.
+ = or
* = and
! = not

(a+b) * (!a+!b) * (c+d) * (!c+!d) * (e+f) * (!e+!f)

And (ofcourse) is blows up indeed.
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