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Graduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Parity is non-monotone
A boolean function \(f(x_{1},x_{2},\dots,x_{n})\) is called monotone if it can be written as a formula with only the AND and OR operations. Prove that \(x_1 \oplus x_2 \oplus \dots \oplus x_n\) is n…
Mathematics
Logic
monotone function
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Graduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Size of monotone circuits
Prove that there is a monotone boolean function \(f(x_{1}, x_{2},\dots,x_{n})\) such that any circuit (consisting of only AND, OR gates) computing \(f\) requires at least …
Computer Science
Complexity Theory
circuit complexity
lower bound
monotone function
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Graduate
By
diego
on June 22, 2012 | Updated Dec. 6, 2017
The power of the majority function
A boolean function \(f(x_{1},x_{2},\dots,x_{n})\) is called monotone if it can be written as a formula with only the AND and OR operations and constants 0 and 1; and it is called self-dual if …
Mathematics
Logic
monotone function
self dual function
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