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Boolean circuits with fan-out of each gate is 2
I am following the book of Arora and Barak book.
We consider Boolean circuits as we do, Specifically, inner nodes are either AND, OR (both – fan-in 2), or NOT (fan-in 1) gates. The fan-out of each ...
user172436
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Given a boolean circuit that computes a boolean function, can we always find an equivalent circuit with optimal size?
Let's say that we have a decision problem $P$. Let's also say that $I_n$ is the set of all instances of size $n$ that exist for this problem, and that its cardinality is finite.
There is a sequence of ...
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3
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Shannon's result that some Boolean functions require exponential circuits
In 1949 Shannon proved, using a non-constructive counting argument, that some boolean functions have exponential circuit complexity, see [1] and many texts on computational complexity. This result has ...
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