# Questions tagged [circuits]

A computation model in which the computation is described via circuits of various logic gates.

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### Universality of the Toffoli gate

Regarding the quantum Toffoli gate: is it classicaly universal, and if so, why? is it quantumly universal, and why?
287 views

### Creating a logical circuit

Task: Design a 2 bit comparator. Input: 2x 2 bit (I take it as 2 2-bit values, let them be unsigned for simplicity) Output: 1 if result input1>input2 is true, 0 otherwise Develop truth table and ...
2k views

### How to understand the SR Latch

I can't wrap my head around how the SR Latch works. Seemingly, you plug an input line from R, and another from S, and you are supposed to get results in $Q$ and $Q'$. However, both R and S require ...
175 views

### Simple example of exponential gap between monotone and non-monotone circuits

Is there a simple example of a Boolean function $f:\{0,1\}^m \to \{0,1\}$ that we know can be computed by a polynomial-size circuit, but cannot be computed by any polynomial-size monotone circuit? ...
270 views

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### Definition of uniform boolean circuit

Definition A family of circuits $(C_{1}, C_{2}, \ldots)$ is uniform if some log space transducer $T$ outputs $\langle C_{n}\rangle$ where $T$'s input is $1^{n}$. (from http://en.wikipedia.org/wiki/...
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### Is it assumed that lower bounds on the size of monotone circuits apply to general Boolean circuits too?

A "general" Boolean (combinatoiral) circuit is a labeled (with the labels: AND, OR, NOT, IN, OUT), directed, acyclic graph, that satisfies: fan-in=2 for the AND and OR nodes fan-n=1 for the NOT ...
508 views

### How to read $NC^1\subset L \subset NL \subset SAC^1$, $SAC^1=LOGCFL/poly$, and similar statements?

The (complexity zoo) description of $NC^1$ says that it is contained in $L$, i.e. $NC^1\subset L$. The description of $SAC^1$ says that it is equal to $LOGCFL$$/poly$, i.e. $SAC^1=LOGCFL/poly$. The ...
186 views

### Someone explain the venn diagram for the logic equation A*(B+C)

So, I am studying logic circuits and how to prove them with Venn diagrams. When drawing a Venn diagram for the equation A*(B+C) I figured it would look something like this: But according to the ...