# Questions tagged [circuits]

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

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### Prove that the number of circuits with bounded fan-in (of 2) of size $s$ is at most $s^{O(s)}$

Prove that the number of circuits with bounded fan-in (of 2) of size $s$ is at most $s^{O(s)}$. Give the best explicit bound you can get. I know that for a circuit of size $s$ in order to generate a ...
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### Question about numbering of internal nodes in circuit diagrams when one circuit element has more than 1 internal node

I have the following circuit diagram that I've added labels for the internal nodes to using outside sources. I understand what an internal node is, however what I'm confused about is-- for example-- ...
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### Problem with understanding Multi-party security circuit for secure stable matching

I am reading the following paper: MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation Paper Link I have following question: We have two groups shown in the circuit. Why we ...
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### How does this circuit work?

I saw a Computerphile video explaining how a simple circuit could store memory using some logic gates. However, I couldn't wrap my mind around how one could find the value of q if one needs not, ...
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### Which gates are “pre computation” universal?

In the following, by “functions” I will mean 2 input 1 output Boolean logic functions (for conciseness). A function is called “universal” if by using it (sometimes multiple times, chained together), ...
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### Boolean circuit size of $i$th bit of determinant?

Berkowitz algorithm provides a polynomial size circuit with logarithmic depth for determinant of a square matrix using matrix powers. Is there a polynomial size boolean circuit for $i$th bit of ...
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### Is the succinct version of P-complete problems out of P?

Consider the succinct versions of the P-complete problems as a Boolean circuit which represents its input in exponential more succinct ways. Could these succinct versions are in P or out of P?
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### Every circuit of size at most $S$ can be representd as a string of $9S \log S$ bits

I'm trying to understand this claim. I see that if there are $S$ vertices, then we can identify each vertex using $\log S$ bits. Now each vertex can be connected to, let's say, $S$ other ones (is ...
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### Circuit Lower bound for $EXP^{NP}$

By Burhman, Fortnow and Thierauf result Paper Link, we know that $MA_{EXP} \not\subset P/poly$. Also, we know that $MA \subseteq P^{NP}$ (or $\Delta_{2}^{P}$ in some literatures). By using the ...
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### circuit for finding the index of first zero entry in a binary string

finding the index of first zero entry in a binary string: Input: binary string ($0$'s and $1$'s) Output: index of first zero entry Can you give a circuit for finding the index of first zero entry ...
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### Division circuit - problem

I have a question about the logic circuit performing the division ( http://userpages.umbc.edu/~squire/cs313_l20.html ). I implemented it to some software but does not work. I drew the schematic ...
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### 2-depth arithmetic circuits and VP vs VNP

the field of arithmetic circuit complexity is undergoing major discoveries in recent years as mentioned by Fortnow. am looking for a more layman-readable summary: is this new paper Sums of ...