Questions tagged [circuits]

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

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Deducing upper bound for Boolean Circuit size from well-known algorithms

Given an algorithm A for computing binary function $f$. Assuming that A runs in time $t(n)$, what could we say about the size of the minimal Boolean circuit C that calculates f? I think that it ...
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Is there a 2SAT encoding for a NAND gate

I am trying to encode some circuit checking algorithms, but encountered difficulty creating a 2SAT representation for a NAND circuit. Is there a proof that this is not possible?
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Given a language L how can I derive its Boolean formula?

Let: be given by Compute Boolean formulas for the following: This is part of my coursework; I have the answers but can't understand them. I want to develop some intuition on how I can solve these ...
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Investigating the Claim: co-$NP\subseteq NP\text{/}P$ implies $\Sigma_3^P=\Pi_3^P$ and Collapse of the Polynomial Hierarchy?

I have been studying the polynomial hierarchy recently, and I came across an intriguing claim that I would like to explore further: Assuming co-$NP\subseteq NP\text{/}P$, the claim states that it ...
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Are there any typical papers on the impossibility of black-box reduction of circuits?

I am now considering the impossibility of black-box reductions between error-correcting codes and universal hashing without multiplicative overhead in depth. I could hardly find any classical papers ...
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Logical circuit for priority resolution in interrupt controllers (with configurable priority, not fixed)

I'm interested in what the typical solution is for priority resolution in interrupt controllers. I assume a hardware logic circuit is used, and not software. For interrupt controllers with fixed ...
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Computational power of Turing machines vs circuit ensemble

Is it true that for every Turing machine 𝑀, there exists a circuit ensemble 𝐶 such that 𝐿(𝑀) = 𝐿(𝐶), or is it true that for every circuit ensemble 𝐶, there exists a Turing machine 𝑀 such that �...
1 vote
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Does there exist some partial" universal hashing?

Suppose we have sets $X$ and $Y$, $|X|=m$, $|Y|=n$. $H$ is a universal family of hash functions from $X$ to $Y$. Let $S\subsetneq X$ be a proper subset of $X$. Does there exist some "partial"...
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If we let a language L in {0,1}* be dyadic if for each x in L, and each index i with xi = 1, i is a power of 2, then consider the class of languages recognized by a polynomial time oracle machine with ...
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1 vote
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How to construct a carry-lookahead adder of the optimal $O(n)$ size

Problem (TL;DR): I'd like to know how to construct a CLA adder that has $O(n)$ size and $O(\log n)$ depth using only fan-in 2 AND gates and XOR gates, as suggested in this answer and this answer. ...
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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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Algorithm to reduce a Circuit-SAT to NAND-SAT

I am trying to construct an algorithm to reduce OR, AND and NOT gates into NAND-SAT. Can someone give me a hint as to where to start?
1 vote
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What class is the language $(C,(v_i)_{i=1}^m,x)$ complete to s.t. $C(x)$ is a boolean circuit with $m$ gates with values $\{v_i\}_{i=1}^m$

Given the following language:  L=\left\{\,(\,C,\,\{v_i\}_{i=1}^m, \,x\,) \enspace :\enspace \substack{C(x) \text{ is a boolean circuit with } m \text{ gates} \\i\text{'th gate value is } v_i \text{...
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Decidable languages unconditionally not in P/poly

What are some nice/natural examples of languages not contained in $P/\mathit{poly}$, preferably decidable ones? I'm interested in unconditional results rather than examples such as the Karp–Lipton ...
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Make the forward counter go down

Suppose, I have a 4-bit binary Incrementor that uses XOR gates to increment the inputted number by the value of 1 (b0001, to be precise). Suppose, we connect it to 4 D-Flip-Flops (DFF) to create a ...
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How does fan-out change circuit complexity?

Edit: Here's maybe a clearer presentation of my question. In a Boolean formula, all the gates have fan-out 1, and the graph representing the formula is a tree. In a Boolean circuit, the gates can have ...
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1 vote
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Details wanted on the reduction from Circuit Value to CFG Membership

Consider a Boolean Circuit $C$ which takes $n$ inputs and has one output. Notation: Let $\textit{size}(C)$ be the size of circuit $C$: the total number of gates in $C$. Let $G = (V,\Sigma,R,S)$ be a ...
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