Questions tagged [circuits]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
30 views

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 ...
1
vote
1answer
47 views

What is $f(n)$ in $NTIME(n)\subseteq DTIME(f(n))$ if $CIRCUITSAT$ is in $P$?

If $CIRCUITSAT$ in $n$ variables and $m$ gates has an $O((nm)^c)$ algorithm for a fixed $c>0$ then $NTIME(n)\subseteq DTIME(O(f(n)))$ for large enough $f(n)$. What is the smallest $f(n)$ in $NTIME(...
2
votes
1answer
43 views

Construct a Circuit computing all boolean functions over n bits

Let $ n∈N $ . Construct a circuit with $ C_n(x_1,\dots,x_n) $ with $ 2^{2^n} $ outputs $ y_1,\dots,y_{2^{2^n}} $ which computes all distinct boolean functions $ f_i:\{0,1\}^n→\{0,1\}$ such that $ ...
1
vote
2answers
23 views

Proof that uniform circuit families can efficiently simulate a Turing Machine

Can someone explain (or provide a reference for) how to show that uniform circuit families can efficiently simulate Turing machines? I have only seen them discussed in terms of specific complexity ...
0
votes
2answers
41 views

Minimize circuit functions

$\begin{array}{rrrr | rr } 0& 0 & 0 & 0 & 1 &1 &1 &1 &1 & 1&0 \\ 0& 0 & 0 & 1 & 0 &1 &1 &0 &0 & 0&0 \\ 0& 0 & 1 &...
4
votes
1answer
37 views

Can the W hierarchy by defined by circuits having a satisfying assignment of weight at most k?

Traditionally, the $W$ hierarchy is defined around the problem of weighted circuit satisfiability. More precisely, the class $W[t]$ is defined as the closure under $\mathrm{fpt}$-reductions of the ...
0
votes
1answer
16 views

How to prove quantum circuit identity in Qiskit?

I am working on a simple quantum circuit identity. I proved it on paper with the tensor product, but i'm having trouble showing that with qiskit. I know I need to measure them somehow but i don't know ...
1
vote
1answer
33 views

Polysize bounded depth circuit for modified MAJORITY problem

I am trying to show the existence of a polynomial size, bounded depth monotone circuit on the inputs $(x_1,\ldots, x_n)$ that gives $1$ if $\sum x_i \geq n/2 + n/\log n$ and $0$ if $\sum x_i \leq n/2 -...
1
vote
0answers
176 views

Example of *small* non monotone circuit such that any equivalent monotone circuit has greater size?

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 ...
6
votes
1answer
647 views

Is it possible to construct a C^5(U) with V^2=U and no work qubits (Nielsen & Chuang Exercise 4.28)

My question is related to the exercise 4.28 in the book of Nielsen and Chuang (Quantum Computation and Quantum Information). Here is the exercise For $U=V^2$ with $V$ unitary, construct a $C^5(U)$ ...
1
vote
1answer
63 views

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 ...
2
votes
2answers
192 views

Circuit satisfiability problem : SAT-C to SAT-2C

I have the following language : $L=\{\langle C_1,C_2\rangle \text{ | } C_1 \text{ and } C_2 \text{ are two circuits that calculate different function}\}$. We can call this language SAT-2C. Prove that ...
1
vote
0answers
12 views

Examples of relatively complex truth tables/logic gates in real life?

I'm researching truth tables, logical gates, and boolean algebra expressions. I'm trying to find specific real-life examples of logic gates and/or truth tables used in algorithm or circuit design in ...
2
votes
1answer
49 views

Multiplication mod 2 without extra registers

For an arbitrary bitstring $(x_1, x_2,\ldots, x_n)$ and an $n\times n$ invertible binary matrix $M$ (fixed ahead of time), I would like to construct a circuit $C$ acting on these $n$ bits whose output ...
1
vote
0answers
11 views

Boolean circuit multigraph

Let us say that our definition of a circuit is the one of a boolean circuit from [Vollmer]. He uses directed acyclic graphs to represent circuits where the computation nodes are labeled with some ...
2
votes
0answers
54 views

Are minimum boolean circuit sizes for small problem sizes of an NP-complete problem known?

I think that a table with the following numeric values would be very interesting, but I could not find any table online displaying them: Choose any NP-complete problem (say, clique, but a problem ...
0
votes
0answers
51 views

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, ...
3
votes
1answer
27 views

Lower bound on number of (different) circuits of given size?

For circuits with $n$ input bits, we know that, for any function $s$, there are at most $O(s(n)^{s(n)}) = O(2^{s(n) \log s(n)})$ circuits with size at most $s(n)$. Say two circuits $C_1$ and $C_2$ ...
1
vote
1answer
28 views

Smallest Circuit for Square of Sparse Symmetric Matrix

I have an n by n symmetric matrix, and I would like to compute its square in as small a circuit complexity as possible. It's sparse: there are sqrt(n) nonzero entries in each row/column, so the input ...
1
vote
1answer
22 views

Relationship between circuit size and formula size in Sipser text

The Sipser text (3rd edition) contains a proof that 3-SAT is NP-Complete based on Boolean circuits. Part of the proof contains the remark that the reduction from the circuit to the Boolean formula can ...
0
votes
0answers
9 views

Circuit : Switching function. Can I ignore RESET and CLOCK for the functions?

So if I have to state any function like state transition function or switching function can I ignore CLOCK and RESETS?
2
votes
2answers
329 views

Is it possible to make N-way Controlled-NOTs out of Toffoli gates, without extra work bits?

I'm working on exercise 4.29 of Nielsen and Chuang: Find a circuit containing O(n^2) Toffoli, CNOT, and single qubit gates which implements a $C^n(X)$ gate (for n >3), using no work qubits. As ...
1
vote
0answers
83 views

Class of languages recognizable by n-bit formulas of size at most $T(n)$

A 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 nodes fan-...
2
votes
0answers
36 views

Circuit complexity of random Boolean functions

I just saw a YouTube video where Ryan Williams gives a talk about circuit complexity. He stated that random Boolean functions require exponential size circuits to compute, but I don't understand why ...
0
votes
1answer
23 views

Is this truth table possbile

I am trying to figure out if this truth table is possible. I've tried inverting the numbers, adding them, subtracting them, but I still cant find anything that works. I am starting to think that this ...
0
votes
0answers
18 views

Simulating Boolean Circuit with RAM

Statement: Every $T(n)$ size bounded Boolean circuit family, could be simulated with $(T(n))^2$ time bounded Random Access Turing Machine (RAM). Could you please supply me with a reference to an ...
0
votes
0answers
22 views

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), ...
1
vote
0answers
56 views

Nandgame--I am not sure I understand the Data Flip-Flop specifications

Nandgame (nandgame.com) has you solve puzzles of increasing complexity which culminate in constructing a simple CPU. You start at the level of nand gates, and build everything else up out of those. I'...
1
vote
1answer
28 views

What does it mean when a dot appears in a logic gate other than the NOT gate? (in logic diagrams)

For example, this gate: looks like an OR gate, except there's a dot to the right. The dot is reminiscent of the fact that there's a dot in the NOT gate, so I wonder if it has something to do with ...
4
votes
0answers
101 views

Perfect Halver Construction?

A sorting network is a circuit-based approach to sorting, built out of CompareExchange gates, which compute the function: $$\mathsf{CompareExchange}(x,y) = (\min(x,y), \max(x,y))$$ The input to the ...
2
votes
1answer
66 views

Addition, multiplication, and apostrophe used to represent boolean algebra expressions?

I'm looking at a worksheet that expresses boolean logic expressions using multiplication, addition, and apostrophes; something I've never seen before. I can make a guess that the apostrophe is ...
2
votes
2answers
37 views

How to show all false outputs in a circuit?

I have 3 input variables and the output for all 8 possible combinations is 0 (false). When making a circuit, how would I show this using gates or no gates at all? Thanks!
5
votes
1answer
65 views

How does $\mathsf{NP} \subset \mathsf{P}/\mathsf{poly}$ imply these two inclusions?

In the proof of Theorem 1 in this paper by Chen, McKay, Murray, and Williams the authors assume $\mathsf{NP} \subset \mathsf{P}/\mathsf{poly}$ and (in different parts of the proof) state this implies ...
4
votes
1answer
352 views

Proving that EXP doesn't have polynomial-size circuits

How to prove for all $i\in\mathbb{N}$, there exists a language $A\in\mathrm{EXP}$ such that no family of boolean circuits of size $n^i$ decides $A$? I have a reminder that says $$ \mathrm{EXP} =\...
0
votes
0answers
33 views

Number of circuits with at most $m$ logic gates

I'm working on the same exercise as described in this post: How to show that hard-to-compute Boolean functions exist? In the answer there I don't understand how the number of circuits with at most $...
2
votes
0answers
38 views

Does Cook and Ruzzo's result also hold for logspace-uniform AC0?

In Cook's famous paper on $\mathsf{NC}$, he cites the following result: PROPOSITION 4.7 (Cook and Ruzzo, 1983). $\mathsf{AC}^k$ consists of those problems solvable by uniform unbounded fan-in ...
0
votes
1answer
23 views

What is the difference between a collection of Turing Machines and a family of Circuits?

Given a Collection of Turing Machines $T_1, T_2, T_3,...T_n$ where $T_1$ denotes that the Turing machine can only take in an input of size 1. Is there any difference in computational power to a family ...
1
vote
1answer
29 views

How to show that the product of two binary numbers can be determined in AC1?

I was working on a proof to determine that a product cannot be done in AC0, how can a proof that can be done in AC1?
0
votes
0answers
25 views

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 ...
0
votes
0answers
19 views

Constucting QAP in the pinoccho paper

In this paper Pinocchio: Nearly Practical Verifiable Computation, on page 3 there is a way to construct the QAP and example doing it. Question : they say We pick an arbitrary root rg ∈ F for ...
1
vote
2answers
56 views

Why sum of two binary numbers cannot be determined in $NC^0$ but in $AC^0$?

Why sum of two binary numbers cannot be determined in $NC^0$ but it can be determined in $AC^0$?
1
vote
1answer
31 views

Logical characterization of $NC^1$

Morioka in his 2005 dissertation [1] referenced "On Uniformity within $NC^1$" by Barrington, Immerman, and Straubing. Using the following statement: Every $\mathbf{NC^1}$-predicate is computed by ...
0
votes
1answer
125 views

Turing machine and boolean circuits

As an example of languages that are in P/poly is the UHALT Problem : UHALT = { 1^n: n's binary expansion encodes a pair such that M halts on input x} We can create a boolean circuit of just AND ...
2
votes
1answer
28 views

Programs to circuit conversion

Suppose we have an algorithm for a decision problem with $n$ bit inputs that runs in $DTIME[f(n)]$ is there ways to convert to circuits of $O(f(n))$ size with AND, OR and NOT gates? How about when ...
2
votes
1answer
24 views

Satisfiability Toward A Sequential Circuit

Define a sequential circuit model be a directed graph with each vertices being a boolean gate. The difference is that we allow cycles in the boolean circuit. Each cycle will determine a boolean ...
0
votes
1answer
2k views

Circuits for Modular Arithmetic

I've read this which describes how to do do integer arithmetic in circuits. The one thing that it does not describe is how to do these operations with a modulus. How can modular arithmetic be done in ...
2
votes
0answers
58 views

Implementing depth-3 circuit for XOR

In this set of notes, they claim that there is a size $O(2^{\sqrt n})$ depth-3 circuit (OR -AND -OR) that implements XOR. I tried for a little bit to figure out how to do this, but couldn't find ...
10
votes
1answer
884 views

Why isn't P and P/poly trivially the same?

The definition of P is a language that can be decided by a polynomial time algorithm. The definition of P/poly can be taken to mean a language that can be decided by a polynomial-size circuit (see ...
1
vote
2answers
449 views

Quantum NAND gate

Wondering how a quantum NAND gate would be implemented, and if it would be considered universal. I saw for quantum computing the Hadamard, phase, CNOT and π/8 gates are universal, but didn't see NAND ...
1
vote
2answers
97 views

If a NAND gate is universal, why you don't have NAND OISCs

If a NAND gate can be used to construct all other of the basic logic gates, then I'm wondering why you don't/can't have a purely NAND-based One Instruction Set Computer (OISC). All the OISC single ...

1
2 3 4 5