A computation model in which the computation is described via circuits of various logic gates.
Questions tagged [circuits]
304 questions
78
votes
9 answers
Why is addition as fast as bit-wise operations in modern processors?
I know that bit-wise operations are so fast on modern processors, because they can operate on 32 or 64 bits on parallel, so bit-wise operations take only one clock cycle. However addition is a complex operation that consists of at least one and…
Teodor Dyakov
- 1,341
- 1
- 13
- 22
21
votes
1 answer
Why do all recent SAT solvers work on CNF instead of circuit SAT?
After the release of the AIGER library to handle and-inverter graphs sometime in 2006 (I think), some circuit SAT solvers were released in 2006-2008, and in a few SAT Races/Competitions there were AIG tracks. However since then it seems the focus…
Sami Liedes
- 393
- 1
- 4
21
votes
2 answers
Universality of the Toffoli gate
Regarding the quantum Toffoli gate:
is it classicaly universal, and if so, why?
is it quantumly universal, and why?
Ran G.
- 20,884
- 3
- 61
- 117
18
votes
1 answer
Why aren'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…
wdc
- 291
- 2
- 6
12
votes
1 answer
Which non-regular languages are in $AC^0$?
For example, I know that the non-regular language $a^nb^n$ is in $AC^0$. I would like to know more examples like this.
Alex Grilo
- 313
- 1
- 6
11
votes
1 answer
Depth-2 circuits with OR and MOD gates are not universal?
It is well-known that every boolean function $f:\{0,1\}^n\to \{0,1\}$ can be realized using a boolean circuit of depth 2 (over the variables, their negation and constant values) containing AND gates in the first level and one single OR gate in the…
Gadi A
- 223
- 1
- 6
10
votes
1 answer
Creating bigger controlled nots from single qubit, Toffoli, and CNOT gates, without workspace
Exercise 4.29 from Quantum Computation and Quantum Information by Nielsen and Chuang has me stumped.
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.
I've…
Craig Gidney
- 5,992
- 1
- 26
- 51
10
votes
1 answer
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 input from the other's output, and the other's…
CodyBugstein
- 3,017
- 11
- 31
- 46
9
votes
2 answers
What does "AC0 many-one reduction" mean?
What does $\mathsf{AC^0}$ many-one reduction mean?
I know about polynomial time reductions, but I'm not familiar with $\mathsf{AC^0}$ reductions.
sssa
- 424
- 3
- 6
9
votes
1 answer
How to show that hard-to-compute Boolean functions exist?
How can one show that there exist Boolean functions on $n$ inputs which require at least $2^n/\log{n}$ logic gates to compute?
This problem was originally stated in Exercise 3.16 of Nielsen & Chuang's Quantum Computation and Quantum Information.
SLesslyTall
- 223
- 1
- 7
9
votes
3 answers
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 $C^5(U)$ gate analogous to that
in Figure 4.10, but using no…
Alex Go
- 91
- 3
9
votes
1 answer
Combinational Logic Circuits and Theory of Computation
I'm trying to link Combinational Logic Circuits ( computers based on logical gates only ) with everything I have learned recently in Theory of Computation.
I was wondering whether combinational logic circuits can implement computations in the…
nerdy
- 381
- 1
- 7
8
votes
0 answers
Connections between circuit complexity and Unique Games Conjecture?
Circuit complexity has connections to many questions in complexity theory.
For a couple examples, Ryan Williams shared some in a recent talk and Section 3 of these notes gives simple relations to $\mathbf{P}$ vs. $\mathbf{NP}$ and $\mathbf{P}$ vs.…
Andrew
- 286
- 1
- 14
8
votes
1 answer
Assumption on weights in threshold circuits
A threshold gate implementing a linear threshold function on $n$ boolean inputs $x_1, x_2 \ldots, x_n$ is given by the equation:
$w_1 x_1 + w_2 x_2 + \ldots, w_n x_n \ge t$
where $w_1, \ldots, w_n, t \in \mathbb{R}$. The $w_i$'s are called the…
Nikhil
- 639
- 6
- 12
8
votes
3 answers
Isn't polynomial identity testing over arithmetic *expressions* trivial?
Polynomial identity testing is the standard example of a problem known to be in co-RP but not known to be in P. Over arithmetic circuits, it does indeed seem hard, since the degree of the polynomial can be made exponentially large by repeated…
Aaron Rotenberg
- 3,583
- 14
- 20