In computational complexity theory, a problem is NP-complete when:
a brute-force search algorithm can solve it, and the correctness of each solution can be verified quickly, and
the problem can be used to simulate any other problem with similar solvability.The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a deterministic algorithm to check a single solution, or for a nondeterministic Turing machine to perform the whole search. "Complete" refers to the property of being able to simulate everything in the same complexity class.
More precisely, each input to the problem should be associated with a set of solutions of polynomial length, whose validity can be tested quickly (in polynomial time), such that the output for any input is "yes" if the solution set is non-empty and "no" if it is empty. The complexity class of problems of this form is called NP, an abbreviation for "nondeterministic polynomial time". A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If any NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC.
Although a solution to an NP-complete problem can be verified "quickly", there is no known way to find a solution quickly. That is, the time required to solve the problem using any currently known algorithm increases rapidly as the size of the problem grows. As a consequence, determining whether it is possible to solve these problems quickly, called the P versus NP problem, is one of the fundamental unsolved problems in computer science today.
While a method for computing the solutions to NP-complete problems quickly remains undiscovered, computer scientists and programmers still frequently encounter NP-complete problems. NP-complete problems are often addressed by using heuristic methods and approximation algorithms.
Hi,
I have a basic knowledge of chemistry from high school days.
I remember once being told that a neutral hydrogen has one electron in its shell but it wants to complete its outer shell by having two electrons, and this makes hydrogen atom to create bonds with other atoms.
Likewise, a...
Hello,
I am looking for a comprehensive resource (paper, book or any kind of document) that contains the most relevant properties of most nuclear fuels. To be more specific, the information i am looking for are thermophysical properties, chemical compatibility with other materials and...
Proof:
Suppose for the sake of contradiction that ## aa_{i}\equiv aa_{j}\pmod {n} ## for some ## i,j\in\mathbb{Z} ## such that ## 1\leq i<j\leq n ##.
Then ## aa_{i}\equiv aa_{j}\pmod {n}\implies n\mid (aa_{i}-aa_{j})\implies n\mid [a(a_{i}-a_{j})] ##.
Note that ## n\mid b ## if ## n\mid (ab) ##...
https://www.feynmanlectures.caltech.edu/I_08.html Page 9-3. It says “In these terms, we see that Newton’s second law, in saying that the force is in same direction as the acceleration,is really three laws, in the sense that the components of force in the x, y,z directions is equal to the mass...
Hi, I'm reading Zavialov's book on QFT and there's a statement there I was interested in finding how to prove it. The statement is as follows:
If ##[A(x), j_{\{\lambda\}}(y)]=0## for ##(x-y)^2<0## then ##A(x)## is a local polynomial.
The relevant definitions are:
$$A = \sum_n \int...
The resistance y (in ohms) of 1000 feet
of solid copper wire at 68 degrees Fahrenheit is y = 10,370/(x^2) where x is the diameter of the wire in mils (0.001 inch).
Complete the table.
x...60 70 80 90 100
y...
Solution:
Let x = 60
y = 10,370/(60)^2
y = 10,370/3600
y = 2.8805555556
This...
The balanced reaction wil be :
##2C_6H_{6(l)}+15O_{2(g)}->12CO_{2(g)}+6H_2O_(l)##
in order to compute the the standard enthalpy of reaction :
##\Delta H°_{f} H_2O_(l)= -285,8 \frac {KJ}{mol}##;
##\Delta H°_{f} CO_{2(g)}= -393,5 \frac {KJ}{mol}##;
##\Delta H°_{f} C_6H_{6(l)}=49,04 \frac...
We are trying to find the complete solution to the matrix equation ##A\vec x = \vec b## where A is an m x n matrix and ##\vec b## can be anything except the zero vector. The entire solution is said to be:
##\vec x = \vec x_p + \vec x_n##
where ##\vec x_p## is the solution for a particular ##\vec...
I am solving the wave equation in z,t with separation of variables. As I understand it, Z(z) = acos(kz) + bsin(kz) is a complete solution for the z part. Likewise T(t) = ccos(ω t) + dsin(ωt) forms a complete solution for the t part. So what exactly is ZT = [acos(kz) + bsin(kz)][ccos(ωt) +...
Car A has a dead battery and car B gives a jump to it. I connect the positive of battery B to the positive of battery A and the negative of battery B to the body of car A.
1. Am I essentially creating a separate circuit by choosing a different ground than that of battery A? How is the current...
Hi I'm looking at David Tong notes on QHE http://www.damtp.cam.ac.uk/user/tong/qhe/two.pdf (page 56), I've attached the relevant screenshot below also.
I understand we are working in the interaction picture whereby states evolve via the Unitary Operataor EQ 2.10 in the notes(I think this is...
Asking for a friend. Hypothetically.
Say my friend, hypothetically, had an injunction that forbade him from entering his own apartment or having any "direct or indirect contact" with his partner.
Say there's a court date pending in a few weeks.
Let's assume it's an interim injunction.
And...
Gödel numbers are used to encode wffs of formal systems that are strong enough in order to deal with Arithmetic.
In my question, Gödel numbers are used to encode wffs as follows:
Syntactically (by formalism without semantics) there is set A (the set which is postulated to be infinite), such...
Is it complete in the sense that there's nothing further to investigate in terms of its mathematical formulation?
I mean, in the sense that we don't need to introduce new mathematical tools or review existing ones for the theory.
I raise this question because at a fundamental level I still do not understand how a Capacitor works and how a circuit completes thru capacitor. The live electric tester screwdriver uses stray body capacitance to lit a neon when one end comes in contact with live wire and another with a human...
$\quad\displaystyle
y^{\prime}=
\frac{e^{-x}-e^x}{3+4y},
\quad y(0)=1$
rewrite
$\frac{dy}{dx}=\frac{e^{-x}-e^x}{3+4y}$
separate
$3+4y \, dy = e^{-x}-e^x \, dx$
integrate
$2y^2+3y=-e^{-x}-e^x+c$
well if so far ok presume complete the square ?book answer
$(a)\quad...
Supposed you have a box of size 1 square foot and the insulation is 100% efficient.. meaning there is no transfer of any heat outside.. and you put a lamp with glass surface temperature of say 50 Celsius (155 Fahrenheit). Would the air temperature in the box keep increasing... can it reach 1000...
In texts treating Hilbert spaces, it's usually given as an example that "any finite dimensional unitary space is complete", but I've found no proof so far and failed prove it myself.
Homework Statement
What will be the complete equation if an oxide of a metal is MO?
3. The Attempt at a Solution
M + O2 = MO or M2 + O2 = MO
As far as I know, non-metals come as molecules such as O2, N2 etc But I am confused about metals. in the reactant, do metals react as a molecule or as...
Hi,
I have difficulty understanding the term screening.
Screening is reducing of the electric field, as far as I have understood until now.
1. Why does screening occurs? Is it due to collective interaction of plasmons?
2. If we have a slow electric field, will screening occur or will it not...
Homework Statement
The book I'm using provided a proof, however I'd like to try my hand on it and I came up with a different argument. I feel that something might be wrong.
Proposition: Let ##<X,d>## be a metric space, ##<Y,D>## a complete metric space. Then ##<C(X,Y), \sup D>## is a complete...
-Definition of complete space: if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in converges in M. (and from this definition we can define Hilbert Space)
-Definition of Hilbert space:
A Hilbert space is a vector space with an...
Hi, I have a Dell Inspiron core i5 PC. It beeps in sequences of 4 bbebeeps at a time shortly after power goes on , won't boot up nor complete Post . It may have to see with ram problem I have been told. Is this correct? Ultimately, what can I do?
Homework Statement
A conducting rod makes contact with rails to complete a circuit. If the rails are 50 cm apart ina uniform magnetic field B = 0.38 [T] directed out of the paper. The total resistance of the circuit is R = 9 [ohms] and is constant.
1) what is the magnitude and direction of EMF...
I can see intuitively that each complete graph ##K_n## is a subgraph of complete graph ##K_m## when ##m \ge n##. What would a rigorous proof consist of? This is just out of curiosity.
Hello Everybody! My name is TanX and I got a figure in my mind while studting concepts related to Vertical Circular Motion. I tried finding a solution to it (i.e) I tried finding the condition for movement of the particle in the figure that had come in my mind...
Homework Statement
So here is...
I am reading John B. Conway's book: Ä First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.2: Sequences and Completeness ...
I need some help/clarification with Conway's defintion of completeness of a metric space ...
Can someone tell me how we know that our physical universe is geodesically complete? In response to a question I had about why we assign any meaning to the other side of a black hole’s event horizon (or its interior), I got an answer prompting me to look into the concept of geodesic...
I was wondering if I read Kiselev's geometry books, would it count as a whole high school geometry curriculum? Currently, I am reading his first book, Planimetry, which is coming out as promising. I am planning to self-study geometry.
Homework Statement
Let ##({a, b, c}, *,+)## be a finite field. Complete the field table for the operations ##*## and ##+##
##\begin{array}{|c|c|c|c|}
\hline * & a & b & c \\
\hline a & ? & ? & ? \\
\hline b & ? & ? & ? \\
\hline c & ? & ? & b \\
\hline
\end{array}##
##\begin{array}{|c|c|c|c|}...
Homework Statement
I have been given the world's longest transistor problem as an assignment :wink: Here is the circuit:
I am asked to find:
a) V1, V2 and V3 using DC analysis
b) AC equivalent circuit
c) AC tension gain: Ava=Vx/Vsig
d) AC tension gain: Avb=Vo/Vx
e) Total AC tension gain...
Homework Statement
I am working on this question from the textbook:
Homework EquationsThe Attempt at a Solution
I would use Cramer's method and solve for i2, then get the characteristic equation and find the roots. from there I would attempt to find the natural response. I am not sure how I...
Homework Statement
Let ##E## be a metric subspace to ##M##. Show that ##E## is closed in ##M## if ##E## is complete. Show the converse if ##M## is complete.
Homework Equations
A set ##E## is closed if every limit point is part of ##E##.
We denote the set of all limit points ##E'##.
A point...
Prove that if a subsequence of a Cauchy sequence converges then so does the original Cauchy sequence.
I'm assuming that we're not allowed to use the fact that every Cauchy sequence converges. Here's my attempt:
Let $\displaystyle\{s_n\}$ be the original Cauchy sequence. Let $\displaystyle...
Problem
First you are asked to,
write this expression as a complete square $x^2+2ax+a^2$
& ii. Using that find the factors of $x^2+2ax+a^2-9$
Workings
i $(a + x)^2$
Where do I need help
ii. Using that find the factors of $x^2+2ax+a^2-9$
Many Thanks :)
so for resistance I've gotten r1=6 r2=5 r3=8 and r4=12. then for current i got r1-.30 r2=.24 r3=.06 r4=.06 amd volatge r1=1.8 r2=1.2 r3=.48 r4=.72. I am not sure about my voltage for r3 what i did was Vt-r1-r4 and when i add them up i get 3v so that should be right? and I am also not sure about...
Homework Statement
1. How did they complete the square for these equations in the picture below? What was their thought process?
2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out?
When you divide, how does it cancel out to give you a...
Problem Statement:
my aim is to digitalize a 10ns narrow pulse coming from a photo diode with current ranging from 10nA-70mA, as its impossible to cover this dynamic range of >60dB using a single TIA i have an option of separating it to two channels as below using two diodes ofcourse
Lowest...
Homework Statement
one gram of each of the following gases is introduced into a 10 L container at 25 degrees C
a) propane
b) ethane
c) methane
d) pentane
which gas will consume the greatest mass of oxygen upon complete combustion?
The solutions says that the right answer is D. I do not know...
Homework Statement
Show that finite dimensional normed vector spaces are complete.
Homework Equations
##E## is a finite dimensional vector space and ##N## a norm on ##E##
The Attempt at a Solution
If ##\{x_n\}_n## is a Cauchy sequence in ##(E,N)##, then it is bounded and each term of the...
Homework Statement
why the author gave that the complete turbulenece is indpendent on the Reynold number ?Homework EquationsThe Attempt at a Solution
For the turbulence to occur , the Reynold number must be higher than certain value , am i right . So , IMO , turbulenet is dependent on the...