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# Is CAP theorem wrong?

## Is CAP theorem wrong? Tag : sql , By : Nick Pegg Date : November 28 2020, 11:01 PM

will help you C and A mean that the system provides these guarantees in the face of partitions. So abandoning these properties during a partition makes the property not hold.
The CA trade-off is only relevant during a partition (because without partitions we can give up P and obtain CA). Then, you need to decide.

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## PCP Theorem

Tag : algorithm , By : user113409
Date : March 29 2020, 07:55 AM
it helps some times Targeted towards the layman computer scientist:
The PCP theorem says that you can make proofs that are so easy to check that you only need to look at a constant number of (randomly selected) bits to (usually) tell a bad proof from a good one.

## Z3 Theorem Prover: Pythagorean Theorem (Non-Linear Artithmetic)

Tag : development , By : Yolanda N. Ceron
Date : March 29 2020, 07:55 AM
Any of those help Z3 has a new solver (nlsat) for nonlinear arithmetic. It is more efficient than other solvers (see this article). The new solver is complete for quantifier-free problems. However, the new solver does not support proof generation. If we disable proof generation, then Z3 will use nlsat and easily solve the problem. Based on your question, it seems you are really looking for solutions, thus disabling proof generation does not seem to be an issue.
Moreover, Z3 does not produce approximate solutions (like hand calculators). It uses a precise representation for real algebraic numbers. We can also ask Z3 to display the result in decimal notation (option :pp-decimal). Here is your example online.
``````(root-obj (+ (^ x 2) (- 2)) 1)
``````
``````(- 1.4142135623?)
``````
``````(set-option :pp-decimal true)
(declare-const a Real)
(declare-const b Real)
(declare-const c Real)
(assert (= a 1.0))
(assert (= b 1.0))
(assert (> c 0))
(assert (= (+ (* a a) (* b b)) (* c c)))
(check-sat)
(get-model)
``````
``````(set-option :pp-decimal true)
(declare-const a Real)
(declare-const b Real)
(declare-const c Real)
(assert (> c 0))
(assert (> a c))
(assert (= (+ (* a a) (* b b)) (* c c)))
(check-sat)
``````

## Whats wrong in this Binomial Theorem calculator?

Tag : java , By : shehan
Date : March 29 2020, 07:55 AM
this one helps. 0! = 1 by convention. Not 0. This might cause problem to you.
Moreover, for loop should go from 0 to n, not from 1 to n as there are n+1 terms.
``````for(int i = 0; i <= n; i++) {

int product = 0;

coefficient = factorial(n) / (factorial(i) * factorial(n - i));
product = (int) (coefficient*Math.pow(a, n - i)*Math.pow(b, i));

}
``````

## Master Theorem: comparing two versions of the theorem

Tag : algorithm , By : BinaryBoy
Date : March 29 2020, 07:55 AM
I wish did fix the issue. Second version because it does not have a constrain on f(n).
As you see, in the first version your f(n) can be only in a specific form, the second case f(n) is any function, so you can solve recurrences like T(n) = 2 T(n/2) + nlog(n) + n^2 * sin(n)

## How to check convolution theorem in MATLAB? My result is wrong

Tag : matlab , By : mylonov
Date : March 29 2020, 07:55 AM
will help you I am trying to check convolution theorem in MATLAB. I have a signal called sine_big_T. Then I have a filter called W. W and sine_big_T have the same length. , Using conv with 'same' is correct. You are seeing two things:
``````test = ifftshift( conv( fftshift(I_fft), fftshift(W_fft), 'same' ) );
``````
``````plot(1:129,fft(sine_big_T.*W)*length(W));
``````