# The results of minimizing PDNF do not converge

• MHB
• urugvai
In summary, the conversation discussed using a function defined by a vector of values to compose a PDNF from a truth table. The PDNF was then minimized using both the Quine method and the Karnaugh map, resulting in a difference of one term. The error was identified as the second term from the Quine method being redundant and already covered by the first and third term. The Karnaugh diagram was then used to verify the minimal form.
urugvai
I have a function defined by a vector of values (2 3 4 6 7 12 15), from the truth table I compose the PDNF, I minimize it first by the Quine method, then by the Karnaugh map, the results differ by one term
I can’t understand what the error is
Karnaugh map

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urugvai said:
I have a function defined by a vector of values (2 3 4 6 7 12 15), from the truth table I compose the PDNF, I minimize it first by the Quine method, then by the Karnaugh map, the results differ by one term
I can’t understand what the error is
Karnaugh map

Hi urugvai,

The second term from your application of the Quine method can be omitted without loss of coverage.
We can map it in the Karnaugh diagram and see that it is already covered by the first and third term of the Quine form.

Klaas van Aarsen said:
Hi urugvai,

The second term from your application of the Quine method can be omitted without loss of coverage.
We can map it in the Karnaugh diagram and see that it is already covered by the first and third term of the Quine form.

Thank you for saying that this is part of the norm.
As I understand it, the Quine method with four variables gives an abbreviated PDNF, and the Karnaugh diagram gives minimal?

## What is PDNF and why is it important in scientific research?

PDNF stands for Partially Disordered Normal Form, which is a mathematical representation of a probability distribution. It is important in scientific research because it allows for the analysis and comparison of different data sets.

## How is PDNF minimized and what does it mean if the results do not converge?

PDNF is minimized through various mathematical algorithms, such as gradient descent, in order to find the optimal solution. If the results do not converge, it means that the algorithm was not able to find the optimal solution and may have reached a local minimum instead of a global minimum.

## What factors can affect the convergence of PDNF minimization?

There are several factors that can affect the convergence of PDNF minimization, such as the choice of algorithm, the starting point of the optimization, and the complexity of the data set. Additionally, numerical errors and noise in the data can also impact the convergence.

## How can the issue of non-convergence in PDNF minimization be addressed?

There are several ways to address the issue of non-convergence in PDNF minimization, such as using a different algorithm, adjusting the starting point of the optimization, or applying regularization techniques. It may also be helpful to check for any errors in the data or to increase the precision of the calculations.

## What are the implications of non-convergence in PDNF minimization for the validity of the results?

Non-convergence in PDNF minimization can affect the validity of the results, as it indicates that the optimal solution may not have been found. This can lead to incorrect conclusions and interpretations of the data. Therefore, it is important to address and resolve the issue of non-convergence in order to ensure the accuracy of the results.

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