Boolean Polynomial Value Comparison

Title: Boolean Polynomial Value Comparison

Abstract: This research article explores the computational complexity of comparing the values of Boolean polynomials. It focuses on the case where the polynomials have a fixed degree. The authors present a method to determine the value comparison problem for polynomials of degree 3, which is shown to be PP-complete. This is achieved using techniques from quantum computation and the results of previous research.

Main Research Question: How can we determine the value comparison problem for Boolean polynomials of a fixed degree, particularly for those of degree 3?

Methodology: The authors use techniques from quantum computation and the class PP, which is a class of promise problems in computational complexity. They also rely on the concept of quadratically signed weight enumerators, which are used to determine the value of the polynomials.

Results: The authors show that the value comparison problem for polynomials of degree 3 is PP-complete. They also provide a method to determine the value of the polynomials using techniques from quantum computation.

Implications: This research has implications for the field of computational complexity, as it provides a method to determine the value comparison problem for Boolean polynomials of degree 3. This could potentially lead to advancements in the field of quantum computation and the class PP.

In conclusion, this research article presents a method to determine the value comparison problem for Boolean polynomials of degree 3 using techniques from quantum computation and the class PP. This could have significant implications for the field of computational complexity and potentially lead to advancements in the field of quantum computation.

Link to Article: https://arxiv.org/abs/0111052v1 Authors: arXiv ID: 0111052v1