Data Structures and Algorithms

2610 Submissions

[2] viXra:2610.0097 [pdf] submitted on 2026-10-27 10:32:13

Proof P ̸= N P Using a New Method of Circuit Analysis on 3SAT

Authors: Michael Marquard
Comments: 22 Pages.

The following paper shows that some 3SAT (3-Satisfiability) problems containing only one unique solution cannot be solved in polynomial time. To do so a new technique I call "boolean isolation" is used to create an equation defining eachvariable in the 3SAT problem thus creating a system of equations. From there circuit analysis and other methods are used to show that any possible equation to find the values in the 3SAT problem would have to be equivalent to the equationcreated by boolean isolation allowing minimum bounds to be established. This paper will also discuss the possible impacts of these findings on other fields including cryptography.Keywords: P Versus NP, Computational Complexity, SAT, Polynomial Time, Exponential Time, Cryptography
Category: Data Structures and Algorithms

[1] viXra:2610.0069 [pdf] replaced on 2026-10-19 20:58:03

Scaled Bergman Numeral System (SBNS) and a New Filter as a New Basis for Computing

Authors: Andrey V. Voron
Comments: 14 Pages.

The paper proposes and formalizes the Scaled Bergman Numeral System (SBNS) — a new numerical basis for computing that utilizes an irrational base (the golden ratio) and a fixed weight scale factor of k = 0.2. This approach aims to overcome the physical limitations of the von Neumann architecture. The introduction of the 0.2 scale factor successfully eliminates the primary drawbacks of the traditional Bergman system: the "wandering carry effect" and the "infinite information tail". The paper demonstrates the invariance of the sum of truncated weights of active digits for a pair of valid code states (the working code "A" and the check code "B") isolated by the hardware filter. It is also shown that within the SBNS framework, fractional noise and rounding errors mutually cancel each other out.
Category: Data Structures and Algorithms