arXiv subjects

Charles Sauerbier

Publications and source records attributed to Charles Sauerbier.

10 recordsLinked to original sources

arXiv2021

Answering Hilbert's 1st Problem

Hilbert's first problem is of importance in relation to work being done in computational systems. It is the question of equipollence of natural and real numbers. By construction equipollence is established for real numbers in open interval (0, 1) and natural numbers and, from such to all real numbers. Construction stands in contradiction of the generally accepted diagonal argument of Cantor. Mathematics being irrefutable, in absence rejection of all theory of mathematics and logic, the problem exists in acceptance; that itself arises of more fundamental a problem in science generally. The problem within Hilbert's problem is of Schopenhauer's, et al, "will and representation" born.

cs.LO↗

arXiv2019

Three complete deterministic polynomial algorithms for 3SAT

Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The algorithms are each deterministic and of polynomial complexity. The algorithms determining existence are complete as each produces a certificate of non-satisfiability, for instances where no satisfying assignment exists, and of satisfiability for such assignment does exist.

cs.CC↗

arXiv2017

Factoring Odd Integers without Multiplication and Division

A method of determining two factors of an odd integer without need of multiplication or division operation in iterative portion of computation is presented. It is feasible for an implementing algorithm to use only integer addition and subtraction throughout. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non academic and theoretical practitioners.

cs.DM↗

arXiv2016

Prime Factoring and The Complexity Of

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non academic and theoretical practitioners.

cs.DM↗

arXiv2011

Computing an Integer Prime Factoring in O(n^2.5)

Paper is withdrawn. On review the paper contributes little of significance. The runtime analysis of the algorithms presented, while correct in terms of number of operations, does not represent the complexity of the algorithms in terms of "bits input". A naive mistake in reasoning.

cs.DS↗

arXiv2010

A Polynomial Diophantine Generator Function for Integer Residuals

Two Diophantine equation generator function for integer residuals produced by integer division over closed intervals are presented. One each for the closed intervals [1,Floor(n^0.5)] and [Ceiling(n^0.5),n], respectively.

cs.DM↗

arXiv2010

Computing a Frobenius Coin Problem decision problem in O(n^2)

Expanding on recent results of another an algorithm is presented that provides solution to the Frobenius Coin Problem in worst case O(n^2) in the magnitude of the largest denomination.

cs.DS↗

arXiv2009

Computing a Discrete Logarithm in O(n^3)

This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros of two periodic functions in the real numbers. The problem is treated as an analog to a form of analog rotor-code computed cipher.

cs.DS↗

arXiv2009

Discovery of Elliptic Curve Cryptographic Private Key in O(n)

An algorithm is presented that in context of public key use of Elliptic Curve Cryptography allows discovery of the private key in worst case O(n).

cs.CR↗

arXiv2002

Mathematical basis for polySAT implication operator

The mathematical basis motivating the "implication operator" of the polySAT algorithm and its function is examined. Such is not undertaken with onerous rigor of symbolic mathematics; a more intuitive visual appeal being employed to present some of the mathematical premises underlying function of the implication operator.

cs.CC↗