Does NP not equal P?

Stephen Cook posited SAT is NP-Complete in 1971. If SAT is NP-Complete then, as is generally accepted, any polynomial solution of it must also present a polynomial solution of all NP decision problems. It is here argued, however, that NP is not of necessity equivalent to P where it is shown that SAT is contained in P. This due to a paradox, of nature addressed by both Godel and Russell, in regards to the P-NP system in total.Comment: withdrawn. It was a rediculously absurd notio

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.Comment: 18 Pages; 7 Figures; Paper is a revision, correction, and expansion 2002 version; Example using prior algorithm version failure case in appendice

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.Comment: 6 pages, source cod

Does P = NP?

This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it remains theoretically possible for there to yet exist a non-deterministically polynomial (NP) problem for which the algorithm does not provide a polynomial (P) time solution. The paper leaves open as subject of continuing research the question of existence of instance of conjectured problem.Comment: withdrawn. It was a rediculously stupid notio

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.Comment: 7 pages, 0 figures; corrected misspelling of Chemakani's name, reformated, added larger images of algorithm listing

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.Comment: 5 pages, 0 figures, example source code in c#; v2 expanded to include computation without projection into real number field; v3 edits to more explicitly make the association with periodic functions of a specific form; v4 edits correct y periodic aside and to clarify loop identification, note respective difference expression and modular exponentiatio

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.Comment: 6 page

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).Comment: 2 pages, 0 figure

Cantor's Problem

In 1891 a paper by Georg Cantor was published in which he addressed the relative cardinality of two sets, the set of integers and the set of real numbers, in effort to demonstrate that the two sets were of unequal cardinality. This paper offers a contrary conclusion to Cantor's argument, together with implication of such to the theory of computation.Comment: 7 pages, 0 figures; correct typographical errors, wordin

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.Comment: 7 pages, 0 figure