919 research outputs found
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problem.Comment: withdrawn.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
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
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
- …