arXiv subjects

C. Sauerbier

Publications and source records attributed to C. Sauerbier.

2 recordsLinked to original sources

arXiv2002

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.

cs.CC↗

arXiv2002

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.

cs.CC↗