Does NP not equal P?

After examining the {\bf P} versus {\bf NP} problem against the Kleene-Rosser paradox of the $\lambda$-calculus [94], it was found that it represents a counter-example to NP-completeness. We prove that it contradicts the proof of Cook's theorem. A logical formalization of the liar's paradox leads to the same result. This formalization of the liar's paradox into a computable form is a 2-valued instance of a fuzzy logic programming paradox discovered in the system of [90]. Thre...

The analysis discussed in this paper is based on a well-known NP-complete problem which is called satisfiability problem or SAT. From SAT a new NP-complete problem is derived, which is described by a Boolean function called core function. In this paper it is proved that the cost of the minimal implementation of core function increases with n exponentially. Since the synthesis of core function is an NP-complete problem, this result is equivalent to proving that P and NP do not...

This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).

In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set E(A) containing propositional calculus formulae, each of which requires the algorithm A to take non-polynomial time to find the truth-values of its propositional letters satisfying it. Moreover, E(A)'s size is an exponential function of n,...

In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of computation and information was clearly stated. Then the complexities of three specific problems: logical compare, sorting and SAT, were analyzed and measured. The result showed SAT was a problem with exponential complexity which naturally leads...

This is the final article in a series of four articles. Richard Karp has proven that a deterministic polynomial time solution to K-SAT will result in a deterministic polynomial time solution to all NP-Complete problems. However, it is demonstrated that a deterministic polynomial time solution to any NP-Complete problem does not necessarily produce a deterministic polynomial time solution to all NP-Complete problems.

This submission has been withdrawn at the request of the author.

Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.

There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit goes toward infinity. Due to the halting problem, whether a word is accepted can only be determined at runtime. It can be shown by Rice's theorem, if a finite set of words are to be checked, they all have to be tested by brute force.

This paper has been withdrawn Abstract: This paper has been withdrawn by the author due to the publication.