Related papers: A "Proof" of $P\neq NP$
We obtain simple proofs of certain inequalites for bivariate means.
We illustrate the concept of mathematical proof.
This paper discusses why P and NP are likely to be different. It analyses the essence of the concepts and points out that P and NP might be diverse by sheer definition. It also speculates that P and NP may be unequal due to natural laws.
We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We claim to resolve the P=?NP problem via a formal argument for P=NP.
The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
This work evidences that a sentence cannot be denominated by P and written as P IS NOT TRUE. It demonstrates that in a system in which Q denominates the sentence Q IS NOT PROVABLE it is not provable that Q is true and not provable.
The open question, P=NP?, was presented by Cook (1971). In this paper, a proof that P is not equal to NP is presented. In addition, it is shown that P is not equal to the intersection of NP and co-NP. Finally, the exact inclusion…
In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].
This note is a commentary on, and critique of, Andre Luiz Barbosa's paper entitled "P != NP Proof." Despite its provocative title, what the paper is seeking to do is not to prove P \neq NP in the standard sense in which that notation is…
In this article, we discuss the question of whether P equals NP, we do not follow the line of research of many researchers, which is to try to find such a problem Q, and the problem Q belongs to the class of NP-complete, if the problem Q is…
In this note, we will give a short proof of an identity for cubic partitions.
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
Withdrawn. Silly notion and out of context.