Related papers: Critique of Barbosa's "P != NP Proof"

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…

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…

This paper demonstrates that P \not= NP. The way was to generalize the traditional definitions of the classes P and NP, to construct an artificial problem (a generalization to SAT: The XG-SAT, much more difficult than the former) and then…

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 this paper we discusses the relationship between the known classes P and NP. We show that the difficulties in solving problem "P versus NP" have methodological in nature. An algorithm for solving any problem is sensitive to even small…

The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…

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 will give a simple proof of the ambiguous class number formula.

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…

This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L. The point about this paper is the depend relation of the problem that need other problem's result to compute it. I show the structure of depend…

We show that the class BPP is in NP and coNP. This paper has been withdrawn by the author because B and B' are probabilistic and nonequalities 10 cannot be checked in polynomial time.

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.

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

In this critique, we examine the technical report by Daniel Uribe entitled "P vs. NP." The paper claims to show an exponential lower bound on the runtime of algorithms that decide CLIQUE. We show that the paper's proofs fail to generalize…

We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…

We critique Javier Arroyo-Figueroa's paper titled ``The existence of the Tau one-way functions class as a proof that $\mathrm{P} \neq \mathrm{NP}$,'' which claims to prove $\mathrm{P} \neq \mathrm{NP}$ by showing the existence of a class of…

Over the course of the last 50 years, many questions in the field of computability were left surprisingly unanswered. One example is the question of $P$ vs $NP\cap co-NP$. It could be phrased in loose terms as "If a person has the ability…

Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on…