Related papers: Proofs of NP = coNP = PSPACE: Current upgrade
We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…
We show that it is coNP-complete to decide whether a given proof structure of pomset logic is a correct proof net, using the graph-theoretic used in a previous paper of ours (arXiv:1901.10247).
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
In this note, we find a new way to prove several properties of 2-alternating capacities.
In this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1).
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
This paper shows that P = NP = PSPACE. It also tackles Graph Isomorphism.
We give a new simpler proof of a theorem of Jayne and Rogers.
This paper provides a further refinement to the previous response by introducing new structures and algorithms for counting VMPs of common \emph{Edge Requirement} (ER) and hence for counting the perfect matchings.
We survey recent developments on the Restriction conjecture.
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
It was shown in Alur et al. [1] that the problem of verifying finite concurrent systems through Linearizability is in EXPSPACE. However, there was still a complexity gap between the easy to obtain PSPACE lower bound and the EXPSPACE upper…
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
This text contains the material discussed by the author in the Bourbaki seminar of June 2018, on the recent developments in the theory of the Monge-Amp\`ere equation.
We explain the Elekes Szabo paper in more details and improve the constant in one dimensional case in \mathbb{R} and \mathbb{C}.
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
I review and discuss a selected sample of recent results in pNRQCD.