Related papers: A Brief Note on a Recent Claim About NP-Hard Probl…
This paper investigates why and when the edge-based districting problem becomes computationally intractable. The overall problem is represented as an exact mathematical programming formulation consisting of an objective function and several…
This paper is withdrawn due to unclearness of some notions on which the material is based.
In this note we prove a weighted version of the Khintchine inequalities.
The notes contain a streamlined account on stability of univariate polynomials and related problems
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
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…
Controversies arise when specialists disagree on some particular issue. This normally occurs in any scientific brunch. We analyze some controversies, which have a good cause in Special Relativity. The paper does not question Special…
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…
A decade ago, a beautiful paper by Wagner developed a ``toolkit'' that in certain cases allows one to prove problems hard for parallel access to NP. However, the problems his toolkit applies to most directly are not overly natural. During…
Recently a large number of graph separator problems have been proven to be \textsc{NP-Hard}. Amazingly we have found that $\alpha$-Subgraph-Balanced-Vertex-Separator, an important variant, has been overlooked. In this work ``Yet Another…
The strong CP problem is that SU(3) gauge field instantons naturally induce a CP violating term in the QCD Lagrangian which is constrained by experiment to be very small for no obvious reason. We show that this problem disappears if one…
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
Motivated by the theory of proof complexity generators we consider the following $\Sigma^p_2$ search problem $\mbox{DD}_P$ determined by a propositional proof system $P$: given a $P$-proof $\pi$ of a disjunction $\bigvee_i {\alpha}_i$, no…
This letter contains a brief discussion on the leading-order canonical correction to the Bekenstein-Hawking (black hole) entropy. In particular, we address some recent criticism directed at an earlier commentary.
The salient features of CP-violating interactions in the standard electroweak theory and in a few of its popular extensions are discussed. Moreover a brief overview is given on the status and prospects of searches for CP non-conservation…
One possible escape from the Gibbard-Satterthwaite theorem is computational complexity. For example, it is NP-hard to compute if the STV rule can be manipulated. However, there is increasing concern that such results may not re ect the…
This is a summary of a talk given at the CP01 meeting on possible Lorentz anomalies in canonical quantum gravity. It briefly reviews some initial explorations on the subject that have taken place recently, and should be only be seen as a…
The material of the article is devoted to the most complicated and interesting problem -- a problem of P = NP?. This research was presented to mathematical community in Hyderabad during International Congress of Mathematicians. But there it…
The status of the QCD-based heavy quark expansion is briefly reviewed. A good agreement between properly applied theory and new precision data is observed. Critical remarks on certain recent claims from HQET are presented. Recent…