Related papers: The Linear Correlation of $P$ and $NP$
Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
We sharpen the result that polarity and monopolarity are NP-complete problems by showing that they remain NP-complete if the input graph is restricted to be a $3$-colourable comparability graph. We start by presenting a construction…
Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the behavior of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed being…
We review some semantic and syntactic complexity classes that were introduced to better understand the relationship between complexity classes P and NP. We also define several new complexity classes, some of which are associated with…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
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…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL)…
In this short note, the author shows that the gap problem of some 3-XOR is NP-hard and can be solved by running Charikar\&Wirth's SDP algorithm for two rounds. To conclude, the author proves that $P=NP$.
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
The notion of nondeterminism has disappeared from the current definition of NP, which has led to ambiguities in understanding NP, and caused fundamental difficulties in studying the relation P versus NP. In this paper, we question the…
In this note we consider a tent-like family with a cusp at the singular point and show that the linear response holds for certain perturbations of this family. This contrasts the tent-like maps with finite derivatives at the singularity.…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
Identifying spurious correlations learned by a trained model is at the core of refining a trained model and building a trustworthy model. We present a simple method to identify spurious correlations that have been learned by a model trained…