We study the complexity of telling whether a set of bit-vectors represents the set of all satisfying truth assignments of a Boolean expression of a certain type. We show that the problem is coNP-complete when the expression is required to be in conjunctive normal form with three literals per clause (3CNF). We also prove a dichotomy theorem analogous to the classical one by Schaefer, stating tha...

let x1;x2;...;xn have a jointly multivariate exchangeable normal distribution. in this work we investigate another proof of the independence of x and s2 using order statistics. we also assume that (xi ; yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

This paper considers statistical process control (SPC) of univariate processes, and tries to make two contributions to the univariate SPC problem. First, we propose a continuously variable sampling scheme, based on a quantitative measure of the likelihood of a process distributional shift at each observation time point, provided by the p-value of the conventional cumulative sum (CUSUM) charting...

We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we show that the problem cannot be solved in outputpolynomial time in the case of Horn expressions, ...

The frequency distribution of the extreme ultraviolet (EUV) emission line intensities in the quiet Sun has in the past often been modelled using two Gaussians. This gives adequate fits to observed distributions of average statistical significance. In this paper we test this and other distribution functions against observed distributions with exceptional statistical significance. The data were o...

The first step of the approach in [1] is a transformation which eliminates the negated variables in the monomials of the DNF representation and in the clauses of the CNF representation of the functions computed at the nodes of the given standard network resulting into the so-called reduced DNF and CNF representations of these functions. Theorem 5 characterizes the reduced DNF and CNF representa...

A new algorithm for testing satissability of propositional formulas in conjunctive normal form (CNF) is described. It applies reasoning in the form of certain resolution operations, and identiication of equivalent literals. Resolution produces growth in the size of the formula, but within a global quadratic bound; most previous methods avoid operations that produce any growth, and generally do ...

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from the viewpoint of logical (inter-)definability. All problems that we consider are decidable in polynomial time, but not expressible in fixedpoint ...

The behavior of the disjunctive operator, defined by Balas, Ceria and Cornuéjols, in the context of the “antiblocker duality diagram” associated with the stable set polytope,QSTAB(G), of a graph and its complement, was first studied byAguilera, Escalante and Nasini. The authors prove the commutativity of this diagram in any number of iterations of the disjunctive operator. One of the main conse...