Weak lumpability in the k-SAT problem

Weak lumpability in the k-SAT problem

On Weak Lumpability of Denumerable Markov Chains

We consider weak lumpability of denumerable discrete or continuous time Markov chains. Firstly, we are concerned with irreducible recurrent positive and R-positive Markov chains evolving in discrete time. We study the properties of the set of all initial distributions of the starting chain leading to an aggregated homogeneous Markov chain with respect to a partition of the state space. In parti...

The K-sat problem in a simple limit

The statistical mechanics of the random K-satisfiability (K-SAT) problem has been the object of many studies in the last years [1][2][3]. The K-SAT was the first problem to be shown to be Nondeterministic Polynomial (NP) complete [4] and the importance of such a model is that it provides a prototype for all the NP complete problems in complexity theory of computer science as well as in statisti...

Weak Adversaries for the k-Server Problem

We study the -server problem when the off-line algorithm has fewer than servers. We give two upper bounds of the cost WFA of the Work Function Algorithm. The first upper bound is OPT OPT , where OPT denotes the optimal cost to service by servers. The second upper bound is OPT OPT for . Both bounds imply that the Work Function Algorithm is -competitive. Perhaps more important is our technique wh...

Weak signed Roman k-domination in graphs

Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$.A weak signed Roman $k$-dominating function (WSRkDF) on a graph $G$ is a function$f:V(G)rightarrow{-1,1,2}$ satisfying the conditions that $sum_{xin N[v]}f(x)ge k$ for eachvertex $vin V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSRkDF $f$ is$w(f)=sum_{vin V(G)}f(v)$. The weak si...