Weighted dependency graphs

The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context. We also provide generic tools to prove that some weighted graph is a weighted dependency graph for a given family of random variables. To illustrate the power of the theory, we give applications to the following objects: uniform random pair partitions, the random graph model $G(n,M)$, uniform random permutations, the symmetric simple exclusion process and multilinear statistics on Markov chains. The application to random permutations gives a bivariate extension of a functional central limit theorem of Janson and Barbour. On Markov chains, we answer positively an open question of Bourdon and Vall\'ee on the asymptotic normality of subword counts in random texts generated by a Markovian source.Comment: 57 pages. Third version: minor modifications, after review proces

The Lefthanded Local Lemma characterizes chordal dependency graphs

Shearer gave a general theorem characterizing the family \LLL of dependency graphs labeled with probabilities $p_v$ which have the property that for any family of events with a dependency graph from \LLL (whose vertex-labels are upper bounds on the probabilities of the events), there is a positive probability that none of the events from the family occur. We show that, unlike the standard Lov\'asz Local Lemma---which is less powerful than Shearer's condition on every nonempty graph---a recently proved `Lefthanded' version of the Local Lemma is equivalent to Shearer's condition for all chordal graphs. This also leads to a simple and efficient algorithm to check whether a given labeled chordal graph is in \LLL.Comment: 12 pages, 1 figur

Positive Dependency Graphs Revisited

Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results

Detecting and Refactoring Operational Smells within the Domain Name System

The Domain Name System (DNS) is one of the most important components of the Internet infrastructure. DNS relies on a delegation-based architecture, where resolution of names to their IP addresses requires resolving the names of the servers responsible for those names. The recursive structures of the inter dependencies that exist between name servers associated with each zone are called dependency graphs. System administrators' operational decisions have far reaching effects on the DNSs qualities. They need to be soundly made to create a balance between the availability, security and resilience of the system. We utilize dependency graphs to identify, detect and catalogue operational bad smells. Our method deals with smells on a high-level of abstraction using a consistent taxonomy and reusable vocabulary, defined by a DNS Operational Model. The method will be used to build a diagnostic advisory tool that will detect configuration changes that might decrease the robustness or security posture of domain names before they become into production.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Building dependency graph for slicing erlang programs

Program slicing is a well-known technique that utilizes dependency graphs and static program analysis. Our goal is to perform impact analysis of Erlang programs based on the resulted program slices, that is we want to measure the impact of any change made on the source code: especially we want to select a subset of test cases which must be rerun after the modification. However impact analyzer tools exist for object oriented languages, the used dependency graphs heavily depend on the syntax and semantics of the used programming language, thus we introduce dependency graphs for a dynamically typed functional programming language, Erlang