Sylvain Peyronnet

Approximate Probabilistic Model Checking

Symbolic model checking methods have been extended recently to the verification of probabilistic systems. However, the representation of the transition matrix may be expensive for very large systems and may induce a prohibitive cost for the model checking algorithm. In this paper, we propose an approximation method to verify quantitative properties on discrete Markov chains. We give a randomized algorithm to approximate the probability that a property expressed by some positive LTL formula is satisfied with high confidence by a probabilistic system. Our randomized algorithm requires only a succinct representation of the system and is based on an execution sampling method. We also present an implementation and a few classical examples to demonstrate the effectiveness of our approach.

Approximate Verification of Probabilistic Systems

General methods have been proposed [2,4] for the model checking of probabilistic systems, where the verification of a probabilistic statement is reduced to the solution of a linear system over the system’s state space. To overcome the state space explosion problem, some probabilistic model checkers, such as PRISM [3], use MTBDDs. We propose a different solution, in which we use a Monte-Carlo algorithm [6] to approximate Prob[ψ], the probability that a temporal formula is true. We show how to obtain a randomized estimator of Prob[ψ] for a fragment of LTL formulas. This fragment is sufficient to express interesting properties such as reachability and liveness.

Probabilistic abstraction for model checking: An approach based on property testing

The goal of model checking is to verify the correctness of a given program, on all its inputs. The main obstacle, in many cases, is the intractably large size of the programs transition system. Property testing is a randomized method to verify whether some fixed property holds on individual inputs, by looking at a small random part of that input. We join the strengths of both approaches by introducing a new notion of probabilistic abstraction, and by extending the framework of model checking to include the use of these abstractions. Our abstractions map transition systems associated with large graphs to small transition systems associated with small random subgraphs. This reduces the original transition system to a family of small, even constant-size, transition systems. We prove that with high probability, “sufficiently” incorrect programs will be rejected (ϵ-robustness). We also prove that under a certain condition (exactness), correct programs will never be rejected (soundness). Our work applies to programs for graph properties such as bipartiteness, k-colorability, or any ∃∀ first order graph properties. Our main contribution is to show how to apply the ideas of property testing to syntactic programs for such properties. We give a concrete example of an abstraction for a program for bipartiteness. Finally, we show that the relaxation of the test alone does not yield transition systems small enough to use the standard model checking method. More specifically, we prove, using methods from communication complexity, that the OBDD size remains exponential for approximate bipartiteness.

Approximate planning and verification for large markov decision processes

We study the planning and verification problems for very large or infinite probabilistic systems, like Markov Decision Processes (MDPs), from a complexity point of view. More precisely, we deal with the problem of designing an efficient approximation method to compute a near-optimal policy for the planning problem of MDPs and the satisfaction probabilities of interesting properties like reachability or safety, over the Markov chain obtained by restricting the MDP to the near-optimal policy. The complexity of the approximation method is independent of the size of the state space and uses only a probabilistic generator of the MDP.

A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures

In this paper we consider the l1-compressive sensing problem. We propose an algorithm specifically designed to take advantage of shared memory, vectorized, parallel and many-core microprocessors such as the Cell processor, new generation Graphics Processing Units (GPUs) and standard vectorized multi-core processors (e.g. quad-core CPUs). Besides its implementation is easy. We also give evidence of the efficiency of our approach and compare the algorithm on the three platforms, thus exhibiting pros and cons for each of them.

Grid Services for MPI

Institutional grids consist of the aggregation of clusters belonging to different administrative domains to build a single parallel machine. To run an MPI application over an institutional grid, one has to address many challenges. One of the first problems to solve is the connectivity of the different nodes not belonging to the same administrative domain. Techniques based on communication relays, dynamic port opening, among others, have been proposed. In this work, we propose a set of Grid or Web Services to abstract this connectivity service, and we evaluate the performances of this new level of communication for establishing the connectivity of an MPI application over an experimental grid.

QCG-OMPI: MPI applications on grids

Computational grids present promising computational and storage capacities. They can be made by punctual aggregation of smaller resources (i.e., clusters) to obtain a large-scale supercomputer. Running general applications is challenging for several reasons. The first one is inter-process communication: processes running on different clusters must be able to communicate with one another in spite of security equipments such as firewalls and NATs. Another problem raised by grids for communication-intensive parallel application is caused by the heterogeneity of the available networks that interconnect processes with one another. In this paper we present how QCG-OMPI can execute efficient parallel applications on computational grids. We first present an MPI programming, communication and execution middleware called QCG-OMPI. We then present how applications can make use of the capabilities of QCG-OMPI by presenting two typical, parallel applications: a geophysics application combining collective operations and a master-worker scheme, and a linear algebra application.

Evaluating Complex MAC Protocols for Sensor Networks with APMC

In this paper we present an analysis of a MAC (Medium Access Control) protocol for wireless sensor networks. The purpose of this protocol is to manage wireless media access by constructing a Time Division Media Access (TDMA) schedule. APMC (Approximate Probabilistic Model Checker) is a tool that uses approximation-based verification techniques in order to analyse the behavior of complex probabilistic systems. Using APMC, we approximately computed the probabilities of several properties of the MAC protocol being studied, thus giving some insights about it performance.

Lightweight Clustering Methods for Webspam Demotion

To make sure they can quickly respond to a specific query, the main search engines have several mechanisms. One of them consists in ranking web pages according to their importance, regardless of the semantic of the web page. Indeed, relevance to a query is not enough to provide a high quality result, and popularity is used to arbitrate between equally relevant web pages. Webspam widely denotes any web page created with the only purpose of fooling ranking algorithms such as the PageRank. The aim of Webspam is to promote a target page by increasing its rank. It is an important issue for Web search engines to spot and discard Webspam to provide their users with a non biased list of results. Webspam techniques have to evolve constantly to remain efficient but most of the time they consist in creating a specific linking architecture around the target page to increase its rank. In this paper we propose to study the effects of graph clustering on the well known ranking algorithm of Google (the PageRank) in presence of Webspam. Since the web graph is way to big to apply classic clustering techniques, we present three lightweight techniques to realise a clustering of the web graph. Experimental results show the interest of the approach, which is moreover confirmed by statistical evidence.

Brief announcement: Lower bounds on communication for sparse Cholesky factorization of a model problem

Previous work has shown that a lower bound on the number of words moved between large, slow memory and small, fast memory of size M by any conventional (non-Strassen like) direct linear algebra algorithm (matrix multiply, the LU, Cholesky, QR factorizations,...) is Ω(# flops / √ (M)). This holds for dense or sparse matrices. There are analogous lower bounds for the number of messages, and for parallel algorithms instead of sequential algorithms. Our goal here is to find algorithms that attain these lower bounds on interesting classes of sparse matrices. We focus on matrices for which there is a lower bound on the number of flops of their Cholesky factorization. Our Cholesky lower bounds on communication hold for any possible ordering of the rows and columns of the matrix, and so are globally optimal in this sense. For matrices arising from discretization on two dimensional and three dimensional regular grids, we discuss sequential and parallel algorithms that are optimal in terms of communication. The algorithms turn out to require combining previously known sparse and dense Cholesky algorithms in simple ways