Jean-Xavier Rampon

Reachability Analysis on Distributed Executions

The paper presents basic algorithms for trace checking of distributed programs. In distributed systems, detecting global properties requires a careful analysis of the causal structure of the execution. Based on the on-the-fly observation of the partial order of message causality, we show how to build the lattice of all the reachable states of the distributed system under test. The regular structure of this graph makes it possible to build it with a quasi-linear complexity, which improves substantially the state-of-theart.

Towards the reconstruction of poset

The reconstruction conjecture for posets is the following: “Every finite posetP of more than three elements is uniquely determined — up to isomorphism — by its collection of (unlabelled) one-element-deleted subposets 〈P−{x}:x∈V(P)〉.”We show that disconnected posets, posets with a least (respectively, greatest) element, series decomposable posets, series-parallel posets and interval orders are reconstructible and that N-free orders are recognizable.We show that the following parameters are reconstructible: the number of minimal (respectively, maximal) elements, the level-structure, the ideal-size sequence of the maximal elements, the ideal-size (respectively, filter-size) sequence of any fixed level of the HASSE-diagram and the number of edges of the HASSE-diagram.This is considered to be a first step towards a proof of the reconstruction conjecture for posets.

Computing on-line the lattice of maximal antichains of posets

AbstractWe consider the on-line computation of the lattice of maximal antichains of a finite poset

Graph invariants as necessary conditions for global constraints

\tilde P

Width two posets are reconstructible

. This on-line computation satisfies what we call the “linear extension hypothesis”: the new incoming vertex is always maximal in the current subposet of

Interval dimension and MacNeille completion

\tilde P