The ANR project REACHARD proposes several PostDoc positions on reachability problems for counter systems, including vector addition systems and related models. Each position can take place either - at LaBRI, University of Bordeaux, France (http://www.labri.fr/), or - at LSV, ENS Cachan, France (http://www.lsv.ens-cachan.fr). See also http://www.lsv.ens-cachan.fr/Projects/anr-reachard/. ** HOW TO APPLY ** Candidates for PostDoc positions should send to anr-reachard@lsv.ens-cachan.fr a detailed curriculum vitae, a reference letter by the PhD supervisor and a link to the PhD thesis. ** THE PROJECT REACHARD IN A NUTSHELL ** Many standard verification problems can be rephrased as reachability problems, and there exist powerful methods for infinite-state systems; see e.g. the theory of well-structured transition systems. However, obtaining decision procedures is not the ultimate goal, which we rather see in crafting provably optimal algorithms---required for practical use. In the ANR project REACHARD, we focus on algorithmic issues for the verification of counter systems, more specifically to reachability problems for vector addition systems with states (VASS) and related models. More specifically, the main objective of the ANR project REACHARD is to propose a satisfactory solution to the reachability problem for vector addition systems, that will provide significant improvements both conceptually and computationally. Recent breakthroughs on the problem and on related problems for variant models should also allow us to propose solutions for several extensions, including for instance VASS with one zero-test or branching VASS. Furthermore, the goal is to take advantage of the new proof techniques involving semilinear separators designed by J. Leroux in order to design algorithms that are amenable for implementation. We propose to develop original techniques in order to solve the following difficult issues: - to understand the mathematical structure of reachability sets and relations in vector addition systems, - to develop new techniques for the computational analysis of reachability problems that are verification problems connected in some way to the reachability problem for VASS or their extensions, - to design algorithms, most probably on the lines of Karp & Miller algorithms, plus relating flattening methods and semilinearity, - to widen the scope of our analysis to models richer than VASS, including models with restricted zero-tests or with branching computations. ** FURTHER INQUIRY ** Any further inquiry should be sent to anr-reachard@lsv.ens-cachan.fr.