+ Title:  Verification of Counter Systems

+ Abstract:

In order to represent the behavior of complex software systems, numerous models have been proposed 
among them the class of counter systems which are finite automata whose transitions are labelled by 
guards and updates on integer variables. It is well known that most of the verification problem 
are undecidable for very simple counter systems manipulating only two integer variables, however 
many restrictions have been proposed on these systems in order to regain decidability. Many 
abstractions techniques have also been developed in order to solve approximatively verification 
problems on this family of systems. The thematic of the post-doctoral stay could follow one (or 
both of) the following axis:

1. How to compose decidable classes of Petri nets. The restrictions proposed to gain decidability 
in counter systems restrict either the syntax of the model (like in Vector Addition System with 
States or in flat counter systems) or its semantic (like in reversal-bounded counter machines). We 
wish to investigate in which measure different restrictions on counter systems can be composed in 
order to obtain larger class of systems for which decidability of verification problems still holds.
Our objective are both to perform a complete analysis of the decidability status of some classical 
verification problem (reachability, safety,
liveness,etc) taking into account different compositions.

2. Development and implementation of efficient techniques to analyze counter systems. There already
exist tools to analyze counter systems likeTREX, FAST, FLATA, ASPIC, etc. But most of these tools 
only study reachability properties by computing the reachability set and when their approach 
computes an approximation of the reachability set, they either do under-approximations or 
over-approximations. The idea would be to build another tool that could compute under and over 
approximation of the reachability set but also could verify other properties than reachability. 
Furthermore this tool could implement different algorithms according to the property that one wish 
to verify, the aim being to be efficient.

+ Length of the postdoctoral stay: 12 months

+ Beginning date: Before the 1st of June 2012

+Supervisors:

   -Arnaud Sangnier
     Assistant Professor
     LIAFA - Université Paris Diderot - Paris VII
     http://www.liafa.jussieu.fr/~sangnier

   -Stéphane Demri
     Senior Researcher
     LSV - CNRS - ENS Cachan
     http://www.lsv.ens-cachan.fr/~demri

+Location:
    LIAFA (Laboratoire d'Informatique Algorithmique: Fondements et Applications)
    http://www.liafa.jussieu.fr
    In the team Modelisation and Verification leaded by Professor Ahmed Bouajjani

+Salary: 2100 euros per month

+Source of funding: DIGITEO (http://www.digiteo.fr/)

+Contact: sangnier@liafa.jussieu.fr, demri@lsv.ens-cachan.fr