Section: New Results

Model-based Verification

We have investigated extensions of regular model-checking to new classes of rewrite relations on terms. We have studied specification and proof of modular imperative programs, as well as of modal workflows.

Tree Automata with Constraints

Participants : Pierre-Cyrille Héam, Olga Kouchnarenko.

Tree automata with constraints are widely used to tackle data base algorithmic problems, particularly to analyse queries over XML documents. The model of Tree Automata with Global Constraints (TAGED) has been introduced for these purposes. The membership problem for TAGED is known to be NP-complete. The emptiness problem for TAGED is known to be decidable and the best known algorithm in the general case is non elementary. Following our NP-hardness result  [74] , we are still working in collaboration with Vincent Hugot on the complexity of the emptiness problem.

Random Generation of Finite Automata

Participant : Pierre-Cyrille Héam.

Developing new algorithms and heuristics raises crucial evaluation issues, as improved worst-case complexity upper-bounds do not always transcribe into clear practical gains. A classical way for software performance evaluation is to randomly generate inputs.

In collaboration with Jean-Luc Joly, we investigate the problem of randomly and uniformly generating deterministic pushdown automata [40] . Based on a recursive counting approach, we propose a polynomial time algorithm for this purpose. The influence of the accepting condition on the generated automata is also experimentally studied.

Partially ordered automata are finite automata where simple loops have length one. We have used a Markov chain based approach  [75] to randomly - and uniformly - generate deterministic partially ordered automata.

In [39] we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. We show how to use a Monte-Carlo approach to uniformly sample a NFA. The main result is to show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time.

Verification of Linear Temporal Patterns over Finite and Infinite Traces

Participants : Pierre-Cyrille Héam, Olga Kouchnarenko.

In the regular model-checking framework, reachability analysis can be guided by temporal logic properties, for instance to achieve the counter example guided abstraction refinement (CEGAR) objectives. A way to perform this analysis is to translate a temporal logic formula expressed on maximal rewriting words into a “rewrite proposition” – a propositional formula whose atoms are language comparisons, and then to generate semi-decision procedures based on (approximations of) the rewrite proposition. In collaboration with Vincent Hugot, we have investigated suitable semantics for LTL on maximal rewriting words and their influence on the feasibility of a translation. We have expended the work in  [76] by providing a general translation scheme giving exact results for a fragment of LTL corresponding mainly to safety formulæ, and approximations for a larger fragment.

Constraint Solving for Verifying Modal Workflow Specifications

Participants : Hadrien Bride, Olga Kouchnarenko.

Workflow Petri nets are well suited for modelling and analysing discrete event systems exhibiting behaviours such as concurrency, conflict, and causal dependency between events. They represent finite or infinite-state processes, and several important verification problems, like reachability or soundness, are known to be decidable. Modal specifications introduced in [77] allow loose or partial specifications in a framework based on process algebras.

Our work in [26] aims at verifying modal specifications of coloured workflows with data assigned to the tokens and modified by transitions. To this end, executions of coloured workflow nets are modelled using constraint systems, and constraint solving is used to verify modal specifications specifying necessary or admissible behaviours. An implementation supporting the proposed approach and promising experimental results on an issue tracking system constitute a practical contribution.