Didier Le Botlan

Nicolas Amat, Silvano Dal Zilio, Didier Le Botlan

We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.

Nouha Abid, Silvano Dal Zilio, Didier Le Botlan

An issue limiting the adoption of model checking technologies by the industry is the ability, for non-experts, to express their requirements using the property languages supported by verification tools. This has motivated the definition of dedicated assertion languages for expressing temporal properties at a higher level. However, only a limited number of these formalisms support the definition of timing constraints. In this paper, we propose a set of specification patterns that can be used to express real-time requirements commonly found in the design of reactive systems. We also provide an integrated model checking tool chain for the verification of timed requirements on TTS, an extension of Timed Petri Nets with data variables and priorities.