Nicolas Amat ; Silvano Dal Zilio ; Didier Le Botlan - On the Complexity of Proving Polyhedral Reductions

fi:12854 - Fundamenta Informaticae, November 10, 2024, Volume 192, Issues 3-4: Petri Nets 2023
On the Complexity of Proving Polyhedral ReductionsArticle

Authors: 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.


    Volume: Volume 192, Issues 3-4: Petri Nets 2023
    Published on: November 10, 2024
    Accepted on: August 19, 2024
    Submitted on: January 11, 2024
    Keywords: Computer Science - Logic in Computer Science

    Consultation statistics

    This page has been seen 8 times.
    This article's PDF has been downloaded 5 times.