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On the Complexity of Proving Polyhedral Reductions

On the Complexity of Proving Polyhedral Reductions

Verification Petri Reductions
Table of Contents

Nicolas Amat, Silvano Dal Zilio, Didier Le Botlan
Fundamenta Informaticae 192(3-4), sep 2024.

journal

 PDF  DOI〈10.3233/FI-242197〉  HAL-04712076

Abstract
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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.

References
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  • This is the extended version of a paper presented at the 44th International Conference on Application and Theory of Petri Nets and Concurrency, jun 2023.  Link

Citation
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@Article{DalzilioS:fi2023polyprove,
   author  = {Amat, Nicolas and {Dal Zilio}, Silvano and {Le Botlan}, Didier},
   title   = {{On the Complexity of Proving Polyhedral Reductions}},
   journal = {Fundamenta Informaticae},
   number  = {3-4},
   volume  = {192},
   doi = {10.3233/FI-242197},
   month   = sep, 
   year    = 2024
}