arXiv subjects

Nicolas Amat

Publications and source records attributed to Nicolas Amat.

8 recordsLinked to original sources

arXiv2026

Deciding Serializability in Network Systems

We present the SER modeling language for automatically verifying serializability of concurrent programs, i.e., whether every concurrent execution of the program is equivalent to some serial execution. SER programs are suitably restricted to make this problem decidable, while still allowing for an unbounded number of concurrent threads of execution, each potentially running for an unbounded number of steps. Building on prior theoretical results, we give the first automated end-to-end decision procedure that either proves serializability by producing a checkable certificate, or refutes it by producing a counterexample trace. We also present a network-system abstraction to which SER programs compile. Our decision procedure then reduces serializability in this setting to a Petri net reachability query. Furthermore, in order to scale, we curtail the search space via multiple optimizations, including Petri net slicing, semilinear-set compression, and Presburger-formula manipulation. We extensively evaluate our framework and show that, despite the theoretical hardness of the problem, it can successfully handle various models of real-world programs, including stateful firewalls, BGP routers, and more.

cs.FL↗

arXiv2024

Project and Conquer: Fast Quantifier Elimination for Checking Petri Net Reachability

We propose a method for checking generalized reachability properties in Petri nets that takes advantage of structural reductions and that can be used, transparently, as a pre-processing step of existing model-checkers. Our approach is based on a new procedure that can project a property, about an initial Petri net, into an equivalent formula that only refers to the reduced version of this net. Our projection is defined as a variable elimination procedure for linear integer arithmetic tailored to the specific kind of constraints we handle. It has linear complexity, is guaranteed to return a sound property, and makes use of a simple condition to detect when the result is exact. Experimental results show that our approach works well in practice and that it can be useful even when there is only a limited amount of reductions.

cs.LO↗

arXiv2023

On the Complexity of Proving Polyhedral Reductions

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.

cs.LO↗

arXiv2023

SMPT: A Testbed for Reachability Methods in Generalized Petri Nets

SMPT (for Satisfiability Modulo Petri Net) is a model checker for reachability problems in Petri nets. It started as a portfolio of methods to experiment with symbolic model checking, and was designed to be easily extended. Some distinctive features are its ability to benefit from structural reductions and to generate verdict certificates. Our tool is quite mature and performed well compared to other state-of-the-art tools in the Model Checking Contest.

cs.LO↗

arXiv2023

Leveraging polyhedral reductions for solving Petri net reachability problems

We propose a new method that takes advantage of structural reductions to accelerate the verification of reachability properties on Petri nets. Our approach relies on a state space abstraction, called polyhedral abstraction, which involves a combination between structural reductions and sets of linear arithmetic constraints between the marking of places. We propose a new data-structure, called a Token Flow Graph (TFG), that captures the particular structure of constraints occurring in polyhedral abstractions. We leverage TFGs to efficiently solve two reachability problems: first to check the reachability of a given marking; then to compute the concurrency relation of a net, that is all pairs of places that can be marked together in some reachable marking. Our algorithms are implemented in a tool, called Kong, that we evaluate on a large collection of models used during the 2020 edition of the Model Checking Contest. Our experiments show that the approach works well, even when a moderate amount of reductions applies.

cs.LO↗

arXiv2022

A Polyhedral Abstraction for Petri nets and its Application to SMT-Based Model Checking

We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability property on a reduced version of this net. This method relies on a new state space abstraction based on systems of constraints, called polyhedral abstraction. We prove the correctness of this method using a new notion of equivalence between nets. We provide a complete framework to define and check the correctness of equivalence judgements; prove that this relation is a congruence; and give examples of basic equivalence relations that derive from structural reductions. Our approach has been implemented in a tool, named SMPT, that provides two main procedures: Bounded Model Checking (BMC) and Property Directed Reachability (PDR). Each procedure has been adapted in order to use reductions and to work with arbitrary Petri nets. We tested SMPT on a large collection of queries used in the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions.

cs.LO↗

arXiv2022

Property Directed Reachability for Generalized Petri Nets

We propose a semi-decision procedure for checking generalized reachability properties, on generalized Petri nets, that is based on the Property Directed Reachability (PDR) method. We actually define three different versions, that vary depending on the method used for abstracting possible witnesses, and that are able to handle problems of increasing difficulty. We have implemented our methods in a model-checker called SMPT and give empirical evidences that our approach can handle problems that are difficult or impossible to check with current state of the art tools.

cs.LO↗

arXiv2021

Accelerating the Computation of Dead and Concurrent Places using Reductions

We propose a new method for accelerating the computation of a concurrency relation, that is all pairs of places in a Petri net that can be marked together. Our approach relies on a state space abstraction, that involves a mix between structural reductions and linear algebra, and a new data-structure that is specifically designed for our task. Our algorithms are implemented in a tool, called Kong, that we test on a large collection of models used during the 2020 edition of the Model Checking Contest. Our experiments show that the approach works well, even when a moderate amount of reductions applies.

cs.LO↗