arXiv subjects

Silvano Dal Zilio

Publications and source records attributed to Silvano Dal Zilio.

At least 19 recordsLinked to original sources

arXiv2024

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↗

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

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↗

arXiv2020

Checking marking reachability with the state equation in Petri net subclasses

Although decidable, the marking reachability problem for Petri nets is well-known to be intractable in general, and a non-elementary lower bound has been recently uncovered. In order to alleviate this difficulty, various structural and behavioral restrictions have been considered, allowing to relate reachability to properties that are easier to check. For a given initial marking, the set of potentially reachable markings is described by the state equation solutions and over-approximates the set of reachable markings. In this paper, we delineate several subclasses of weighted Petri nets in which the set of reachable markings equals the set of potentially reachable ones, a property we call the PR-R equality. When fulfilled, this property allows to use linear algebra to answer the reachability questions, avoiding a brute-force analysis of the state space. Notably, we provide conditions under which this equality holds in classes much more expressive than marked graphs, adding places with several ingoing and outgoing transitions, which allows to model real applications with shared buffers. To achieve it, we investigate the relationship between liveness, reversibility, boundedness and potential reachability in Petri nets. We also show that this equality does not hold in classes with close modeling capability when the conditions are relaxed.

cs.LO↗

arXiv2020

On the Petri Nets with a Single Shared Place and Beyond

Petri nets proved useful to describe various real-world systems, but many of their properties are very hard to check. To alleviate this difficulty, subclasses are often considered. The class of weighted marked graphs with relaxed place constraint (WMG=< for short), in which each place has at most one input and one output, and the larger class of choice-free (CF) nets, in which each place has at most one output, have been extensively studied to this end, with various applications. In this work, we develop new properties related to the fundamental and intractable problems of reachability, liveness and reversibility in weighted Petri nets. We focus mainly on the homogeneous Petri nets with a single shared place (H1S nets for short), which extend the expressiveness of CF nets by allowing one shared place (i.e. a place with at least two outputs and possibly several inputs) under the homogeneity constraint (i.e. all the output weights of the shared place are equal). Indeed, this simple generalization already yields new challenging problems and is expressive enough for modeling existing use-cases, justifying a dedicated study. One of our central results is the first characterization of liveness in a subclass of H1S nets more expressive than WMG=< that is expressed by the infeasibility of an integer linear program (ILP) of polynomial size. This trims down the complexity to co-NP, contrasting with the known EXPSPACE-hardness of liveness in the more general case of weighted Petri nets. In the same subclass, we obtain a new reachability property related to the live markings, which is a variant of the well-known Keller's theorem. Another central result is a new reversibility characterization for the live H1S class, simplifying its checking. Finally, we apply our results to use-cases, highlight their scalability and discuss their extensibility to more expressive classes.

cs.DS↗

arXiv2020

MCC: a Tool for Unfolding Colored Petri Nets in PNML Format

MCC is a tool designed for a very specific task: to transform the models of High-Level Petri nets, given in the PNML syntax, into equivalent Place/Transition nets. The name of the tool derives from the annual Model-Checking Contest, a competition of model-checking tools that provides a large and diverse collection of PNML models. This choice in naming serves to underline the main focus of the tool, which is to provide an open and efficient solution that lowers the access cost for developers wanting to engage in this competition. We describe the architecture and functionalities of our tool and show how it compares with other existing solutions. Despite the fact that the problem we target is abundantly covered in the literature, we show that it is still possible to innovate. To substantiate this assertion, we put a particular emphasis on two distinctive features of MCC that have proved useful when dealing with some of the most challenging colored models in the contest, namely the use of a restricted notion of higher-order invariant, and the support of a Petri net scripting language.

cs.LO↗

arXiv2020

Formal Approach for the Verification of Onboard Autonomous Functions in Observation Satellites

We propose a new approach for modelling the functional behaviour of an Earth observation satellite. We leverage this approach in order to develop a safety critical software, a "telecommand verifier", that is in charge of checking onboard whether a sequence of instructions is safe for execution. This new service is needed in order to add more autonomy to satellites. To do so, we propose a new Domain Specific Modelling Language and the toolchain required for integration into an embedded software. This framework is based on the composition of deterministic finite state machines with safety conditions , timeouts, and transitions that accept durations as a parameter. It is able to generate code in the synchronous programming language Lustre from a high-level specification of the satellite. This gives a formal way to derive an event-based algorithm simulating the execution of telecommand sequence and, thereupon, a provably correct onboard verifier.

cs.SE↗

arXiv2019

A State Class Construction for Computing the Intersection of Time Petri Nets Languages

We propose a new method for computing the language intersection of two Time Petri nets (TPN); that is the sequence of labels in timed traces common to the execution of two TPN. Our approach is based on a new product construction between nets and relies on the State Class construction, a widely used method for checking the behaviour of TPN. We prove that this new construct does not add additional expressive power, and yet that it can leads to very concise representation of the result. We have implemented our approach in a new tool, called Twina. We report on some experimental results obtained with this tool and show how to apply our approach on two interesting problems: rst, to dene an equivalent of the twin-plant diagnosability methods for TPN; then as a way to check timed properties without interfering with a system.

cs.LO↗

arXiv2018

Petri Net Reductions for Counting Markings

We propose a method to count the number of reachable markings of a Petri net without having to enumerate these rst. The method relies on a structural reduction system that reduces the number of places and transitions of the net in such a way that we can faithfully compute the number of reachable markings of the original net from the reduced net and the reduction history. The method has been implemented and computing experiments show that reductions are eective on a large benchmark of models.

cs.LO↗

arXiv2018

Time-accurate Middleware for the Virtualization of Communication Protocols

Communication between devices in avionics systems must be predictable and deterministic, and data must be delivered reliably. To help the system architects comply with these requirements, network protocol standards like ARINC 429 and AFDX were created. Even though the behaviour of each component in a network is well defined, it is still necessary to test extensively every applications before deployment. But physical test benches used in the aircraft development process are complex and expensive platforms. In order to limit the need for physical tests, we propose a time-accurate middleware for virtualizing communication protocols that can be used to replace physical tests with simulations. We specified three formal models of AFDX networks that take into account temporal constraints with different levels of precision. We also developed a prototype for a network virtualization middleware based on the AFDX protocol specification that provides an easy-to-setup environment for testing network configurations. Finally, we used formal models together with virtualization in order to define runtime monitors for checking whether the behavior of the middleware is time-accurate with respect to a real system.

cs.NI↗

arXiv2015

On the Complexity of Flanked Finite State Automata

We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic automata. In particular, we show that the universality problem for FFA is in linear time and that language inclusion can be checked in polynomial time. A useful application of FFA is to provide an efficient way to compute the quotient and inclusion of regular languages without the need to use the powerset construction. These operations are the building blocks of several verification algorithms.

cs.FL↗

arXiv2015

Latency Analysis of an Aerial Video Tracking System Using Fiacre and Tina

We describe our experience with modeling a video tracking system used to detect and follow moving targets from an airplane. We provide a formal model that takes into account the real-time properties of the system and use it to compute the worst and best-case end to end latency. We also compute a lower bound on the delay between the loss of two frames. Our approach is based on the model-checking tool Tina, that provides state-space generation and model-checking algorithms for an extension of Time Petri Nets with data and priorities. We propose several models divided in two main categories: first Time Petri Net models, which are used to study the behavior of the system in the most basic way; then models based on the Fiacre specification language, where we take benefit of richer data structures to directly model the buffering of video information and the use of an unbounded number of frame identifiers.

cs.PF↗

arXiv2015

Automating the Verification of Realtime Observers using Probes and the Modal mu-calculus

A classical method for model-checking timed properties-such as those expressed using timed extensions of temporal logic-is to rely on the use of observers. In this context, a major problem is to prove the correctness of observers. Essentially, this boils down to proving that: (1) every trace that contradicts a property can be detected by the observer; but also that (2) the observer is innocuous, meaning that it cannot interfere with the system under observation. In this paper, we describe a method for automatically testing the correctness of realtime observers. This method is obtained by automating an approach often referred to as visual verification, in which the correctness of a system is performed by inspecting a graphical representation of its state space. Our approach has been implemented on the tool Tina, a model-checking toolbox for Time Petri Net.

cs.LO↗

arXiv2014

Time Petri Nets with Dynamic Firing Dates: Semantics and Applications

We define an extension of time Petri nets such that the time at which a transition can fire, also called its firing date, may be dynamically updated. Our extension provides two mechanisms for updating the timing constraints of a net. First, we propose to change the static time interval of a transition each time it is newly enabled; in this case the new time interval is given as a function of the current marking. Next, we allow to update the firing date of a transition when it is persistent, that is when a concurrent transition fires. We show how to carry the widely used state class abstraction to this new kind of time Petri nets and define a class of nets for which the abstraction is exact. We show the usefulness of our approach with two applications: first for scheduling preemptive task, as a poor man's substitute for stopwatch, then to model hybrid systems with non trivial continuous behavior.

cs.LO↗