Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201

Mapping RT-LOTOS specifications into Time Petri Nets

RT-LOTOS is a timed process algebra which enables compact and abstract specification of real-time systems. This paper proposes and illustrates a structural translation of RT-LOTOS terms into behaviorally equivalent (timed bisimilar) finite Time Petri nets. It is therefore possible to apply Time Petri nets verification techniques to the profit of RT-LOTOS. Our approach has been implemented in RTL2TPN, a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN. The latter is verified using TINA, a TPN analyzer developed by LAAS-CNRS. The toolkit made of RTL2TPN and TINA has been positively benchmarked against previously developed RT-LOTOS verification tool

Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page

Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

A Compositional Approach for Schedulability Analysis of Distributed Avionics Systems

This work presents a compositional approach for schedulability analysis of Distributed Integrated Modular Avionics (DIMA) systems that consist of spatially distributed ARINC-653 modules connected by a unified AFDX network. We model a DIMA system as a set of stopwatch automata in UPPAAL to verify its schedulability by model checking. However, direct model checking is infeasible due to the large state space. Therefore, we introduce the compositional analysis that checks each partition including its communication environment individually. Based on a notion of message interfaces, a number of message sender automata are built to model the environment for a partition. We define a timed selection simulation relation, which supports the construction of composite message interfaces. By using assume-guarantee reasoning, we ensure that each task meets the deadline and that communication constraints are also fulfilled globally. The approach is applied to the analysis of a concrete DIMA system.Comment: In Proceedings MeTRiD 2018, arXiv:1806.09330. arXiv admin note: text overlap with arXiv:1803.1105