Parameterised verification of randomised distributed systems using state-based models

Model checking is a powerful technique for the verification of distributed systems but is limited to verifying systems with a fixed number of processes. The verification of a system for an arbitrary number of processes is known as the parameterised model checking problem and is, in general, undecidable. Parameterised model checking has been studied in depth for non-probabilistic distributed systems. We extend some of this work in order to tackle the parameterised model checking problem for distributed protocols that exhibit probabilistic behaviour, a problem that has not been widely addressed to date. In particular, we consider the application of network invariants and explicit induction to the parameterised verification of state-based models of randomised distributed systems. We demonstrate the use of network invariants by constructing invariant models for non-probabilistic and probabilistic forms of a simple counter token ring protocol. We show that proving properties of the invariants equates to proving properties of the token ring protocol for any number of processes. The use of induction is considered for the verification of a class of randomised distributed systems. These systems, termed degenerative, have the property that a model of a system with given communication graph eventually behaves like a model of a system with a reduced graph, where reduction is by removal of a set of nodes. We distinguish between deterministically, probabilistically and semi-degenerative systems, according to the manner in which a system degenerates. For the former two classes we describe induction schemas for reasoning about models of these systems over arbitrary communication graphs. We show that certain properties hold for models of such systems with any graph if they hold for all models of a system with some base graph and demonstrate this via case studies: two randomised leader election protocols. We illustrate how induction can also be employed to prove properties of semi-degenerative systems by considering a simple gossip protocol

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

Proceedings of Monterey Workshop 2001 Engineering Automation for Sofware Intensive System Integration

The 2001 Monterey Workshop on Engineering Automation for Software Intensive System Integration was sponsored by the Office of Naval Research, Air Force Office of Scientific Research, Army Research Office and the Defense Advance Research Projects Agency. It is our pleasure to thank the workshop advisory and sponsors for their vision of a principled engineering solution for software and for their many-year tireless effort in supporting a series of workshops to bring everyone together.This workshop is the 8 in a series of International workshops. The workshop was held in Monterey Beach Hotel, Monterey, California during June 18-22, 2001. The general theme of the workshop has been to present and discuss research works that aims at increasing the practical impact of formal methods for software and systems engineering. The particular focus of this workshop was "Engineering Automation for Software Intensive System Integration". Previous workshops have been focused on issues including, "Real-time & Concurrent Systems", "Software Merging and Slicing", "Software Evolution", "Software Architecture", "Requirements Targeting Software" and "Modeling Software System Structures in a fastly moving scenario".Office of Naval ResearchAir Force Office of Scientific Research Army Research OfficeDefense Advanced Research Projects AgencyApproved for public release, distribution unlimite

Modelling bacterial regulatory networks with Petri nets

To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling bacterial regulatory networks with Petri nets

To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Separators in Continuous Petri Nets

Leroux has proved that unreachability in Petri nets can be witnessed by a Presburger separator, i.e. if a marking $\vec{m}_\text{src}$ cannot reach a marking $\vec{m}_\text{tgt}$, then there is a formula $\varphi$ of Presburger arithmetic such that: $\varphi(\vec{m}_\text{src})$ holds; $\varphi$ is forward invariant, i.e., $\varphi(\vec{m})$ and $\vec{m} \rightarrow \vec{m}'$ imply $\varphi(\vec{m}'$); and $\neg \varphi(\vec{m}_\text{tgt})$ holds. While these separators could be used as explanations and as formal certificates of unreachability, this has not yet been the case due to their (super-)Ackermannian worst-case size and the (super-)exponential complexity of checking that a formula is a separator. We show that, in continuous Petri nets, these two problems can be overcome. We introduce locally closed separators, and prove that: (a) unreachability can be witnessed by a locally closed separator computable in polynomial time; (b) checking whether a formula is a locally closed separator is in NC (so, simpler than unreachablity, which is P-complete). We further consider the more general problem of (existential) set-to-set reachability, where two sets of markings are given as convex polytopes. We show that, while our approach does not extend directly, we can still efficiently certify unreachability via an altered Petri.Comment: Submitted to LMCS as an extension of the FoSSaCS'22 conference versio