Symbolic analysis of bounded Petri nets

This paper presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.Peer ReviewedPostprint (published version

Getting the Priorities Right: Saturation for Prioritised Petri Nets

Prioritised Petri net is a powerful modelling language that often constitutes the core of even more expressive modelling languages such as GSPNs (Generalized Stochastic Petri nets). The saturation state space traversal algorithm has proved to be efficient for non-prioritised concurrent models. Previous works showed that priorities may be encoded into the transition relation, but doing so defeats the main idea of saturation by spoiling the locality of transitions. This paper presents an extension of saturation to natively handle priorities by considering the priority-related enabledness of transitions separately, adopting the idea of constrained saturation. To encode the highest priority of enabled transitions in every state we introduce edge-valued interval decision diagrams. We show that in case of Petri nets, this data structure can be constructed offline. According to preliminary measurements, the proposed solution scales better than previously known matrix decision diagram-based approaches, paving the way towards efficient stochastic analysis of GSPNs and the model checking of prioritised models

Optimal trajectory generation for Petri nets

Recently, the increasing complexity of IT systems requires the early verification and validation of the system design in order to avoid the costly redesign. Furthermore, the efficiency of system operation can be improved by solving system optimization problems (like resource allocation and scheduling problems). Such combined optimization and validation, verification problems can be typically expressed as reachability problems with quantitative or qualitative measurements. The current paper proposes a solution to compute the optimal trajectories for Petri net-based reachability problems with cost parameters. This is an improved variant of the basic integrated verification and optimization method introduced in [11] combining the efficiency of Process Network Synthesis optimization algorithms with the modeling power of Petri nets

Verifying Computation Tree Logic of Knowledge via Knowledge-Oriented Petri Nets and Ordered Binary Decision Diagrams

Computation Tree Logic of Knowledge (CTLK) can specify many requirements of privacy and security of multi-agent systems (MAS). In our previous papers, we defined Knowledge-oriented Petri Net (KPN) to model MAS, proposed similar reachability graph to verify CTLK, gave their model checking algorithms and developed a related tool. In this paper, we use the technique of Ordered Binary Decision Diagrams (OBDD) to encode similar reachability graph in order to alleviate the state explosion problem, and verify more epistemic operators of CTLK. We design the corresponding symbolic model checking algorithms and improve our tool. We compare our model and method with MCMAS that is the state-of-the-art CTLK model checker, and experiments illustrate the advantages of our model and method. We also explain the reasons why our model and method can obtain better performances

A modular, qualitative modelling of regulatory networks using Petri nets

International audienceAdvances in high-throughput technologies have enabled the de-lineation of large networks of interactions that control cellular processes. To understand behavioural properties of these complex networks, mathematical and computational tools are required. The multi-valued logical formalism, initially defined by R. Thomas and co-workers, proved well adapted to account for the qualitative knowledge available on regulatory interactions, and also to perform analyses of their dynamical properties. In this context, we present two representations of logical models in terms of Petri nets. In a first step, we briefly show how logical models of regulatory networks can be transposed into standard (place/transition) Petri nets, and discuss the capabilities of such representation. In the second part, we focus on logical regulatory modules and their composition, demonstrating that a high-level Petri net representation greatly facilitates the modelling of interconnected modules. Doing so, we introduce an explicit means to integrate signals from various interconnected modules, taking into account their spatial distribution. This provides a flexible modelling framework to handle regulatory networks that operate at both intra-and intercellular levels. As an illustration, we describe a simplified model of the segment-polarity module involved in the segmentation of the Drosophila embryo

Measurements, Models, Systems and Design

531 s.

2-wire time independent asynchronous communications

Communications both to and between low end microprocessors represents a real cost in a number of industrial and consumer products. This thesis starts by examining the properties of protocols that help to minimize these expenses and comes to the conclusion that the derived set of properties define a new category of communications protocol : Time Independent Asynchronous ( TIA) communications. To show the utility of the TIA category we develop a novel TIA protocol that uses only 2-wires and general IO pins on each host. The protocol is analyzed using the Petri net based STG ( Signal Transition Graph) which is widely use to model asynchronous logic. It is shown that STGs do not accurately model the behavior of software driven systems and so a modified form called STG-FT ( STG For Threads) is developed to better model software systems. A simulator is created to take an STG-FT model and perform a full reachability tree analysis to prove correctness and analyze livelock and deadlock properties. The simulator can also examine the full reachability tree for every possible system state ( the cross product of all sub-system states), and analyze deadlock and livelock issues related to unexpected inputs and unusual situations. Reachability pruning algorithms are developed which decrease the search tree by a factor of approximately 250 million. The 2-wire protocol is implemented between a PC and an Atmel Tiny26 microprocessor, there is also a variant that works between microprocessors. Testing verifies the simulation results including an avoidable livelock condition with data throughput peaking at a useful 50 kilobits/second in both directions. The first practical application of 2-wire TIA is part of a novel debugger for the Atmel Tiny26 microprocessor. The approach can be extended to any microprocessor with general IO pins. TIA communications, developed in this thesis, is a serious contender whenever low end microprocessors must communicate with other processors. Consumer and industrial products may be able to achieve cost saving by using this new protocol

Symbolic analysis of bounded Petri nets

This paper presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.Peer Reviewe