A New Approach to Abstract Reachability State Space of Time Petri Nets

2013 ◽  
Author(s):  
Kais Klai ◽  
Naim Aber ◽  
Laure Petrucci
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Time Petri Nets ◽  
New Approach

On Improving Model Checking of Time Petri Nets and Its Application to the Formal Verification

2021 ◽  
Vol 12 (4) ◽  
pp. 68-84
Author(s):  
Naima Jbeli ◽  
Zohra Sbai
Keyword(s):  
Model Checking ◽  
Petri Nets ◽  
Formal Verification ◽  
State Space ◽  
Order Reduction ◽  
The State ◽  
Timing Constraints ◽  
Time Petri Nets ◽  
Explicit Timing ◽  
Class Graph

Time Petri nets (TPN) are successfully used in the specification and analysis of distributed systems that involve explicit timing constraints. Especially, model checking TPN is a hopeful method for the formal verification of such complex systems. For this, it is promising to lean to the construction of an optimized version of the state space. The well-known methods of state space abstraction are SCG (state class graph) and ZBG (graph based on zones). For ZBG, a symbolic state represents the real evaluations of the clocks of the TPN; it is thus possible to directly check quantitative time properties. However, this method suffers from the state space explosion. To attenuate this problem, the authors propose in this paper to combine the ZBG approach with the partial order reduction technique based on stubborn set, leading thus to the proposal of a new state space abstraction called reduced zone-based graph (RZBG). The authors show via case studies the efficiency of the RZBG which is implemented and integrated within the 〖TPN-TCTL〗_h^∆ model checking in the model checker Romeo.

Vulnerability, Uncertainty and Probability (VUP) Quantification of a Network of Interacting Satellites Using Stochastic Petri Nets (SPN)

2013 ◽  
Author(s):  
Atefeh Einafshar ◽  
Farrokh Sassani
Keyword(s):  
Markov Chain ◽  
Quantitative Analysis ◽  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Stochastic Petri Nets ◽  
Discrete State ◽  
New Approach ◽  
Stochastic Petri Net ◽  
Discrete State Space

A new approach to Vulnerability, Uncertainty and Probability (VUP) quantification procedure using Stochastic Petri Nets within a network of interacting satellites is presented. A Stochastic Petri Net based model is developed to quantify VUP in a network of interacting satellites. Three indicators are proposed to determine the VUP definitions in interacting network of satellites. The proposed VUP quantification scheme addresses a methodology which employs a Stochastic Petri Net for quantitative analysis of the behavior of the network. With the random variables associated with the Petri Net transitions, the dynamic behavior of the cooperating satellites in a SPN model can be mapped onto a time-continuous Markov chain with discrete state space. After generating a Markov Stochastic Petri Net model, the probability of a given condition in the network at a specified time can be computed and quantified as well as the vulnerability and uncertainty of the system using the identified indicators.

scholarly journals State space computation and analysis of Time Petri Nets

2006 ◽  
Vol 6 (3) ◽  
pp. 301-320 ◽  
Author(s):  
GUILLAUME GARDEY ◽  
OLIVIER H. ROUX ◽  
OLIVIER F. ROUX
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Timed Automata ◽  
Reactive Systems ◽  
Time Petri Nets ◽  
Classical State ◽  
Time Petri Net ◽  
Reduction Methods ◽  
Timed Automaton

The theory of Petri Nets provides a general framework to specify the behaviors of real-time reactive systems and Time Petri Nets were introduced to take also temporal specifications into account. We present in this paper a forward zone-based algorithm to compute the state space of a bounded Time Petri Net: the method is different and more efficient than the classical State Class Graph. We prove the algorithm to be exact with respect to the reachability problem. Furthermore, we propose a translation of the computed state space into a Timed Automaton, proved to be timed bisimilar to the original Time Petri Net. As the method produce a single Timed Automaton, syntactical clocks reduction methods (DAWS and YOVINE for instance) may be applied to produce an automaton with fewer clocks. Then, our method allows to model-check T-TPN by the use of efficient Timed Automata tools.

scholarly journals Unfolding through processes to compute the complete prefix of Petri nets

2017 ◽  
Vol Volume 27 - 2017 - Special... ◽  
Author(s):  
Médésu Sogbohossou ◽  
Antoine Vianou
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Partial Order ◽  
Petri Net ◽  
The State ◽  
Classical Approach ◽  
New Approach ◽  
State Space Explosion ◽  
Single Process ◽  
Partial Order Semantics

The partial-order technique of the unfolding implicitly represents state-space of a Petri net (PN), by in particular preserving the concurrency relations between the events. That makes it possible to contain state-space explosion problem in case of strong concurrency. A complete prefix of unfolding is used to cover all the state-space of a bounded PN: its computation according to the classical approach is based on the concept of adequate order, taking directly into account only safe PN. In this paper, a new approach independent of the concept of adequate order and faithful to the partial-order semantics, consists in creating the events of the unfolding in the context of a single process at the same time. The results of the tests are conclusive for safe and nonsafe PN. Some solutions are presented to improve compactness of the prefix obtained. La technique d'ordre partiel du dépliage représente implicitement l'espace d'état d'un réseau de Petri (RdP), en conservant notamment les relations de concurrence entre les événements. Cela permet de contenir le phénomène de l'explosion combinatoire en cas de forte concurrence. Un préfixe complet de dépliage sert à couvrir tout l'espace d'état d'un RdP borné: son calcul suivant l'approche classique se base sur le concept d'ordre adéquat, ne prenant directement en compte que les RdP saufs. Dans cet article, une nouvelle approche indépendante du concept d'ordre adéquat et fidèle à la sémantique d'ordre partiel, consiste à créer les événements du dépliage dans le contexte d'un unique processus à la fois. Les résultats des tests sont concluants pour les RdP saufs et non saufs. Des solutions sont présentées pour améliorer la compacité du préfixe obtenu.

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