Exploiting symmetries of high-level Petri games in distributed synthesis

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nick Würdemann
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Distributed System ◽  
Petri Net ◽  
Space Reduction ◽  
Ongoing Work ◽  
Player Game ◽  
High Level ◽  
State Space Reduction

Abstract Distributed Synthesis is the problem of automatically generating correct controllers for individual agents in a distributed system. Petri games model this problem by a game between two teams of players on a Petri net structure. Under some restrictions, Petri games can be solved by a reduction to a two player game. The concept of symmetries in Petri nets is closely related to high-level representations of Petri games. Applying symmetries to the states in the two-player game results in a significant state space reduction. We give an overview about (high-level) Petri games and the application of symmetries in this setting. We present ongoing work aiming to concisely describe solutions of Petri games by a high-level representation.

scholarly journals State Space Reduction on Wireless Sensor Network Verification Using Component-Based Petri Net Approach

2016 ◽  
Author(s):  
Khanh Le ◽  
Thang Bui ◽  
Tho Quan
Keyword(s):  
State Space ◽  
Petri Net ◽  
Ad Hoc ◽  
Logic Model ◽  
Wireless Sensor ◽  
Space Reduction ◽  
Recent Advancement ◽  
Model Size ◽  
Network Verification ◽  
State Space Reduction

With the recent advancement of Internet of Things, the applications of Wireless Sensor Networks (WSNs) are increasingly attracting attention from of both industry and research communities. However, since the deployment cost of a WSN is relatively large, one would want to make a logic model of a WSN and have the model verified beforehand to ensure that the WSN would work correctly and effectively once practically employed. Petri Net (PN) is very suitable to model a WSN, since PN strongly supports modeling concurrent and ad-hoc systems. However, verification of a PN-modeled system suffers from having to explore the huge state space of the system. In order to overcome it, in this paper we suggest a novel component-based approach to model and verify a PN-modeled WSN system. First of all, the original WSN system is divided into components, which can be further abstracted to reduce the model size. Moreover, when verifying the corresponding PN model produced from the abstracted WSN, we introduce a strategy of component-based firing, which can reduce the state space significantly. Compared to typical approach of PN-based verification, our method enjoys an impressive improvement of performance and resource consuming, as depicted in our experimental results.

Verification by State Spaces with Equivalence Classes

1997 ◽  
Vol 26 (515) ◽  
Author(s):  
Jens Bæk Jørgensen ◽  
Lars Michael Kristensen
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
General Notion ◽  
State Spaces ◽  
Space Reduction ◽  
Full State ◽  
Reduction Methods ◽  
High Level

<p>This paper demonstrates the pontential of verification based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by defining equivalence relations on the set of states and the set of actions of a system under consideration. A state space can be constructed, in which the nodes correspond to equivalence classes of states and the arcs correspond to equivalence classes of actions. Such a state space is often much smaller than the ordinary full state space, but does allow derivation of many verification results.</p><p>Other researches have taken advantage of the symmetries of systems, which induce a certain kind of equivalence. The contribution fo this paper is to show that a more general notion of equivalence is useful. As example, a communication protocol modelled in the formalism of Coloured Petri Nets is verified. Aided by a computer tool supporting state spaces with equivalence classes, significant reduction of state spaces are exhibited.</p><p><strong>Topics</strong>. State space reduction methods, equivalence vs. symmetry, High-level Petri Nets, communication protocols.</p>

The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

2008 ◽  
Vol 44-46 ◽  
pp. 537-544
Author(s):  
Shi Yi Bao ◽  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Ning Jiang ◽  
Zeng Liang Gao
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Quantitative Assessment ◽  
Stochastic Petri Nets ◽  
Industrial Park ◽  
Domino Effect ◽  
State Space Explosion ◽  
Stochastic Petri Net ◽  
Chemical Industrial Park

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

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