scholarly journals Analysis and Synthesis of Weighted Marked Graph Petri Nets

2018 ◽  
pp. 19-39 ◽  
Author(s):  
Raymond Devillers ◽  
Thomas Hujsa
Keyword(s):  
Petri Nets ◽  
Analysis And Synthesis ◽  
Marked Graph

scholarly journals CONTINUOUS PETRI NETS: EXPRESSIVE POWER AND DECIDABILITY ISSUES

2010 ◽  
Vol 21 (02) ◽  
pp. 235-256 ◽  
Author(s):  
LAURA RECALDE ◽  
SERGE HADDAD ◽  
MANUEL SILVA
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Expressive Power ◽  
Timed Petri Nets ◽  
Analysis And Synthesis ◽  
Continuous Petri Nets ◽  
Linear Differential ◽  
The One

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of the corresponding discrete model. The expected gains are twofold: improvements in complexity and in decidability. In the case of autonomous nets we prove that liveness or deadlock-freeness remain decidable and can be checked more efficiently than in Petri nets. Then we introduce time in the model which now behaves as a dynamical system driven by differential equations and we study it w.r.t. expressiveness and decidability issues. On the one hand, we prove that this model is equivalent to timed differential Petri nets which are a slight extension of systems driven by linear differential equations (LDE). On the other hand, (contrary to the systems driven by LDEs) we show that continuous timed Petri nets are able to simulate Turing machines and thus that basic properties become undecidable.

scholarly journals Directed Reachability for Infinite-State Systems

2021 ◽  
pp. 3-23
Author(s):  
Michael Blondin ◽  
Christoph Haase ◽  
Philip Offtermatt
Keyword(s):  
Petri Nets ◽  
Program Analysis ◽  
Infinite Graphs ◽  
Reachability Problem ◽  
Graph Exploration ◽  
Concurrent Program ◽  
Domain Specific ◽  
Novel Approach ◽  
Distance Oracles ◽  
Analysis And Synthesis

AbstractNumerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary time, which raises questions about the practical applicability of Petri nets as target models. In this paper, we introduce a novel approach for efficiently semi-deciding the reachability problem for Petri nets in practice. Our key insight is that computationally lightweight over-approximations of Petri nets can be used as distance oracles in classical graph exploration algorithms such as $$\mathsf {A}^{*}$$ A ∗ and greedy best-first search. We provide and evaluate a prototype implementation of our approach that outperforms existing state-of-the-art tools, sometimes by orders of magnitude, and which is also competitive with domain-specific tools on benchmarks coming from program synthesis and concurrent program analysis.

scholarly journals Lower and upper bounds of shortest paths in reachability graphs

2004 ◽  
Vol 2004 (57) ◽  
pp. 3023-3036 ◽  
Author(s):  
P. K. Mishra
Keyword(s):  
Petri Nets ◽  
Shortest Path ◽  
Petri Net ◽  
Free Choice ◽  
Shortest Paths ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Marked Graphs ◽  
Marked Graph

We prove the following property for safe marked graphs, safe conflict-free Petri nets, and live and safe extended free-choice Petri nets. We prove the following three results. If the Petri net is a marked graph, then the length of the shortest path is at most(|T|−1)⋅|T|/2. If the Petri net is conflict free, then the length of the shortest path is at most(|T|+1)⋅|T|/2. If the petrinet is live and extended free choice, then the length of the shortest path is at most|T|⋅|T+1|⋅|T+2|/6, whereTis the set of transitions of the net.

Modelling, analysis and synthesis of asynchronous control circuits using Petri nets

Integration ◽  
1996 ◽  
Vol 21 (3) ◽  
pp. 143-170 ◽  
Author(s):  
A.V. Yakovlev ◽  
A.M. Koelmans ◽  
A. Semenov ◽  
D.J. Kinniment
Keyword(s):  
Petri Nets ◽  
Asynchronous Control ◽  
Modelling Analysis ◽  
Analysis And Synthesis ◽  
Control Circuits
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