Composition of Functional Petri Nets

2013 ◽  
pp. 404-464 ◽  
Author(s):  
Dmitry A. Zaitsev
Keyword(s):  
Graph Theory ◽  
Petri Nets ◽  
Petri Net ◽  
Ad Hoc ◽  
Fundamental Equation ◽  
Weighted Graph ◽  
Sequential Composition ◽  
Speed Up ◽  
Networking Protocols ◽  
Linear Invariants

Functional Petri nets and subnets are introduced and studied for the purpose of speed-up of Petri nets analysis with algebraic methods. The authors show that any functional subnet may be generated by a composition of minimal functional subnets. They propose two ways to decompose a Petri net: via logical equations solution and with an ad-hoc algorithm, whose complexity is polynomial. Then properties of functional subnets are studied. The authors show that linear invariants of a Petri net may be computed from invariants of its functional subnets; similar results also hold for the fundamental equation of Petri nets. A technique for Petri nets analysis using composition of functional subnets is also introduced and studied. The authors show that composition-based calculation of invariants and solutions of fundamental equation provides a significant speed-up of computations. For an additional speed-up, they propose a sequential composition of functional subnets. Sequential composition is formalised in the terms of graph theory and was named the optimal collapse of a weighted graph. At last, the authors apply the introduced technique to the analysis of Petri net models of such well-known networking protocols as ECMA, TCP, BGP.

Extraction of elementary siphons in a class of generalized Petri nets using graph theory

2014 ◽  
Vol 31 (2) ◽  
pp. 331-352 ◽  
Author(s):  
YiFan Hou ◽  
ZhiWu Li ◽  
Mi Zhao ◽  
Ding Liu
Keyword(s):  
Graph Theory ◽  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Design Methodology ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Structural Complexity ◽  
Compact Set ◽  
Content Type

Purpose – Siphon-based deadlock control in a flexible manufacturing system (FMS) suffers from the problems of computational and structural complexity since the number of siphons grows exponentially with respect to the size of its Petri net model. In order to reduce structural complexity of a supervisor, a set of elementary siphons derived from all strict minimal siphons (SMS) is explicitly controlled. The purpose of this paper is through fully investigating the structure of a class of generalized Petri nets, WS3PR, to compute all SMS and a compact set of elementary siphons. Design/methodology/approach – Based on graph theory, the concepts of initial resource weighted digraphs and restricted subgraphs are proposed. Moreover, the concept of augmented siphons is proposed to extend the application of elementary siphons theory for WS3PR. Consequently, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS3PR. Findings – In order to demonstrate the proposed method, an FMS example is presented. All SMS and elementary siphons can be derived from initial resource weighted digraphs. Compared with those obtained by the method in Li and Zhou, the presented method is more effective to design a structural simple liveness-enforcing supervisor for WS3PR. Originality/value – This work presents an effective method of computing SMS and elementary siphons for WS3PR. Monitors are added for the elementary siphons only, and the controllability of every dependent siphon is ensured by properly supervising its elementary ones. A same set of elementary siphons can be admitted by different WS3PR with isomorphic structures.

scholarly journals A Survey of Elementary Object Systems

10.29007/dqbd ◽  
2018 ◽  
Author(s):  
Michael Köhler-Bußmeier
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Computational Effort ◽  
State Machines ◽  
Restricted Class ◽  
Turing Complete ◽  
Relationship Of ◽  
The Relationship ◽  
Linear Invariants

This contribution presents the formalism of ElementaryObjectSystems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. One central aim of this contribution is to compile all our previous works ded- icated to certain aspects of Eos together with recent yet unpublished results within one self-contained presentation. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. In this work we study the relationship of Eos to existing Petri net formalisms. It turns out that Eos are more powerful than classical p/t nets which is demonstrated by the fact that e.g. reachability and liveness become undecidable problems for Eos. Despite these undecidability results other properties can be extended to Eos using a monotonicity argument similar to that for p/t nets. Also linear algebraic techniques, especially the theory of linear invariants and semiflows, can be extended in an appropriate way. The invariant calculus for Eos even enjoys the property of compositionality, i.e. invariants of the whole system can be composed of invariants of the object nets, which reduces the computational effort. To obtain a finer level of insight we also studied several classes like pure, minimal, or semi-bounded Eos. Among these variants the subclass of generalised state machines is worth mentioning since it combines the decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.

Update to "Extraction of elementary siphons in a class of generalized Petri nets using graph theory" [Engineering Computations (2014) 31(2)331-352]

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
YiFan Hou ◽  
Mi Zhao
Keyword(s):  
Graph Theory ◽  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Design Methodology ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Type Design ◽  
Published Paper

Purpose The purpose of this paper is to correct some mistakes in recently published paper (Hou, Y.F., Li, Z.W., Zhao, M., and Liu, D. (2014) “Extraction of elementary siphons in a class of generalized Petri nets using graph theory”, Engineering Computations, Vol.31, No.2, pp.331-352). Design/methodology/approach In (Hou et al., 2014), based on the concepts of initial resource weighted digraphs and restricted subgraphs, a structurally simple liveness-enforcing supervisor for WS3PR was designed. To demonstrate the effectiveness and applicability of the proposed method, a flexible manufacturing system (FMS) example was presented. However, there are some mistakes in the considered example. The derived monitors were incorrect, which caused the result that the final controlled net system is not live. Findings In order to correct the errors in (Hou et al., 2014), a liveness-enforcing Petri nets supervisor with revised monitors for the considered example was redesigned by applying the method in (Hou et al., 2014). Originality/value This paper corrected the mistakes in (Hou et al., 2014). Consequently, a liveness-enforcing Petri net supervisor is redesigned.

scholarly journals Algorithm to Convert Signal Interpreted Petri Net Models to Programmable Logic Controller Ladder Logic Diagram Models

2018 ◽  
Vol 10 (3) ◽  
pp. 905
Author(s):  
Z. Aspar ◽  
Nasir Shaikh-Husin ◽  
M. Khalil-Hani
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Programmable Logic Controller ◽  
Conversion Process ◽  
Programmable Logic ◽  
Logic Diagram ◽  
Speed Up ◽  
High Level ◽  
Ladder Logic ◽  
Matrix Calculation

<span>Signal Interpreted Petri Nets (SIPN) modeling has been proposed as an alternative to Ladder Logic Diagram (LLD) modeling for programming complex programmable logic controllers (PLCs) due to its high level of abstraction and functionalities. This paper proposes an algorithm to efficiently convert existing SIPN models to their LLD models equivalences. In order to automate and speed up the conversion process, matrix calculation approach is used. A complex SIPN model was used to show that existing conversion technique must be expanded in order to cater for a more complex SIPN models.</span>

scholarly journals Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

2022 ◽  
Vol 183 (1-2) ◽  
pp. 1-31
Author(s):  
Raymond Devillers
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Composition Operators ◽  
Original System ◽  
Divide And Conquer ◽  
Transition Systems ◽  
Structure Transition ◽  
Labelled Transition Systems ◽  
Speed Up ◽  
Petri Net Synthesis

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.

Constrained Petri Nets. Part II: Generalizations and extensions

1983 ◽  
Vol 6 (3-4) ◽  
pp. 333-374
Author(s):  
H.J.M. Goeman ◽  
L.P.J. Groenewegen ◽  
H.C.M. Kleijn ◽  
G. Rozenberg
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Theoretical Framework ◽  
General Constraints ◽  
Context Free ◽  
Boolean Expressions

This paper continues the investigation froll1 [Goeman et al.] concerning the use of sets of places of a Petri net as additional (to input places) constraints for granting concession. Now interpretations of more general constraints are considered and expressed as Boolean expressions. This gives rise to various classes of constrained Petri nets. These are compared in the language theoretical framework introduced in [Goeman et al.]. An upperbound for the language defining power is found in the class of context-free programmed languages.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

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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