Analysis of Petri Nets by Partitioning: Splitting Transitions (original) (raw)

Analysis of Petri net models using transitive matrix

SMC 2000 Conference Proceedings. 2000 IEEE International Conference on Systems, Man and Cybernetics. 'Cybernetics Evolving to Systems, Humans, Organizations, and their Complex Interactions' (Cat. No.00CH37166), 2000

In this paper, we are focused on the analysis of Petri nets model using the subnet. Specially, we are proposes a divideconquer method of Petri nets under the condition of oneboundedness for all the Petri nets. The usefulness of the approach is shown by applying the proposed techniques to a illustration model.

Some subclasses of Petri nets and the analysis of their structural properties: a new approach

IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 1999

The purpose of this paper is to consider some special types of Petri nets, introduced by Lien, and to propose a complete and unified approach for the study of their structural properties by using techniques of linear algebra of matrices. We distinguish four subclasses: forward-conflict-free, backward-conflict-free, forward-concurrent-free, and backwardconcurrent-free Petri nets. A modification of the classical incidence matrix results in a square matrix, named a modified incidence matrix, with nonpositive (nonnegative) off-diagonal elements when backward-(forward-) conflict-free or concurrentfree Petri nets are considered. The modified incidence matrix eigenvalues are computed and theorems on matrices of this type are used to prove several sufficient and/or necessary conditions for structural boundedness, liveness, repetitiveness, conservativeness, and consistency of these four subclasses of Petri nets.

A Method of Analysis of Operational Petri Nets

Advanced Computer Systems, 2002

Petri nets, a popular discrete automaton model, are convenient for describing some parallel operations. A net used for such purpose cannot be a closed system but has to contain input and output places. Such a model is defined here as an operational Petri net. Analysis of Petri nets is a difficult task. In the paper the method of analysis is suggested, based on the original approach to decomposition and oriented for the considered class of nets. Applying the approach to the cyclic nets is also considered. Some experimental results are presented.

Linear time analysis of properties of conflict-free and general Petri nets

Theoretical Computer Science, 2011

We introduce the notion of T -path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T -paths in a Petri net and firable sequences of transitions.

Compositional analysis of Petri nets

Cybernetics and Systems Analysis, 2006

Foundations of compositional analysis of Petri nets are presented. This analysis consist of the determination of properties of a given Petri net from the properties of its functional subnets. Compositional analysis covers the investigation of behavioral and structural properties of Petri nets with the help of matrix methods that use fundamental equations and invariants. The exponential acceleration of computations as a function of the dimensionality of a net is obtained.

DESCRIPTION OF THE ALGORITHM FOR FINDING THE SHORTEST SEQUENCE OF TRANSITIONS IN A PETRI NET

2017

The article is structured to present several features of Petri Nets and the reachable tree. Some important descriptions include appropriate access in Petri Nets and reachable tree mechanism construction. The article proves that reachable tree can be recovered, corresponding to Petri Nets. According to the algorithms in the article, the infinite reachable tree is replaced with "finite" tree, with an item, which replaces the idea of an infinite. The designed algorithm describes the minimal sequence of possible transitions. It gets the shortest possible sequence for the net state, making it a covering state. Through algorithm description, the number of transitions in covering state is pointed in its minimal position.

The Possibilities of Modeling Petri Nets and Their Extensions

Computer Simulation [Working Title], 2019

This chapter is dedicated to several structure features of Petri nets. There is detailed description of appropriate access in Petri nets and reachable tree mechanism construction. There is an algorithm that describes the minimum sequence of possible transitions. The algorithm developed by us finds the shortest possible sequence for the network promotion state, which transfers the mentioned network state to the coverage state. The corresponding theorem is proven, which states that due to the describing algorithm, the number of transitions in the covering state is minimal. This chapter studies the interrelation of languages of colored Petri nets and traditional formal languages. The Venn diagram, modified by the author, is presented, which shows the relationship between the languages of the colored Petri nets and some traditional languages. As a result, it is shown that the language class of colored Petri nets includes an entire class of context-free languages and some other classes. The results obtained show that it is not possible to model the Patil problem using the well-known semaphores P and V or classical Petri nets, so the mentioned systems have limited properties.

Parallel computation of the reachability graph of petri net models with semantic information

Software: Practice and Experience, 2016

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Mathematical programming approach to the Petri nets reachability problem

European Journal of Operational Research, 2007

This paper focuses on the resolution of the reachability problem in Petri nets, using the mathematical programming paradigm. The proposed approach is based on an implicit traversal of the Petri net reachability graph. This is done by constructing a unique sequence of Steps that represents exactly the total behaviour of the net. We propose several formulations based on integer and/or binary linear programming, and the corresponding sets of adjustments to the particular class of problem considered. Our models are validated on a set of benchmarks and compared with standard approaches from IA and Petri nets community.