Applications of Petri nets

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2008Includes bibliographical references (leaves: 51-52)Text in English; Abstract: Turkish and Englishix, 52 leavesPetri nets are powerful formalism for modeling a wide range of dynamic systems and system behaviors. This thesis surveys the basic concept and application of Petri nets. The structure of Petri nets, their marking and execution and several examples of Petri net modeling. In this thesis we research into the analysis of Petri nets. Also we give the structure of Reachability graphs of Petri nets and their advantages for analyzing the Petri nets. The reachability problem for Petri nets is the problem of finding if Mn 2 R(M0) for a given marking Mn in a net (N,M0).We present several different kinds of Petri nets, together with computer tools based on Mathematica. We give the Mathematica commands for Reachability problem and also we created Mathematica commands for Incidence matrix of Petri nets. We study the concept of Petri nets and applications of Petri nets.We especially focus on Biological applications on Petri nets and we work on modeling of Hashimoto.s Thyroiditis in Petri Nets

Efficient Reachability Graph Representation of Petri Nets With Unbounded Counters

AbstractIn this paper, we define a class of Petri nets, called Petri nets with counters, that can be seen as place/transition Petri nets enriched with a vector of integer variables on which linear operations may be applied. Their semantics usually leads to huge or infinite reachability graphs. Then, a more compact representation for this semantics is defined as a symbolic state graph whose nodes possibly encode infinitely many values for the variables. Both representations are shown behaviourally equivalent

Efficient reachability graph representation of Petri nets with unbounded counters

International audienceIn this paper, we define a class of Petri nets, called Petri nets with counters, that can be seen as place/transition Petri nets enriched with a vector of integer variables on which linear operations may be applied. Their semantics usually leads to huge or infinite reachability graphs. Then, a more compact representation for this semantics is defined as a symbolic state graph whose nodes possibly encode infinitely many values for the variables. Both representations are shown behaviourally equivalent

Performance analysis using timed Petri Nets

Petri Nets have been successfully used to model and evaluate the performance of distributed systems. Several researchers have extended the basic Petri Net model to include time, and have demonstrated that restricted classes of Petri Nets can be analyzed efficiently. Unfortunately, the restrictions prohibit the techniques from being applied to many interesting systems, e.g. communication protocols. This paper proposes a version of timed Petri Nets which accurately models communication protocols, and which can be analyzed using Timed Reachability Graphs. Procedures for constructing and analyzing these graphs are presented. The analysis is shown to be applicable to a larger class of Timed Petri Nets than previously thought. The model and the analysis technique are demonstrated using a simple communication protocol

Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

The derivation of performance expressions for communication protocols from timed Petri net models

Petri Net models have been extended in a variety of ways and have been used to prove the correctness and evaluate the performance of communication protocols. Several extensions have been proposed to model time. This work uses a form of Timed Petri Nets and presents a technique for symbolically deriving expressions which describe system performance. Unlike past work on performance evaluation of Petri Nets which assumes a priori knowledge of specific time delays, the technique presented here applies to a wide range of time delays so long as the delays satisfy a set of timing constraints. The technique is demonstrated using a simple communication protocol

Tools for efficient analysis of concurrent software systems

The ever increasing use of distributed computing as a method of providing added computing power and reliability has sparked interest in methods to model and analyze concurrent hardware/ software systems. Efficient automated analysis tools are needed to aid designers of such systems. The Distributed Systems Project at UCI has been developing a suite of tools (dubbed the P-NUT system) which supports efficient analysis of models of concurrent software. This paper presents the principles which guide the development of P-NUT tools and discusses the development of one of the tools: the Reachability Graph Builder (RGB). The P-NUT approach to tool development has resulted in the production of a highly efficient tool for constructing reachability graphs. The careful design of data structures and associated algorithms has significantly enlarged the class of models which can be analyzed

Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

From RT-LOTOS to Time Petri Nets new foundations for a verification platform

The formal description technique RT-LOTOS has been selected as intermediate language to add formality to a real-time UML profile named TURTLE. For this sake, an RT-LOTOS verification platform has been developed for early detection of design errors in real-time system models. The paper discusses an extension of the platform by inclusion of verification tools developed for Time Petri Nets. The starting point is the definition of RT-LOTOS to TPN translation patterns. In particular, we introduce the concept of components embedding Time Petri Nets. The translation patterns are implemented in a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN in the format admitted by the TINA tool. The efficiency of the proposed solution has been demonstrated on various case studies

Computer-aided analysis of concurrent systems

The introduction of concurrency into programs has added to the complexity of the software design process. This is most evident in the design of communications protocols where concurrency is inherent to the behavior of the system. The complexity exhibited by such software systems makes more evident the needs for computer-aided tools for automatically analyzing behavior.The Distributed Systems project at UCI has been developing a suite of tools, based on Petri nets, which support the design and evaluation of concurrent software systems. This paper focuses attention on one of the tools: the reachability graph analyzer (RGA). This tool provides mechanisms for proving general system properties (e.g., deadlock-freeness) as well as system-specific properties. The tool is sufficiently general to allow a user to apply complex user-defined analysis algorithms to reachability graphs. The alternating-bit protocol with a bounded channel is used to demonstrate the power of the tool and to point to future extensions