Reflexive Incidence Matrx (RIM) Representation of Petr Nets

Das, Sajal Kumar and Agrawal, VK and Sarkar, Dilip and Patnaik, LM and Goel, PS (1987) Reflexive Incidence Matrx (RIM) Representation of Petr Nets. In: IEEE Transactions on Software Engineering, 13 (6). 643 -653.

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Abstract

Although incidence matrix representation has been used to analyze the Petri net based models of a system, it has the limitation that it does not preserve reflexive properties (i.e., the presence of selfloops) of Petri nets. But in many practical applications self-loops play very important roles. This paper proposes a new representation scheme for general Petri nets. This scheme defines a matrix called "reflexive incidence matrix (RIM) c which is a combination of two matrices, a "base matrix Cb,,, and a "power matrix CP." This scheme preserves the reflexive and other properties of the Petri nets. Through a detailed analysis it is shown that the proposed scheme requires less memory space and less processing time for answering commonly encountered net queries compared to other schemes. Algorithms to generate the RIM from the given net description and to decompose RIM into input and output function matrices are also given. The proposed Petri net representation scheme is very useful to model and analyze the systems having shared resources, chemical processes, network protocols, etc., and to evaluate the performance of asynchronous concurrent systems.

Item Type:	Journal Article
Publication:	IEEE Transactions on Software Engineering
Publisher:	IEEE
Additional Information:	Copyright 1987 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords:	Incidence matrix,Petri net,reflexivity,self-loop, space complexity,time complexity.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	12 Jan 2010 06:49
Last Modified:	05 Mar 2019 06:56
URI:	http://eprints.iisc.ac.in/id/eprint/21249

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