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Composition of Functional Petri Nets

Composition of Functional Petri Nets

Dmitry A. Zaitsev
Copyright: © 2013 |Pages: 61
ISBN13: 9781466640344|ISBN10: 1466640340|EISBN13: 9781466640351
DOI: 10.4018/978-1-4666-4034-4.ch017
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MLA

Zaitsev, Dmitry A. "Composition of Functional Petri Nets." Formal Methods in Manufacturing Systems: Recent Advances, edited by Zhiwu Li and Abdulrahman M. Al-Ahmari, IGI Global, 2013, pp. 404-464. https://doi.org/10.4018/978-1-4666-4034-4.ch017

APA

Zaitsev, D. A. (2013). Composition of Functional Petri Nets. In Z. Li & A. Al-Ahmari (Eds.), Formal Methods in Manufacturing Systems: Recent Advances (pp. 404-464). IGI Global. https://doi.org/10.4018/978-1-4666-4034-4.ch017

Chicago

Zaitsev, Dmitry A. "Composition of Functional Petri Nets." In Formal Methods in Manufacturing Systems: Recent Advances, edited by Zhiwu Li and Abdulrahman M. Al-Ahmari, 404-464. Hershey, PA: IGI Global, 2013. https://doi.org/10.4018/978-1-4666-4034-4.ch017

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Abstract

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.

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