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Journal of Information Science and Engineering, Vol. 23 No. 2, pp. 371-385 (March 2007)

Virtual First-Order Structure

Daniel Yuh Chao
Department of Management and Information Science
National Chengchi University
Taipei, 116 Taiwan
E-mail: yaw@mis.nccu.edu.tw

The proof of liveness for various new classes of nets is not intuitive and rather hard to understand. We propose to find the maximum class, called non-virtual-net (NV-net) that are live as long as all minimal siphons never get empty of tokens and the maximum class, called virtual-net (V-net) that may be weakly live if all minimal siphons never get empty of tokens. In the future, when a new system is developed, if it is an NV-net, then it is live as long as no siphons ever get empty. We show that weakly liveness is closely related to a structure called Virtual First Order Structure. We show that both Synchronized Choice Net and Extended Synchronized Choice Net belong to non-virtual-net.

Keywords: Petri nets, synchronized choice nets, siphons, traps, weakly live

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Received November 26, 2004; revised March 1, 2004; accepted June 6, 2005.
Communicated by Hsu-Chun Yen.