Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

Basic Petri Net Concepts


Pauline N. Kawamoto
Shinshu University, Nagano
Yasushi Fuwa
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

This article presents the basic place/transition net structure definition for building various types of Petri nets. The basic net structure fields include places, transitions, and arcs (place-transition, transition-place) which may be supplemented with other fields (e.g., capacity, weight, marking, etc.) as needed. The theorems included in this article are divided into the following categories: deadlocks, traps, and dual net theorems. Here, a dual net is taken as the result of inverting all arcs (place-transition arcs to transition-place arcs and vice-versa) in the original net.

MML Identifier: PETRI

The terminology and notation used in this paper have been introduced in the following articles [3] [1] [5] [6] [7] [4] [2]

Contents (PDF format)

  1. Basic Place/Transition Net Structure Definition
  2. Deadlocks
  3. Traps
  4. Duality Theorems for Place/Transition Nets

Bibliography

[1] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[2] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[3] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[4] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[5] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[6] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received November 27, 1992


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