Volume 5, 1993

University of Bialystok

Copyright (c) 1993 Association of Mizar Users

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

- Contains basic concepts for Petri nets with Boolean markings and the firability$\slash$firing of single transitions as well as sequences of transitions [6]. The concept of a Boolean marking is introduced as a mapping of a Boolean TRUE$\slash$FALSE to each of the places in a place$\slash$transition net. This simplifies the conventional definitions of the firability and firing of a transition. One note of caution in this article - the definition of firing a transition does not require that the transition be firable. Therefore, it is advisable to check that transitions ARE firable before firing them.

- Preliminaries
- Boolean Marking and Firability$\slash$Firing of Transitions

- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [6] Pauline N. Kawamoto, Masayoshi Eguchi, Yasushi Fuwa, and Yatsuka Nakamura. The detection of deadlocks in Petri nets with ordered evaluation sequences. In \em Institute of Electronics, Information, and Communication Engineers (IEICE) Technical Report, pages 45--52. Institute of Electronics, Information, and Communication Engineers (IEICE), January 1993.
- [7]
Pauline N. Kawamoto, Yasushi Fuwa, and Yatsuka Nakamura.
Basic Petri net concepts.
*Journal of Formalized Mathematics*, 4, 1992. - [8]
Andrzej Trybulec.
Binary operations applied to functions.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Andrzej Trybulec.
Domains and their Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [11]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Edmund Woronowicz.
Many-argument relations.
*Journal of Formalized Mathematics*, 2, 1990.

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