# The Formalization of Decision-Free Petri Net

Pratima K. Shah; Pauline N. Kawamoto; Mariusz Giero

Formalized Mathematics (2014)

- Volume: 22, Issue: 1, page 29-35
- ISSN: 1426-2630

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topPratima K. Shah, Pauline N. Kawamoto, and Mariusz Giero. "The Formalization of Decision-Free Petri Net." Formalized Mathematics 22.1 (2014): 29-35. <http://eudml.org/doc/266925>.

@article{PratimaK2014,

abstract = {In this article we formalize the definition of Decision-Free Petri Net (DFPN) presented in [19]. Then we formalize the concept of directed path and directed circuit nets in Petri nets to prove properties of DFPN. We also present the definition of firing transitions and transition sequences with natural numbers marking that always check whether transition is enabled or not and after firing it only removes the available tokens (i.e., it does not remove from zero number of tokens). At the end of this article, we show that the total number of tokens in a circuit of decision-free Petri net always remains the same after firing any sequences of the transition.},

author = {Pratima K. Shah, Pauline N. Kawamoto, Mariusz Giero},

journal = {Formalized Mathematics},

keywords = {specification and verification of discrete systems; Petri net;; Petri net},

language = {eng},

number = {1},

pages = {29-35},

title = {The Formalization of Decision-Free Petri Net},

url = {http://eudml.org/doc/266925},

volume = {22},

year = {2014},

}

TY - JOUR

AU - Pratima K. Shah

AU - Pauline N. Kawamoto

AU - Mariusz Giero

TI - The Formalization of Decision-Free Petri Net

JO - Formalized Mathematics

PY - 2014

VL - 22

IS - 1

SP - 29

EP - 35

AB - In this article we formalize the definition of Decision-Free Petri Net (DFPN) presented in [19]. Then we formalize the concept of directed path and directed circuit nets in Petri nets to prove properties of DFPN. We also present the definition of firing transitions and transition sequences with natural numbers marking that always check whether transition is enabled or not and after firing it only removes the available tokens (i.e., it does not remove from zero number of tokens). At the end of this article, we show that the total number of tokens in a circuit of decision-free Petri net always remains the same after firing any sequences of the transition.

LA - eng

KW - specification and verification of discrete systems; Petri net;; Petri net

UR - http://eudml.org/doc/266925

ER -

## References

top- [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
- [6] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [9] Pauline N. Kawamoto, Yasushi Fuwa, and Yatsuka Nakamura. Basic Petri net concepts. Formalized Mathematics, 3(2):183-187, 1992.
- [10] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
- [11] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
- [12] Robert Milewski. Subsequences of almost, weakly and poorly one-to-one finite sequences. Formalized Mathematics, 13(2):227-233, 2005.
- [13] Karol Pak. Continuity of barycentric coordinates in Euclidean topological spaces. Formalized Mathematics, 19(3):139-144, 2011. doi:10.2478/v10037-011-0022-5.[Crossref] Zbl1276.57020
- [14] Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics, 5 (3):317-322, 1996.
- [15] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [16] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
- [17] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
- [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [19] Jiacun Wang. Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, 1998.
- [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.