The Theory of regions is an approach for synthesizing a
Petri net
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that ...
from a
transition system
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled wi ...
. As such, it aims at recovering concurrent, independent behavior from transitions between global states. Theory of regions handles elementary net systems as well as P/T nets and other kinds of nets. An important point is that the approach is aimed at the synthesis of unlabeled Petri nets only.
Definition
A region of a transition system
is a mapping assigning to each state
a number
(
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
for P/T nets,
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that ta ...
for ENS) and to each transition label a number
such that consistency conditions
holds whenever
.
Intuitive explanation
Each region represents a potential place of a Petri net.
Mukund: event/state separation property, state separation property.
References
*
Set theory
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