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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Theory of regions | 1/1 | https://en.wikipedia.org/wiki/Theory_of_regions | reference | science, encyclopedia | 2026-05-05T11:39:47.623283+00:00 | kb-cron |
The Theory of regions is an approach for synthesizing a Petri net from a transition system. 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
(
S
,
Λ
,
→
)
{\displaystyle (S,\Lambda ,\rightarrow )}
is a mapping assigning to each state
s
∈
S
{\displaystyle s\in S}
a number
σ
(
s
)
{\displaystyle \sigma (s)}
(natural number for P/T nets, binary for ENS) and to each transition label a number
τ
(
ℓ
)
{\displaystyle \tau (\ell )}
such that consistency conditions
σ
(
s
′
)
=
σ
(
s
)
+
τ
(
ℓ
)
{\displaystyle \sigma (s')=\sigma (s)+\tau (\ell )}
holds whenever
(
s
,
ℓ
,
s
′
)
∈→
{\displaystyle (s,\ell ,s')\in \rightarrow }
.
=== Intuitive explanation === Each region represents a potential place of a Petri net. Mukund: event/state separation property, state separation property.
== References ==
Badouel, Eric; Darondeau, Philippe (1998), Reisig, Wolfgang; Rozenberg, Grzegorz (eds.), "Theory of regions", Lectures on Petri Nets I: Basic Models: Advances in Petri Nets, Lecture Notes in Computer Science, Berlin, Heidelberg: Springer, pp. 529–586, doi:10.1007/3-540-65306-6_22, ISBN 978-3-540-49442-3{{citation}}: CS1 maint: work parameter with ISBN (link)