Vol-3170/poster2
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| Paper | |
|---|---|
 edit
| |
| description | |
| id | Vol-3170/poster2 |
| wikidataid | Q117351468→Q117351468 |
| title | Reset Petri Net Unfolding Semantics for Ecosystem Hypergraphs |
| pdfUrl | https://ceur-ws.org/Vol-3170/poster2.pdf |
| dblpUrl | https://dblp.org/rec/conf/apn/Aguirre-Samboni22 |
| volume | Vol-3170→Vol-3170 |
| session | → |
Reset Petri Net Unfolding Semantics for Ecosystem Hypergraphs
Reset Petri Net Unfolding Semantics for Ecosystem
Hypergraphs
Giann Karlo Aguirre-Samboní1 , Cédric Gaucherel2 , Stefan Haar1 and
Franck Pommereau3
1
Université Paris-Saclay, INRIA, CNRS, ENS Paris-Saclay, LMF, 91190 Gif-sur-Yvette, France
2
AMAP-INRAE, CIRAD, CNRS, IRD, Univ. Montpellier, 34398 Montpellier, France
3
IBISC, Univ. Évry, Univ. Paris-Saclay, 91020 Évry-Courcouronne, France
Ecosystems are complex systems still waiting for a convenient and flexible way to model them.
This article extends the rule-based discrete-event modeling approach for ecosystems developed
by Gaucherel et al. Here, we propose the
systematic use of (1-safe) reset Petri nets r1: Rp+ ≫ Ec, Rp+
for the analysis of such systems. For this r2: Rp+, Ec+ ≫ Wk+, Rp+, Ec+
purpose, we use the translation from RR- r3: Wk+ ≫ Wd+, Te+, Fg+, Ec+, Wk+
systems, and adapt the unfolding methodol- r4: Wk+, Wd+ ≫ Sd+, Rp+, Wk+, Wd+
ogy of Esparza et al. to provide a consistent r5: Wk+, Te+ ≫ Wd-, Wk+, Te+
and compact semantics in ordinary occur- r6: Wd- ≫ Wk-, Te-, Wd-
rence nets for 1-safe reset Petri nets. One eco- r7: Wk- ≫ Fg-, Sd-, Te-, Wk-
logical case study, the evolution of a termite r8: Wk-, Rp- ≫ Ec-, Wk-, Rp-
colony (Gaucherel et al.) is carried out to r9: Ac+, Sd- ≫ Wk-, Rp-, Ac+, Sd-
illustrate how important principles deciding
Figure 1: Rule system for the termites colony
between survival and collapse of this ecosys-
tem can be exhibited by structural properties of prefixes of its corresponding unfolding. The
modelling of the interaction rules in Petri nets requires, in addition to the usual combination
of read and production arcs, also the use of reset arcs to capture side effect relations, i.e. where
a resource is certainly absent after some event but not necessarily present prior to it. In com-
bination with automatizable place replication and complementation procedures, a dedicated
unfolding procedure represents the dynamics of a contextual reset net in an ordinary Petri net,
taking specificities of both read and reset arcs into account. Unfolding prefixes are computed by
the Ecofolder tool developed in this work. Here, we consider as an example of an ecosystem
the network of dominant interactions occurring in a termite colony (fig 1), directly inspired
from Gaucherel & Pommereau. Our model includes the following variables: Inhabitants: Rp:
reproductive termites, i.e. the queen, the king, the eggs and the nymphs; Wk: termite workers,
PNSE’22, International Workshop on Petri Nets and Software Engineering, Bergen, Norway, 2022
" giann-karlo.aguirre-samboni@inria.fr (G. K. Aguirre-Samboní); cedric.gaucherel@inrae.fr (C. Gaucherel);
stefan.haar@inria.fr (S. Haar); franck.pommereau@univ-evry.fr (F. Pommereau)
~ https://www.giannkarlo.info/ (G. K. Aguirre-Samboní); http://www.lsv.fr/~haar/ (S. Haar);
https://www.ibisc.univ-evry.fr/~fpommereau/ (F. Pommereau)
� 0000-0002-3526-7253 (G. K. Aguirre-Samboní); 0000-0002-4521-8914 (C. Gaucherel); 0000-0002-1892-2703
(S. Haar); 0000-0002-9959-3699 (F. Pommereau)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
� i.e. all termites able to work; Sd: termite
soldiers; and Te: termitomyces, i.e fungi grown
by termites for nutrition. 𝑡𝑒− 𝑡𝑒+
𝑟6
𝑤𝑑+ 𝑤𝑑−
Structures: Fg: fungal gardens, i.e. cham-
bers for growing fungi; Ec: egg chambers. 𝑟4 𝑟5
Resources: Wd: wood used to build the 𝑓 𝑔+
𝑟3
𝑤𝑘+
𝑤𝑘−
mound and to grow fungi. 𝑎𝑐+
Competitors: Ac: ant competitors that may 𝑓 𝑔−
𝑠𝑑+
𝑟9
𝑎𝑐−
attack the colony. 𝑟7
Those components can evolve (from an ini-
𝑠𝑑−
tial state) according to their interactions; we 𝑟𝑝−
𝑟2
represent the functional presence or absence
of any of them by adding ‘-’ or ‘+’ to their re- 𝑟8
𝑟𝑝+
𝑒𝑐−
spective labels. Their interaction rules can be
𝑒𝑐+
translated into a Petri net with read and reset 𝑟1
arcs, shown on fig 2. Moreover, fig 3 shows the
Figure 2: Termites ecosystem using a contextual net with re-
corresponding event structure extracted from sets.
the unfolding prefix, both of them created by
Ecofolder. The schema emphasizes those branches on which the colony collapses (r6, r7, r8,
⊥
r3 (e1) r6 (e2) r9 (e39)
r5 (e4)
r4 (e3) r3 (e38) r9 (e5) r6 (e37) r9 (e34) r8 (e35) r7 (e36)
r5 (e6) r5 (e28)
r4 (e29) r3 (e31) r2 (e32) r1 (e33) r8 (e10) r9 (e27) r7 (e9) r6 (e7) r9 (e8) r3 (e30)
r5 (e24)
r3 (e25) r6 (e11) r2 (e26) r8 (e16) r9 (e15) r9 (e17) r7 (e18) r8 (e13) r7 (e12) r9 (e22) r6 (e23) r8 (e14) r9 (e19) r6 (e21) r7 (e20)
Figure 3: Event structure of the termites ecosystem example.
and r9) and survives (r3, r4, r1 and r2), respectively. ⊥ represents the initial cut, causal
precedence is indicated by arrows, and dashed lines represent conflict relations. Note that
instances of R5 allow survival but do not guarantee it, as the downfall of the colony always
remains possible. The crown at every instance of r5 visualizes this tipping point, and to symbolize
a Red Queen. Loosely speaking, workers in the colony have to keep working at a sufficient rate
to prevent a successful attack by the ants. This phenomenon of arms race is suggested by Red
Queen hypotheses as proposed by L. Van Valen in 1973; it states that species must constantly
adapt, evolve and proliferate in the competition with antagonistic species, simply to survive.
Therefore, possibilistic approaches like ours allow an exhaustive exploration of the system’s
trajectory. Our method enables, in the future, to apply finer analysis methods to extract insight
about the system’s ecology from the study of its dynamics.
�