true concurrency - from c.a. petri to telecom and systems ... … · concurrent and asynchronous...
TRANSCRIPT
The Token Game Physics Techniques and Engineering Coming to Life Conclusion
True concurrency - from C.A. Petri to Telecom andSystems Biology
Stefan Haar
INRIA and LSV, CNRS and ENS Cachan
France
September 18, 2014
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1 The Token Game
2 Physics
3 Techniques and EngineeringInvariantsUnfolding
4 Coming to Life
5 Conclusion
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Nets and Concurrency
1 The Token Game
2 Physics
3 Techniques and Engineering
4 Coming to Life
5 Conclusion
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Carl Adam Petri, 12 July 1926 – 2 July 2010
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The Token Game
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The Token Game
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The Token Game
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First Intended Use
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Nets and Concurrency
1 The Token Game
2 Physics
3 Techniques and Engineering
4 Coming to Life
5 Conclusion
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(Source: Petri and Valk 2008)10/57
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From Space-Time to Nets
Minkowski Petri Grid
(Source: Petri/Valk 2008 and Valk 2013)
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From Big to Small
(Source: Petri/Valk 2008 and Valk 2013)
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From Geometry to Topology
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Physics and Concurrency
Concurrency
Relativistic Space-Time:
You don’t see what is going on at Alpha Centaury right now
Quantum systems:
Uncertainty prevents you from obtaining a full global instantaneous snapshot
Some goals from Petri’s program
Axiomatic relational theory of concurrency (Carnap’s spirit)
Capture Lorentz transforms etc
Build finitary but continuous mathematical picture of physics
Here:
PN Techniques and Concurrency in
Engineering
Life Sciences
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Nets and Concurrency
1 The Token Game
2 Physics
3 Techniques and EngineeringInvariantsUnfolding
4 Coming to Life
5 Conclusion
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Formalize !
NET : N = (P ,T ,F )
P ∩ T = ∅, and
F ⊆ (P × T ∪ T × P)
N = (N ,M0) is a Petri net iff
N is a net
M0 : P → N0 a marking of N.
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Matrix Representation
Incidence Matrix
−1 0 1 0 0 01 −1 0 0 0 00 1 −1 0 0 00 −1 1 0 −1 100 0 0 −1 0 1 00 0 0 1 −1 00 0 0 0 1 −1
.
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Incidence Matrix and Invariants
Incidence Matrix N ∈ Z|P|×|t|
N(p,t) =
−1 : p F t1 : t F p0 : o/w
(note: we assume there are no loops)
State change equation
For X,M ,M ′ ∈ Z|P|, M t−→ M ′ ⇔ X>M ′ = X>M +X>W (t)
Definition
A non-negative and non-zero solution of
X>W (t) = 0
is a place invariant of N .
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Running example
For all M ∈ R(N ,M0),
M (p1) +M (p2) +M (p3) = 1
M (p5) +M (p6) +M (p7) = 1
M (p3) +M (p4) +M (p7) = 1
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Production Systems
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T - Invariants
J ∈ N|T |0 is a T -invariant of N iff
At · J = 0
If M0σJ−→ for some σJ ∈ T ∗ such that
∀ t ∈ T : J (t) = |σJ |t ,
then
At · J = 0 ⇒ M0σJ−→ M0.
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Comparison of Invariants
T -invariants
Help find state-reproducing behaviors
Exhibit ”typical” processes
Give hints on liveness
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Comparison of Invariants
P -invariants
Help express properties satisfied by all reachable markings
Tell if the system is bounded → safety properties
May allow decomposition
Useful in control and supervision
Next: Telecommunications , or: when one needs unfoldings
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Telecommunications : need Fault Diagnosis
(Source: Benveniste et al, 2003)
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Seeking a Needle in a Haystack
(Source: Benveniste et al, 2003)
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Seeking a Needle in a Haystack
(Source: Benveniste et al, 2003) 27/57
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Seeking a Needle in a Haystack
(Source: Benveniste et al, 2003)
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Reduce Complexity: Fault modeling
(Source: Benveniste et al, 2003) 29/57
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Reduce Complexity: Fault modeling
(Source: Benveniste et al, 2003)
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Reduce Size: True Concurrency
(Source: Benveniste et al, 2003)
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PN as Propagation + Observation Model
(Source: Benveniste et al, 2003)
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Finding behaviors: unfold
(Source: Benveniste et al, 2003)
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Finding explanations: Correlate and unfold
(Source: Benveniste et al, 2003)
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Nets and Concurrency
1 The Token Game
2 Physics
3 Techniques and Engineering
4 Coming to Life
5 Conclusion
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Systems Biology needs Formal Methods
Source : L. Pauleve 36/57
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Source : L. Pauleve
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Source : L. Pauleve
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Source : L. Pauleve39/57
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Source : L. Pauleve
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Source : L. Pauleve
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Source : L. Pauleve
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Source : L. Pauleve
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Source : L. Pauleve
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Source : L. Pauleve
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Petri Nets are a Natural Choice !
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Building complex networks
Enzymatic Reaction Coupled with Gene Expression
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What For ?
Compute Attractors
Terminal strongly connected components of State graph
E.g.:
Stable state of a cell after de-differentiationReachable mutations
Identify Cut Sets
Sets of factors/actions/ ... that are necessary to reach some attractor
E.g.:
Interventions to prevent a mutationMedication to enforce a certain ”healthy” attractorCell re-programming: move from one attractor to another
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The Petri View: State Graph ...
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The Petri View: State Graph ...
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... vs Unfolding
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Some More Leads for PNs in Biology
Unfoldings
Accelerate search of attractors
Find cut sets for control
Understand cell reprogramming
...
Compositionality, Invariants
Synthetic genetic circuits
Regulatory networks analysis
Control
Monitoring
...
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Nets and Concurrency
1 The Token Game
2 Physics
3 Techniques and Engineering
4 Coming to Life
5 Conclusion
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Conclusion: What was mentioned ...
PNs and concurrency are
meaningful in
Physics
Engineering
(Chemistry)
Biology
Concurrency
is inherent
is intuitive
is helpful to save time
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... and what wasn’t mentioned
More models and mathematics
Contextual nets, time(d) nets, stochastic nets, fluid nets ...
High-level nets, nested nets
Max-Plus analysis
More applications
Verification of protocols, distributed algorithms, ...
Workflows
Railway Networks
... and everything I forgot
References
... follow on next slides
What Remains to be Said
BIG THANKS !!
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References I : Papers
On the subjects here:
T. Murata. Petri Nets: Properties, Analysis and Applications. Proceedings ofthe IEEE, Vol. 77, No 4, April, 1989, pp. 541-580.
J. L. Peterson. Petri Net Theory and the Modeling of Systems.Prentice-Hall, N.J., 1981, ISBN: 0-13-661983-5.
W. Reisig. Petri Nets, An Introduction. EATCS, Monographs on TheoreticalComputer Science, W.Brauer, G. Rozenberg, A. Salomaa (Eds.), SpringerVerlag, Berlin, 1985.
C.A. Petri. Nets, time and space. Theor. Computer Science Vol. 153, 199 pp3-48
E. Fabre, A. Benveniste, S. Haar and C. Jard. Distributed monitoring ofconcurrent and asynchronous systems. Discrete Event Dynamic Systems:Theory and Applications 15(1), pages 33-84, 2005.
Th. Chatain, S. Haar, L. Jezequel, L. Pauleve and S. Schwoon.Characterization of Reachable Attractors Using Petri Net Unfoldings. InCMSB’14.
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References II : Online
Online tutorial:http://www.informatik.uni-hamburg.de/TGI/PetriNets/introductions/aalst/
C.A.Petri and R. Valk. On the Physical Basics of Information Flow. Talk atICATPN 2008, Xi’An;
http://www.informatik.uni-hamburg.de/TGI/....../mitarbeiter/profs/petri/Xian Petri Valk.pdf
R. Valk. Tutorial: Nets, Physics and Coordination, A tribute to the work ofCarl Adam Petri and Anatol W. Holt. Talk at ICATPN 2013, Milano;
http://www.informatik.uni-hamburg.de/TGI/....../mitarbeiter/profs/valk/Tutorium-NPC-Valk-slides.pdf.zipf
http://www-dssz.informatik.tu-cottbus.de/publications/papers/2014/...p72-74 mh Intl Innovation 137 Research Media-small.pdf
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