True concurrency - from C.A. Petri to Telecom and Systems ... … · concurrent and asynchronous...

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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1 The Token Game

2 Physics


4 Coming to Life

5 Conclusion

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(Source: Petri and Valk 2008)10/57


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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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


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(Source: Benveniste et al, 2003) 27/57




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Reduce Complexity: Fault modeling

(Source: Benveniste et al, 2003) 29/57


Reduce Complexity: Fault modeling


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Reduce Size: True Concurrency


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PN as Propagation + Observation Model


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Finding behaviors: unfold


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Finding explanations: Correlate and unfold


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1 The Token Game

2 Physics


4 Coming to Life

5 Conclusion

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Systems Biology needs Formal Methods

Source : L. Pauleve 36/57


Source : L. Pauleve

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Source : L. Pauleve

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Source : L. Pauleve39/57


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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1 The Token Game

2 Physics


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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