When Graffiti Brings Order Didier Buchs University of Geneva, CUI
Alban Linard
[email protected]
21 june 2011
Didier Buchs & Alban Linard
When Graffiti Brings Order
Is this a Petri net? Think0
Right0
Left0
Eat0 Fork0
Fork1 Eat1
Right1
Left1
Think1 1/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Is this a Petri net? Think0
Right0
Left0
Eat0 Fork0
Fork1 Eat1
Right1
Left1
Think1 1/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Is this (also) a Petri net?
Fork 0
Think 1
Left 1
Right 1
Eat 1
Fork 1
Fork 1 Eat 0
Eat 1 Right 0
Right 1 Left 0
Left 1 Think 0
Fork 0
Post
Eat 0 Fork 1
Right 0
0
Eat 1
0
Right 1
0
Left 1
0
Think 1
1
Fork 0
0
Eat 0
0
Right 0
0
r1 , s1 , t1 , u1 , v1
)
Left 0
0
=
r0 , s0 , t0 , u0 , v0
Think 0
1
T
(
Pre
initial
Left 0
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
) Think 1
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Think 0
P=
(
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
1 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 0 1 1 0 0
0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
0 1 1 0 0 1 0 0 1 0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
2/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Is this (also) a Petri net?
Fork 0
Think 1
Left 1
Right 1
Eat 1
Fork 1
Fork 1 Eat 0
Eat 1 Right 0
Right 1 Left 0
Left 1 Think 0
Fork 0
Post
Eat 0 Fork 1
Right 0
0
Eat 1
0
Right 1
0
Left 1
0
Think 1
1
Fork 0
0
Eat 0
0
Right 0
0
r1 , s1 , t1 , u1 , v1
)
Left 0
0
=
r0 , s0 , t0 , u0 , v0
Think 0
1
T
(
Pre
initial
Left 0
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
) Think 1
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Think 0
P=
(
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
1 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 0 1 1 0 0
0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
0 1 1 0 0 1 0 0 1 0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
2/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
What about this one? Places Think0 , Think1 Fork0 , Fork1 Left0 , Right0 , Left1 , Right1 , Transitions Think0 + Fork0 Think0 + Fork1 Left0 + Fork1 Right0 + Fork0 Eat0 Think1 + Fork1 Think1 + Fork0 Left1 + Fork0 Right1 + Fork1 Eat1
= 1 = 1 Eat0 = 0 Eat1 = 0 → → → → → → → → → →
Left0 Right0 Eat0 Eat0 Fork0 + Fork1 + Think0 Left1 Right1 Eat1 Eat1 Fork0 + Fork1 + Think1
3/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
What about this one? Places Think0 , Think1 Fork0 , Fork1 Left0 , Right0 , Left1 , Right1 , Transitions Think0 + Fork0 Think0 + Fork1 Left0 + Fork1 Right0 + Fork0 Eat0 Think1 + Fork1 Think1 + Fork0 Left1 + Fork0 Right1 + Fork1 Eat1
= 1 = 1 Eat0 = 0 Eat1 = 0 → → → → → → → → → →
Left0 Right0 Eat0 Eat0 Fork0 + Fork1 + Think0 Left1 Right1 Eat1 Eat1 Fork0 + Fork1 + Think1
3/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Do they convey the same information?
Is this a Petri net? Think0
Is this a Petri net?
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
Fork 1
0
1 0 0 0 0 0 0 0 0 0
Eat 1
Fork 1
0
0 0 0 0 1 0 0 0 0 0
Think 1
0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
Right 1
Eat 1
?
�
Left 1
0
Fork 0
Fork 0
r0 , s0 , t0 , u0 , v0 r1 , s1 , t1 , u1 , v1
Left 0
Right 1
Right 0
Left 1
�
Right 0
1
=
Eat 0
0 0 0 0 0 0 0 1 0 0
Think 1
Eat 0
0 0 0 0 0 1 1 0 0 0
T
Think 0
0
Right 1
Think 0
0
0 1 1 0 0 1 0 0 1 0
1 0 0 1 0 0 1 1 0 0
Left 0
0
0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0 0 0
�
Post
0
0 0 0 0 0 0 0 0 1 0
Think 1
1
Fork 1
0 0 0 1 0 0 0 0 0 0
Eat 1
0 0 1 0 0 0 0 0 0 0
Eat 0
Left 0
1 1 0 0 0 0 0 0 0 0
Left 1
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
Fork 0
initial
Pre
≡
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0 Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
Right 0
?
�
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
≡
Eat0 Fork0
Fork1 Eat1
Right1
Left1
2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Think1
3/5
Didier Buchs & Alban Linard
Right0
Left0
Is this a Petri net?
P=
Think 0
Places Think0 , Think1 = 1 Fork0 , Fork1 = 1 Left0 , Right0 , Eat0 = 0 Left1 , Right1 , Eat1 = 0 Transitions Think0 + Fork0 → Left0 Think0 + Fork1 → Right0 Left0 + Fork1 → Eat0 Right0 + Fork0 → Eat0 Eat0 → Fork0 + Fork1 + Think0 Think1 + Fork1 → Left1 Think1 + Fork0 → Right1 Left1 + Fork0 → Eat1 Right1 + Fork1 → Eat1 Eat1 → Fork0 + Fork1 + Think1
2/4
When Graffiti Brings Order
Didier Buchs & Alban Linard
When Graffiti Brings Order
4/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Do they convey the same information?
Is this a Petri net? Think0
Is this a Petri net?
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
Fork 1
0
1 0 0 0 0 0 0 0 0 0
Eat 1
Eat 1
Fork 1
0
0 0 0 0 1 0 0 0 0 0
Right 1
0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
Think 1
Right 1
?
�
Left 1
Left 1 0
Fork 0
Fork 0
Think 1
r0 , s0 , t0 , u0 , v0 r1 , s1 , t1 , u1 , v1
Eat 0
1
�
Left 0
0 0 0 0 0 0 0 1 0 0
=
Right 0
Eat 0
Right 0
Fork 1
0 0 0 0 0 1 1 0 0 0
T
Think 0
0
Right 1
Think 0
0
0 1 1 0 0 1 0 0 1 0
1 0 0 1 0 0 1 1 0 0
Left 0
0
0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0 0 0
�
Post
0
0 0 0 0 0 0 0 0 1 0
Think 1
1
Eat 1
0 0 0 1 0 0 0 0 0 0
Eat 0
Left 0 0 0 1 0 0 0 0 0 0 0
Left 1
1 1 0 0 0 0 0 0 0 0
Fork 0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
Right 0
≡
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0 Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
initial Think 0
?
�
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
≡
Eat0 Fork0
Fork1 Eat1
Right1
Left1
2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Think1
3/5
Didier Buchs & Alban Linard
Right0
Left0
Is this a Petri net?
P=
Pre
Places Think0 , Think1 = 1 Fork0 , Fork1 = 1 Left0 , Right0 , Eat0 = 0 Left1 , Right1 , Eat1 = 0 Transitions Think0 + Fork0 → Left0 Think0 + Fork1 → Right0 Left0 + Fork1 → Eat0 Right0 + Fork0 → Eat0 Eat0 → Fork0 + Fork1 + Think0 Think1 + Fork1 → Left1 Think1 + Fork0 → Right1 Left1 + Fork0 → Eat1 Right1 + Fork1 → Eat1 Eat1 → Fork0 + Fork1 + Think1
2/4
When Graffiti Brings Order
Didier Buchs & Alban Linard
When Graffiti Brings Order
4/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Application
5/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Application
AlPiNA 5/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Application Is this a Petri net? Think0
Right0
Left0
Eat0 Fork0
Fork1 Eat1
Right1
Left1
Think1 2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Is this a Petri net?
Eat 1
Right 1 0
0
0 Eat 1
1
Fork 1
0
Right 1
Eat 1
Fork 1 0 1 1 0 0 1 0 0 1 0
Fork 1
Right 1
0 0 0 0 0 0 0 0 0 1
Left 1
Left 1
0 0 0 0 0 0 0 0 1 0
Think 1
Think 1
0 0 0 0 0 0 0 1 0 0
�
Fork 0
Left 0
Fork 0
0 0 0 0 0 1 1 0 0 0
r1 , s1 , t1 , u1 , v1
Eat 0
0
1 0 0 1 0 0 1 1 0 0
r0 , s0 , t0 , u0 , v0
Right 0
Fork 0
0
0 0 0 0 1 0 0 0 0 0
�
Left 0
0
0 0 0 1 0 0 0 0 0 0
=
Think 0
Eat 0
Right 0
0
0 0 1 0 0 0 0 0 0 0
T
Post
1
Eat 0
Think 0 1 1 0 0 0 0 0 0 0 0
Right 0
Pre
initial
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
� Think 1
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
Left 1
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Left 0
�
Think 0
P=
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
AlPiNA
2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
5/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Marking encoding Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1 1
Didier Buchs & Alban Linard
When Graffiti Brings Order
6/14
Optimization using clustering Think0
Think0 1
Right0 0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1
1 process, 1 cluster! Didier Buchs & Alban Linard
When Graffiti Brings Order
1 1
6/14
Methodology
s a Petri net?
Think0
Right0
Left0
Eat0 Fork0
Fork1 Eat1
Right1
Left1
Think1 2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Formal semantics Is this a Petri net?
Eat 1
Right 1 0
0
0 Eat 1
1
Fork 1
0
Right 1
Eat 1
Fork 1 0 1 1 0 0 1 0 0 1 0
Fork 1
Right 1
0 0 0 0 0 0 0 0 0 1
Left 1
Left 1
0 0 0 0 0 0 0 0 1 0
Think 1
Think 1
0 0 0 0 0 0 0 1 0 0
�
Fork 0
Left 0
Fork 0
0 0 0 0 0 1 1 0 0 0
r1 , s1 , t1 , u1 , v1
Eat 0
0
1 0 0 1 0 0 1 1 0 0
r0 , s0 , t0 , u0 , v0
Right 0
Fork 0
0
0 0 0 0 1 0 0 0 0 0
�
Left 0
0
0 0 0 1 0 0 0 0 0 0
=
Think 0
Eat 0
Right 0
0
0 0 1 0 0 0 0 0 0 0
T
Post
1
Eat 0
Think 0 1 1 0 0 0 0 0 0 0 0
Right 0
Pre
initial
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
� Think 1
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
Left 1
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Left 0
�
Think 0
P=
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
7/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Methodology
s a Petri net?
Think0
Optimization?
Right0
Left0
Clustering! Think0
Think0 1
Right0
Graphical clustering
Eat0
0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork1
Fork0
Fork0
Fork1
1 Fork1
Eat1
Eat1
1
Loose semantics
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Right1
Think1
Left1
1 1 Didier Buchs & Alban Linard
6/7
When Graffiti Brings Order
Think1 2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Formal semantics Is this a Petri net?
Eat 1
Right 1 0
0
0 Eat 1
1
Fork 1
0
Right 1
Eat 1
Fork 1 0 1 1 0 0 1 0 0 1 0
Fork 1
Right 1
0 0 0 0 0 0 0 0 0 1
Left 1
Left 1
0 0 0 0 0 0 0 0 1 0
Think 1
Think 1
0 0 0 0 0 0 0 1 0 0
�
Fork 0
Left 0
Fork 0
0 0 0 0 0 1 1 0 0 0
r1 , s1 , t1 , u1 , v1
Eat 0
0
1 0 0 1 0 0 1 1 0 0
r0 , s0 , t0 , u0 , v0
Right 0
Fork 0
0
0 0 0 0 1 0 0 0 0 0
�
Left 0
0
0 0 0 1 0 0 0 0 0 0
=
Think 0
Eat 0
Right 0
0
0 0 1 0 0 0 0 0 0 0
T
Post
1
Eat 0
Think 0 1 1 0 0 0 0 0 0 0 0
Right 0
Pre
initial
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
� Think 1
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
Left 1
Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Left 0
�
Think 0
P=
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
7/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Methodology
s a Petri net?
Think0
Optimization?
Right0
Left0
Clustering! Think0
Think0 1
Right0
Graphical clustering
Eat0
0 Right0
Left0
Left0 0 Eat0 0
Eat0
Fork0
Fork1
Fork0
Fork0
Fork1
1 Fork1
Eat1
Eat1
1
Loose semantics
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Right1
Think1
Left1
1 6/7
1 Didier Buchs & Alban Linard
When Graffiti Brings Order
Think1 2/4
Didier Buchs & Alban Linard
When Graffiti Brings Order
Formal semantics Is this a Petri net? Think 0 , Left 0 , Right 0 , Eat 0 , Fork 0
Right0
Left0
Left0 0 Eat0 0
Eat0
Eat 1
0 Right 1
0
Fork 1
Eat 1
0
Right0 0
PNXDD
Left 1
Right 1
Fork 1
0
Think0 1
Think 1
Fork 0
1
Clustering!
Think0
Fork 0
0 0 0 0 0 0 0 0 1 0
0
Optimization?
�
Eat 0
0 0 0 0 0 0 0 1 0 0
r1 , s1 , t1 , u1 , v1
Right 0
0 0 0 0 0 1 1 0 0 0
r0 , s0 , t0 , u0 , v0
Left 0
1 0 0 1 0 0 1 1 0 0
�
Left 1
Eat 0
0 0 0 0 1 0 0 0 0 0
=
Think 0
0 0 0 1 0 0 0 0 0 0
T
Think 1
Right 0
Right 1
0 0 1 0 0 0 0 0 0 0
�
Post
Left 1
Left 0
Think 1
0
Left 0
0
Fork 0
1 1 0 0 0 0 0 0 0 0
0
Eat 0
Think 0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
1
Right 0
Pre
initial
Think 0
Think 1 , Left 1 , Right 1 , Eat 1 , Fork 1
Eat 1
�
Fork 1
P=
0 0 0 0 0 0 0 0 0 1
0 1 1 0 0 1 0 0 1 0
r0 s0 t0 u0 v0 r1 s1 t1 u1 v1
0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 1 0
0 0 0 0 1 0 0 0 0 1
Fork0
Fork0
Fork1
1 Fork1
Eat1 1
Structural clustering
Eat1 0 Right1
Left1
Left1 0 Right1 0
Think1
Think1 1
2/4
Didier Buchs & Alban Linard
1 Didier Buchs & Alban Linard
6/7
When Graffiti Brings Order
When Graffiti Brings Order
7/14
Didier Buchs & Alban Linard
When Graffiti Brings Order
Experiment 1: FMS
