Dagstuhl

Local/Global
Behaviour/Specification
Producing a

Global/Local

Outcome

Group Discussion Outbrief

Guy Lemieux, Daniel Coore

Dagstuhl 06361

Overview

•
Global to local


•
Local to global


•
Middle ground?

Ixodes Ricinus

Global to Local

•
These global objectives and behaviours
can be “compiled down” into locally
specified solutions

–
Coordinate systems

–
Sorting

–
List homomorphisms

–
Boundary value problems


Questions about G to L

•
How should these be manifested in a programming
language ?


•
How should we go about finding more of them?

–
Biomimetics

–
Complex Systems Community


•
Should the global behaviour specification be vague?

–
Are there multiple correct global behaviours (non
-
determinism)?

–
Does the global algorithm have to be completely specified?
(imperative versus declarative)

–
Is it agnostic of actual embedding of the processors?

Local to Global Issues

•
Can we infer/prove global outcome, or do we have to simulate?

–
Can we restrict L to make inference possible?

–
If restriction allows us to characterize trajectory in “robust” way, answer
is yes/maybe (could be difficult)

–
It may be chaotic with attractor states (good and/or bad)

–
Example: PDE solving is a form of “local specification/behaviour”
(difference equations) that are run to produce a global outcome


•
Is Local to Global a convex optimization problem?

–
If yes, then outcome may be easily predictable


•
Is this a robust control problem?

–
Maybe this is how we restrict L to make inference possible

–
Can this property be used to compile a global specification into local
rules?

… merging G to L

with L to G …

aka “The Conclusion”

“G to L” vs. “L to G” …

How about “G to M to L” instead?

•
Add an interface “M” between G and L

–
This may give both G and L something to concretely
refer to as a middle ground

–
Like an instruction set architecture merges an
algorithm/language to the microarchitecture


•
Do we need an M ?


•
The G
-
M
-
L relationship is a recursive hierarchy

–
G can be replaced by G
-
M2
-
L to give G
-
M2
-
L
-
M
-
L

–
L can be replaced by G
-
M3
-
L …

Possible Primitives for M

•
Primitive (vote count to question)

–
Question: Is this “easy” to do in your “spatial computing paradigm”?

•
Gradients (7)

•
Majority votes (7)

•
Movement transaction (3)

•
Atomic messages (maybe too low level) (6)

•
Compartmentalization (across ensemble) (5)

•
Reduction (maybe too high level) (1)

•
Maintaining connectedness (1)

•
Scatter/gather (0)

•
Globally unique ID (0)

•
Almost globally unique ID (4)

–
Can be achieved by generating a large random number at each node