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
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