Sun Jan 27 22:11:52 CET 2013
Composition of structure: commutation of space and time combinators
Problems: how to individually name dimensions?
What I'm looking at is loop nesting:
- state machine threading the time dimension (i.e. filter)
- state machine threading the space dimension (summation of output of a couple of filters)
- any other form of nesting
Each "feedback" operation stores state at a particular loop level.
How to identify this syntactically?
Whether these levels commute depends on the commutation of the
operations used. For summation there is no problem.
Example: sum a bank of integrators (summers).
signals s_n(t) n : 1..N t : 1..T
the integrators sum each individual signal into N integrated streams
the output at any particular moment in time is the "spatial" integral.
the trouble now is: when I use the `feedback' mechanism to implement
the integrators, does the feedback correspond to the time or space
This is all quite simple when all multi-dimensionality is named
explicitly. It is probably safe to assume that state feedback always
refers to the inner-most loop.
A more concrete example:
for t in Time:
bus = 0;
for f in Freqs:
bus += osc(f)