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Assume we have a number of transducers with limited information processing capabilities. Are there theoretical results (proofs) on how these transducers can be combined by some sort of communication into one joint transducer to reach a maximum of information processing capabilities? Does this work for universal transducers or only for certain problems?

Illustrative example: Let's say I have 3 signal-processing computers and need to combine them to steer a self-driving car. The cameras and other sensors provide a lot of information, e.g., x GBit/s. Each single computer would be overwhelmed by the amount of information. But by combining the computers the information processing capabilities might be sufficient. Are there theoretical results on how or how not to do that to make the best use of the available computers?

Background: I recently came across Stafford Beer's "Viable Systems Model". In my interpretation, it claims to be such an optimal architecture for combination. But I have only found anecdotal evidence or reference to common sense for most parts of that claim, no formal proof.

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  • $\begingroup$ I am not optimistic that you're going to find what you're hoping for. You'd have to define what you mean by 'optimal' (in what sense?), or how you plan to measure processing capability (normally not something that is measured in a fine-grained way for theoretical analysis). I'm not familiar with the Viable Systems Model, but after a quick skim, it looks like nothing I'd want to try to emulate, if I cared about formal proof or computer science theory, so it doesn't change my impressions about you being unlikely to find what you want from CS theory. $\endgroup$ – D.W. Jun 2 at 8:03
  • $\begingroup$ Actually, I'm not hoping for much ;) Partial proofs, similar problems or non-trivial negative results (e.g., "optimal designs do not do ...") would also be interesting. If it's currently an unsolved problem, that's also good to know. And if anybody managed to find a less vague definition of the problem, that would also be a large step forwards. Regarding "processing capabilities", I had something like "Bits per unit of time" (in the cybernetic sense) in mind. $\endgroup$ – Tobias B. Jun 3 at 16:42
  • $\begingroup$ I'm not familiar with what the "bits per unit of time" metric is, how it measures processing capabilities, or what you mean by a cybernetic sense -- perhaps you could edit the question to define that metric and how you propose to measure processing capability. $\endgroup$ – D.W. Jun 3 at 18:28

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