C.40:5.16 - Two good encoders need one real output history

Suppose a stipulated stream writer accepts normal and bulky jobs. Two available encoders produce valid payloads: A uses four payload units for a normal job and twelve for a bulky job; B uses eight and five respectively. These exact sizes are given for this finite exercise. The receiving requirement is at most six payload units per job. Job kind is observable before encoding, so choosing A for normal jobs and B for bulky jobs supplies the required payload sizes; neither encoder alone meets both limits.

The complete stream protocol also requires headers X, Y, X, Y in order. Each original encoder maintains its own alternating header state, initialized at X. Each works correctly alone. A selector that sends the first normal job to A and the next bulky job to B produces X followed by X, violating the protocol. The two good individual performances did not supply a correct combined operation.

In this exercise the developer may separate each encoder’s payload operation from its header generator. The available atomic emission operation reports either a successful complete output or failure with no output. Construct one stream writer that owns the actual next header, starts at X, selects the payload encoder using the observed job kind, emits the header and payload, and toggles the shared header only after an emission succeeds. On a normal job followed by a bulky job it produces X with four payload units and Y with five. Examine later alternation and a failed emission too: an unperformed output must not advance the actual stream history. The retained encoders become usable together through this additional construction and its checked conditions.

Suppose further development produces A-prime, using five payload units for a normal job and ten for a bulky one. Its standalone total over the two jobs is fifteen, smaller than A’s sixteen. In the actual arrangement with B and the same selector, however, substituting A-prime raises the total from nine to ten. Both combinations satisfy the per-job limit; when smaller total output is preferred, retain A for this combination. That feedback concerns A’s role with B and this selector. A different partner or selection rule can change the answer.

Now suppose job kind becomes available only after encoding. The previous selector can no longer use it for that action. A classification or trial-and-buffer arrangement could supply another candidate if its observation, delay and cost fit the receiving requirement. No such operation is stipulated here, so the selected combination remains unsupported under the changed condition. More retained encoders or more training examples alone supply no timely observation. Return that missing operation or a different sufficient whole way.