C.40:5.17 - Obtain corrections where the learner actually arrives

A small generator emits opening and closing parentheses, then stops. The stipulated task accepts a nonempty balanced string of at most four symbols. An available training demonstration is (): its next outputs are ( at the empty prefix, ) after (, and stop after (). These examples contain no target after ((.

In a permitted simulation, an imperfect trained generator sometimes emits a second opening symbol and reaches ((, where it stops. Its result fails the task. Replaying the remaining suffix of the original demonstration would append one closing symbol and stop, leaving ((), which also fails.

The simulator can retain the exact prefix, and a checking construction can count unmatched opening symbols. At ((, that construction supplies the target ); after fitting this target, another simulated run can reach the new prefix ((). Obtain ) there and stop at the resulting (()). Fit those targets with the still-required earlier behavior, then examine complete generation again, including (), recovery through (()), premature stops and the length limit. The targets refer to the learner’s reached prefixes, not to positions in a different demonstration. They establish corrections for this finite exercise, not a guarantee for every generator or longer language.

The teacher can itself need preparation. Suppose its response at (( is selected from the continuation strings ) and )), but its current table chooses ). In this finite exercise, the developer can evaluate both completions and change that table. Appending ) produces the invalid ((); appending )) produces (()), which passes the supplied check. Select )) for that teacher entry, use its first correction for the learner at ((, and examine the learner’s subsequent completion. The check and editable table supply the teacher-improvement operation. If either is unavailable, the original demonstration alone does not obtain this prepared teacher.

A direct counter or a fixed generator already solves this small task. Use one when it is the actual receiving problem. The example exposes what an ongoing learner-development arrangement must obtain when it is being retained for a broader justified use.

Now remove the distinguishing input: at the decision point, both (( and (()) are reported to a stateless learner as the same present symbol, and neither the prefix nor earlier observations are recoverable. The first case needs a closing symbol next to finish within four symbols; the second must stop. Training on more copies of that same input with both targets supplies no reliable distinction. Restore an adequate observation or retained state, retain the checking construction as an operating supplier, or leave that proposed learner unsupported. If the correction supplier itself cannot handle ((, its competence on () does not fill the missing target either.