C.29.2:4.1 - Specify the answer before selecting its representation

State the admitted inputs and the answer the receiver needs. Say whether the result is a value, a witness satisfying a condition, a bound, an approximation or a continuing response to inputs. These are illustrative result forms; choose the one used by the task.

Distinguish the answer condition from the proposed calculation. For a value, ask how it will be obtained. For a witness, ask how candidates will be constructed and tested. For a negative answer, ask what establishes that no admitted witness was missed. A search that eventually finds a witness need not decide the cases in which none exists.

Make an approximation requirement operational. |y_hat - y| <= epsilon means an absolute error bound on the requested quantity; relative error uses a different comparison and needs care near zero. A probability guarantee must state what is random and the event whose probability is bounded. Neither a small residual in a different equation nor a favorable average automatically supplies the required result.

For stochastic computation, distinguish a requested distribution, samples from it and an estimated statistic. Those outputs require different constructions and resources. For an approximate distribution, name the events, statistics or distance over which accuracy is required. A distribution’s definition does not by itself supply a sampler; a sample average needs an argument connecting it with the requested population quantity.

Identify an input distinction that would change the answer. If two such inputs have the same proposed representation, retain the missing information, add an obtainable input, restrict the admitted cases, or obtain agreement to answer a weaker question. C.29.1 develops the preservation argument when that comparison is itself the difficulty.