CMP.4:4.1 - Define a partial choice and its completions

State what constitutes a complete candidate, when it is admissible, and which result is wanted: one witness, a best value and witness, every optimum, a count, or a counterexample. For optimization, state the criterion and its direction.

Choose a representation s of partial choices. Explain which complete candidates it represents and what information is still undecided. Include past choices when they change future feasibility or cost. If several histories have the same remaining question, CMP.3 can share that question while preserving the history-dependent contribution.

Construct extensions that cover the relevant completions. Binary inclusion/exclusion, a variable’s remaining values and legal next transitions are common forms. Overlap is permitted for finding one witness but can duplicate results; counting and enumeration need a way to handle it. A symmetry reduction needs an account of which answers it identifies and whether the recipient accepts that identification.