Problemswhere

Problemswhere is a term used in theoretical computer science and problem-solving to describe a class of problem instances defined by a predicate over the instances themselves. Rather than referring to a single problem, problemswhere denotes the subset of all possible problems that satisfy certain conditions. The concept is useful for organizing, generating, and analyzing problem spaces, particularly when researchers want to study how algorithm performance varies with specific constraints.

Formally, suppose P is a universe of problem instances and W is a predicate that maps each instance p in P to true or false. The problemswhere of W is the set { p in P | W(p) = true }. W can express properties such as size, structure, resource limits, or any combination of parameters. In practice, W may be implemented as a filter, a generator constraint, or a rule in a benchmarking framework.

Applications include benchmarking and comparing algorithms across uniform subsets of problems, generating targeted test suites for stress testing, and exploring the sensitivity of results to particular problem features. Problemswhere can support automated instance generation by sampling from the predicate-defined space or by enforcing constraints during construction.

Relation to other concepts: problemswhere is related to constraint satisfaction problems, instance spaces, and problem generators. It emphasizes the selection of problems rather than solving them, and it is compatible with stochastic sampling, deterministic filtering, or hybrid approaches. Limitations include dependence on the chosen universe P and the predicate W, which can bias results if not carefully designed.

Related topics include constraint satisfaction problems, instance generators, and the notion of a problem space.