Problemwhether

Problemwhether is not a standard technical term in most formal literature, but it is sometimes used informally to denote a class of decision problems posed as yes/no questions. In this sense, a problemwhether asks, given an input, whether a particular property holds.

Formally, if P is a property of objects from a domain D, the problemwhether P takes input x in D and outputs true if P(x) is true and false otherwise. Equivalently, it is the decision problem associated with the language L = { x in D : P(x) }. The study of such problems concerns decidability, complexity, and efficiency of determining the truth of P for arbitrary inputs.

Examples include problemwhether n is prime, problemwhether a graph is connected, or problemwhether a string belongs to a given formal language. These illustrate the typical yes/no questioning structure: given an instance, determine whether the property holds. This contrasts with search problems, which require producing a witness or solution, and with optimization problems, which seek best or extreme values.

In practice, the phrase reflects the linguistic notion of forming a yes/no question with the word “whether.” In logic and computer science, these questions are usually treated as decision problems and encoded as languages to study their computability and complexity properties. The term “problemwhether” is not universally standardized, so many authors prefer formulations like “the problem of deciding whether P(x)” or “the decision problem for P.”

Overall, the concept centers on deciding the truth of a given property for inputs, a cornerstone of decision problems in theoretical computer science and logic.