Problemets

Problemets are a term used to describe the smallest units of a problem that are self-contained and solvable in isolation. A problemet has a clearly specified input set and a desired output, and adheres to a defined scope that prevents it from depending on external state. The concept is intended to formalize the intuition behind problem decomposition: complex tasks can be broken into many problemets that, taken together, realize the overall goal.

Typical properties include a well-defined interface (input and output types), a finite description of the allowed operations, and a solution that can be verified independently. Problemets can be deterministic or nondeterministic; some definitions permit non-unique solutions as long as a correct one exists. They are designed to be composable: multiple problemets can be sequenced, parallelized, or nested to form larger problems, enabling modular design and analysis of algorithms.

Examples: a problemet might be 'compute the sum of two integers', 'check whether a string is a palindrome', or 'find the maximum value in a fixed-size list'. More complex problemets may involve a small graph, such as 'determine if a given 3-node graph is connected', with the caveat that the problemet's scale remains bounded. In education, problemets are used to teach divide-and-conquer strategies and to study how algorithms compose.

Criticism and usage: some scholars argue that the term is pedagogical and its formalization is variable, which can hinder cross-domain communication. Nevertheless, the problemet concept remains a useful heuristic for analyzing problem-solving workflows and software design, particularly in contexts that emphasize modular reasoning and stepwise refinement.

See also: problem, subproblem, decomposition, modularity, algorithm, computational problem.