British Museum algorithm

Definition: 
A general approach to find a solution by checking all possibilities one by one, beginning with the smallest. The term refers to a conceptual, not a practical, technique where the number of possibilities are enormous.

See also breadth first search, brute force, exhaustive search.

Note: For instance, one may, in theory, find the smallest program which solves a particular problem in the following way: Generate all possible source codes of length one character. Check each one to see if it solves the problems. If not, generate and check all programs of two characters, three characters, etc. Conceptually this finds the smallest program, but in practice it takes far more time than the age of the universe.

Similar arguments can be made to show that optimizations, theorem proving, language recognition, etc. is possible or impossible