How are lookup tables described from the perspective of complexity theory? Lookup tables can convert a piece of computational time into space. I remember that it was a part of a complexity theory course, but I cannot recall how it's called in its terms. I know how to use lookup tables in code to increase performance of my applications, so I don't need a definition of it in common sense.

I want to know a formal definition of an approach like lookup tables in complexity theory.
Lookup tables take a key, and either provide a value according to the key or tell you that there is no value under this key. 

Time and space requirements will depend on the implementation. It's usually not further mentioned if it is obvious what kind of implementation a reasonable person would use.