The following problem classes are mainstream research topics about numeration systems :

• For a given (Λ, M, D), the decision problem asks whether the triple forms a number system or not.

• The classification problem for a given radix system (Λ, M, D) is the characterization which involves the location, the number and the structure of the periodic points (finding all cycles).

• The construction problem aims at constructing a digit set D to M for which (Λ, M, D) is a number system.