Computability and Complexity/Formal Languages/Other Language Classes
Other Language Classes
The language classes in the Chomsky Hierarchy do not represent an exhaustive list of the possible language classes. There are many other classes that have been defined since, many of which are defined primarily by a machine that recognizes them, and not by a simple or well-defined grammar.
One example of such a class is the Counting Languages.
Note: There should be more examples here.
For a much larger list of language classes, see wikipedia: Complexity class.