On the Intrinsic Complexity of Language Identi

A new investigation of the complexity of language identi cation is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identi cation, employs notions of `weak' and `strong' reduction between learnable classes of languages. The intrinsic complexity of several classes are considered and the results agree with the intuitive di culty of learning these classes. Several complete classes are shown for both the reductions and it is also established that the weak and strong reductions are distinct. An interesting result is that the self referential class of Wiehagen in which the minimal element of every language is a grammar for the language and the class of pattern languages introduced by Angluin are equivalent in the strong sense. This study has been in uenced by a similar treatment of function identication by Freivalds, Kinber, and Smith. E-mail: [email protected]