Finite thickness

In formal language theory, a class of languages $mathcal\; L$ has finite thickness if for every string "s", there are only finite consistent languages in $mathcal\; L$. This condition was introduced by Dana Angluin in connection with learning, as a sufficient condition for language identification in the limit. The related notion of M-finite thickness

We say that $mathcal\; L$ satisfies the MEF-condition if for each string s and each consistent language L in the class, there is a minimal consistent language in $mathcal\; L$, which is a sublanguage of L. Symmetrically, we say that $mathcal\; L$ satisfies the MFF-condition if for every string s there are only finite minimal consistent languages in $mathcal\; L$. Finally, $mathcal\; L$ is said to have M-finite thickness if it satisfies both the MEF and MFF conditions.

M-finite thickness should be compared with finite thickness. While finite thickness implies the existence of a mind change bound, M-finite thickness does not. For example, let $\{L\_n\}$ be a class of languages such that $L\_0\; subseteq\; L\_1\; subseteq\; ldots$ then there is no mind change bound for this class.