In formal language theory, a class of languages has **finite thickness** if for every string *s*, there are only finitely many consistent languages in . 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 satisfies the **MEF-condition** if for each string s and each consistent language L in the class, there is a minimal consistent language in, which is a sublanguage of L. Symmetrically, we say that satisfies the **MFF-condition** if for every string s there are only finitely many minimal consistent languages in . Finally, is said to have **M-finite thickness** if it satisfies both the MEF and MFF conditions.

Finite thickness implies M-finite thickness. However, there are classes that are of M-finite thickness but not of finite thickness (for example, let be a class of languages such that ).

### Other articles related to "finite thickness, finite":

**Finite Thickness**

... A class of languages has

**finite thickness**if for every string s, there are only a

**finite**number of languages in the class that are consistent with s ... that if a class of recursive languages has

**finite thickness**, then it is learnable in the limit ... A class with

**finite thickness**certainly satisfies MEF-condition and MFF-condition in other words,

**finite thickness**implies M-

**finite thickness**...

...

**Finite thickness**implies

**finite**elasticity the converse is not true ...

**Finite**elasticity and conservatively learnable implies the existence of a mind change bound

**Finite**elasticity and M-

**finite thickness**implies the existence of a mind change bound ... However, M-

**finite thickness**alone does not imply the existence of a mind change bound neither does the existence of a mind change bound imply M-

**finite**...

### Famous quotes containing the words thickness and/or finite:

“For his teeth seem for laughing round an apple.

There lurk no claws behind his fingers supple;

And God will grow no talons at his heels,

Nor antlers through the *thickness* of his curls.”

—Wilfred Owen (1893–1918)

“Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very *finite* and fixed creature, I call the classical.”

—Thomas Ernest Hulme (1883–1917)