## Quantitative Generalizations of Languages

*Thomas A. Henzinger*

A *language* is a set of words, i.e., a function from words to booleans.
There are two different quantitative generalizations of languages.
A *probabilistic language* is a set of probability spaces on words.
A *numerical language* is a function from words to reals, where the
value of a word represents a cost.
We review some classical problems about languages in these two quantitative
settings.

*Proceedings of the
11th International Conference on Developments in Language Theory*
(DLT),
Lecture Notes in Computer Science 4588,
Springer, 2007, pp. 20-22.

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