User talk:Lord Farin/Backup/Definition:Formal Language

Definition is weird
Hm, this is not how I learnt the definition of a formal language. Currently this reads:

A formal language is a structure which contains:
 * An alphabet of symbols;
 * A set of words made up of symbols from that alphabet;
 * A formal grammar which determines which words belong to the formal language and which do not.

The third bullet point seems to me extraneous. By my reckoning, a formal language consists of: As I understand it, a grammar is a way to construct a set such as $W$ and thus to define a language; what use is it to include a grammar and a set of words in the definition of a formal language? — Timwi (talk) 22:36, 18 December 2012 (UTC)
 * a set $S$ (the alphabet) and
 * a set of words $W \subseteq \left\{ { \left({ x_1, x_2, ..., x_n }\right) : \forall i, x_i \in S}\right\}$


 * I think this is done from an algorithmic perspective. Both the words and the formal grammar can be more easily realized in a computational context than the arbitrary set $W$ you propose. It seems to explain how in general formal languages are constructed (giving a grammar of WFFs); as such I think the current page is adequate and links well to most sources on the subject (though more general than most texts bother to define things). --Lord_Farin (talk) 22:44, 18 December 2012 (UTC)