Formal Languages
In computability theory in computer science, it is common to consider formal languages. An alphabet is an arbitrary set. A word on an alphabet is a finite sequence of symbols from the alphabet; the same symbol may be used more than once. For example, binary strings are exactly the words on the alphabet {0, 1} . A language is a subset of the collection of all words on a fixed alphabet. For example, the collection of all binary strings that contain exactly 3 ones is a language over the binary alphabet.
A key property of a formal language is the level of difficulty required to decide whether a given word is in the language. Some coding system must be developed to allow a computable function to take an arbitrary word in the language as input; this is usually considered routine. A language is called computable (synonyms: recursive, decidable) if there is a computable function f such that for each word w over the alphabet, f(w) = 1 if the word is in the language and f(w) = 0 if the word is not in the language. Thus a language is computable just in case there is a procedure that is able to correctly tell whether arbitrary words are in the language.
A language is computably enumerable (synonyms: recursively enumerable, semidecidable) if there is a computable function f such that f(w) is defined if and only if the word w is in the language. The term enumerable has the same etymology as in computably enumerable sets of natural numbers.
Read more about this topic: Computable Function
Famous quotes containing the words formal and/or languages:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“Wealth is so much the greatest good that Fortune has to bestow that in the Latin and English languages it has usurped her name.”
—William Lamb Melbourne, 2nd Viscount (1779–1848)