**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

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**languages**are only comfortable representations of the Turing machine any program on a von Neumann computer has the same properties and limitations as the Turing machine or ... Consequently every programming

**language**such as CPU level machine code, assembler, or any high level programming

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**formal languages**... scope than 'proof-theoretic', since it may be applied to properties of

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**Formal Languages**

... In formal languages, truth functions are represented by unambiguous symbols ... These symbols are called "logical connectives", "logical operators", "propositional operators", or, in classical logic, "truth-functional connectives" ...

### Famous quotes containing the words languages and/or formal:

“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)

“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more *formal* one said, “Do you think the Holy Dove could fly down with only one wing?””

—Horace Walpole (1717–1797)