To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Alphabet (formal languages)

From Wikipedia, the free encyclopedia

In formal language theory, an alphabet, sometimes called a vocabulary, is a non-empty set of indivisible symbols/characters/glyphs,[1] typically thought of as representing letters, characters, digits, phonemes, or even words.[2][3] Alphabets in this technical sense of a set are used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and, depending on its purpose, may be finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., ), or even uncountable (e.g., ).

Strings, also known as "words" or "sentences", over an alphabet are defined as a sequence of the symbols from the alphabet set.[4] For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is {0,1}, the binary alphabet, and a "00101111" is an example of a binary string. Infinite sequences of symbols may be considered as well (see Omega language).

It is often necessary for practical purposes to restrict the symbols in an alphabet so that they are unambiguous when interpreted. For instance, if the two-member alphabet is {00,0}, a string written on paper as "000" is ambiguous because it is unclear if it is a sequence of three "0" symbols, a "00" followed by a "0", or a "0" followed by a "00".

YouTube Encyclopedic

  • 1/5
    Views:
    103 239
    81 654
    185 655
    26 298
    4 036
  • [Discrete Mathematics] Formal Languages
  • Introduction to Formal Grammars
  • symbol, alphabet, string | basic definations | TOC | Lec-2 | Bhanu Priya
  • Introduction to Grammars
  • Alphabets and Strings in Discrete Math

Transcription

Notation

If L is a formal language, i.e. a (possibly infinite) set of finite-length strings, the alphabet of L is the set of all symbols that may occur in any string in L. For example, if L is the set of all variable identifiers in the programming language C, L's alphabet is the set { a, b, c, ..., x, y, z, A, B, C, ..., X, Y, Z, 0, 1, 2, ..., 7, 8, 9, _ }.

Given an alphabet , the set of all strings of length over the alphabet is indicated by . The set of all finite strings (regardless of their length) is indicated by the Kleene star operator as , and is also called the Kleene closure of . The notation indicates the set of all infinite sequences over the alphabet , and indicates the set of all finite or infinite sequences.

For example, using the binary alphabet {0,1}, the strings ε, 0, 1, 00, 01, 10, 11, 000, etc. are all in the Kleene closure of the alphabet (where ε represents the empty string).

Applications

Alphabets are important in the use of formal languages, automata and semiautomata. In most cases, for defining instances of automata, such as deterministic finite automata (DFAs), it is required to specify an alphabet from which the input strings for the automaton are built. In these applications, an alphabet is usually required to be a finite set, but is not otherwise restricted.

When using automata, regular expressions, or formal grammars as part of string-processing algorithms, the alphabet may be assumed to be the character set of the text to be processed by these algorithms, or a subset of allowable characters from the character set.

See also

References

  1. ^ Fletcher, Peter; Hoyle, Hughes; Patty, C. Wayne (1991). Foundations of Discrete Mathematics. PWS-Kent. p. 114. ISBN 0-53492-373-9. An alphabet is a nonempty finite set the members of which are called symbols or characters.
  2. ^ Ebbinghaus, H.-D.; Flum, J.; Thomas, W. (1994). Mathematical Logic (2nd ed.). New York: Springer. p. 11. ISBN 0-387-94258-0. By an alphabet we mean a nonempty set of symbols.
  3. ^ Rosen, Kenneth H. (2012). Discrete Mathematics and Its Applications (PDF) (7th ed.). New York: McGraw Hill. pp. 847–851. ISBN 978-0-07-338309-5. A vocabulary (or alphabet) V is a finite, nonempty set of elements called symbols. A word (or sentence) over V is a string of finite length of elements of V.
  4. ^ Rautenberg, Wolfgang (2010). A Concise Introduction to Mathematical Logic (PDF) (Third ed.). Springer. p. xx. ISBN 978-1-4419-1220-6. If 𝗔 is an alphabet, i.e., if the elements 𝐬 ∈ 𝗔 are symbols or at least named symbols, then the sequence (𝐬1,...,𝐬n)∈𝗔n is written as 𝐬1···𝐬n and called a string or a word over 𝗔.

Literature

This page was last edited on 3 September 2024, at 06:39
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.