Strings and Languages
A string is a finite sequence of characters. The empty string is denoted by . The concatenation of two string and is denoted by, or shorter by . Concatenating with the empty string makes no difference: . Concatenation of strings is associtive: .
For example, .
A language is a finite or infinite set of strings. Besides the usual set operations like union, intersection etc., concatenation can be applied to languages: if both and are languages, their concatenation is defined as the set of concatenations of any string from and any string from, formally . Again, the concatenation dot is often omitted for shortness.
The language consisting of just the empty string is to be distinguished from the empty language . Concatenating any language with the former doesn't make any change:, while concatenating with the latter always yields the empty language: . Concatenation of languages is associtive: .
For example, abbreviating, the set of all three-digit decimal numbers is obtained as . The set of all decimal numbers of arbitrary length is an example for an infinite language.
Read more about this topic: String Operations
Other articles related to "language, strings, string":
... Formal language theory mostly studies formalisms to describe sets of strings, such as context-free grammars and regular expressions ... and each regular expression, describes a particular set of strings ... this context, the expressive power of a formalism is the set of sets of strings its instances describe, and comparing expressive power is a matter of comparing these sets ...
... Strings Batio uses Ernie Ball guitar strings, favouring the.009 to.042 models for soloing and most rhythm guitar parts while thicker gauge strings ...
... for orchestra (1959) Overtura da Requiem for orchestra (1963) Metamorphoses for 13 Strings (1966) Tempi Rithmizati for strings, piano and percussion (1968 ...
... of its accepted forms, with any number of additional unstopped strings that can accommodate individual plucking." Additionally, in reference to these instruments ... To qualify in this category, an instrument must have at least one unfretted string lying off the main fretboard ... Further, the unfretted strings can be, and typically are, played as an open string ...
... instrument by the 18th century, with five double courses of strings, tuned in fourths ... The original bandurrias of the Medieval period had three strings ... During the Renaissance they gained a fourth string ...
Famous quotes containing the words strings and, languages and/or strings:
“Met face to face, these Indians in their native woods looked like the sinister and slouching fellows whom you meet picking up strings and paper in the streets of a city. There is, in fact, a remarkable and unexpected resemblance between the degraded savage and the lowest classes in a great city. The one is no more a child of nature than the other. In the progress of degradation the distinction of races is soon lost.”
—Henry David Thoreau (18171862)
“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 (17791848)
“How have you left the ancient love
That bards of old enjoyed in you!
The languid strings do scarcely move!
The sound is forced, the notes are few!”
—William Blake (17571827)