String operations: Difference between revisions

Revision as of 15:29, 20 December 2024

Revision as of 22:27, 8 May 2025

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==Strings and languages==

A string is a '''finite''' sequence of undefined objects called ''characters'' or ''symbols'', usually taken to be digits, letters of the alphabet, or similar.

The unique sequence of length 0 is called the [[empty string]] is, denoted by <math>\varepsilon</math> or sometimes <math>\lambda</math>.

The concatenation of two string <math>s</math> and <math>t</math> is denoted by <math>s \cdot t</math>, or shorter by <math>s t</math>.

Concatenating with theThe empty string makesis noa differenceneutral element for concatenation: <math>s \cdot \varepsilon = s = \varepsilon \cdot s</math> for all <math>s</math>.

Concatenation of strings is [[associative]]: <math>s \cdot (t \cdot u) = (s \cdot t) \cdot u</math>.