Alternation (formal language theory)

In <a href="/facts/Formal_language/crDTyP8q">formal language theory</a> and <a href="/facts/Pattern_matching/CEwptMs9">pattern matching</a>, alternation is the <a href="/facts/Union_(set_theory)/KVVXKfWl">union</a> of two sets of strings, or equivalently the <a href="/facts/Logical_disjunction/jbI2EGlM">logical disjunction</a> of two patterns describing sets of strings.
<a href="/facts/Regular_language/ahxw67T1">Regular languages</a> are <a href="/facts/Regular_language/ahxw67T1">closed</a> under alternation, meaning that the alternation of two regular languages is again regular. In implementations of <a href="/facts/Regular_expression/KFL3veHX">regular expressions</a>, alternation is often expressed with a vertical bar connecting the expressions for the two languages whose union is to be matched, while in more theoretical studies the <a href="/facts/Plus_sign/6RJD4Xt9">plus sign</a> may instead be used for this purpose. The ability to construct <a href="/facts/Finite_automaton/GMusWd0a">finite automata</a> for unions of two regular languages that are themselves defined by finite automata is central to the equivalence between regular languages defined by automata and by regular expressions.
Other classes of languages that are closed under alternation include <a href="/facts/Context-free_language/sHDxB5So">context-free languages</a> and <a href="/facts/Recursive_language/4R0zBWJE">recursive languages</a>.
The vertical bar notation for alternation is used in the <a href="/facts/SNOBOL/cdF7ezMJ">SNOBOL</a> language and some other languages.
In formal language theory, alternation is <a href="/facts/Commutative/WaYxJLxd">commutative</a> and <a href="/facts/Associative/EQX8lV6r">associative</a>. This is not in general true of the form of alternation used in pattern-matching languages, because of the side-effects of performing a match in those languages.

Alternation (formal language theory) open-in-new

Alternation (formal language theory)