In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at a "window" of length two. Equivalently, it is a language recognised by a local automaton, a class of deterministic finite automaton.
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Formally, we define a language L over an alphabet A to be local if there are subsets R and S of A and a subset F of A×A such that a word w is in L if and only if the first letter of w is in R, the last letter of w is in S and no factor of length 2 in w is in F. This corresponds to the regular expression
More generally, a k-testable language L is one for which membership of a word w in L depends only on the prefix, suffix and the set of factors of w of length k; a language is locally testable if it is k-testable for some k. A local language is 2-testable.