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Abstract
We give an algebraic characterization of a new variety of languages that will be called bilateral locally testable languages and denoted as BLT. Given k>0, the membership of a word x to a BLT (k-BT) language can be decided by means of exploring the segments of length k of x, as well as considering the order of appearance of those segments when we scan the prefixes and the suffixes of x. In this paper, we also characterize the syntactic semigroup of BLT languages in terms of the equations of the variety they belong to, as well as in terms of the join of two previously studied varieties.
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