Testing parenthesis languages (2001) [3 citations — 0 self]
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Abstract:
We continue the investigation of properties dened by formal languages. This study was initiated by Alon et. al. [AKNS99] who described an algorithm for testing properties dened by regular languages. Alon et. al. also considered several context free languages, and in particular Dyck languages, which contain strings of properly balanced parentheses. They showed that the rst Dyck language, which contains strings over a single type of pairs of parentheses, is testable in time independent of n, where n is the length of the input string. However, the second Dyck language, dened over two types of parentheses, requires qui n) queries. Here we describe a sublinear-time algorithm for testing all Dyck languages. Specically, the running time of our algorithm is ~ O(n
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