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A Polynomial time Algorithm for the Local Testability Problem of Deterministic Finite Automata
October 1991 (vol. 40 no. 10)
pp. 1087-1093

The local testability problem of deterministic finite automata is investigated. A locally testable language is a language with the property that, for some nonnegative integer k, whether or not a word w is in the language depends on (1) the prefix and suffix of w of length k, and (2) the set of substrings of w length k+1, without regard to the order in which these substrings occur. The local testability problem is, given a deterministic finite automation, to decide whether or not it accepts a locally testable language. The authors present an O(n/sup 2/) time algorithm for the local testability problem based on two simple properties that characterize locally testable automata.

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Index Terms:
polynomial time algorithm; local testability; deterministic finite automata; locally testable language; nonnegative integer; word; prefix; suffix; substrings; computational complexity; deterministic automata; finite automata; formal languages.
Citation:
S.M. Kim, R. McNaughton, R. McCloskey, "A Polynomial time Algorithm for the Local Testability Problem of Deterministic Finite Automata," IEEE Transactions on Computers, vol. 40, no. 10, pp. 1087-1093, Oct. 1991, doi:10.1109/12.93741
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