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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.
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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