Abstract
We investigate the local testability problem of deterministic finite automata. A locally testable language is a language with the property that for some positive 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 intermediate substrings of w of length k+1, without regard to the order in which these substrings occur. The local testability problem is, given a deterministic finite automaton, to decide whether it accepts a locally testable language or not. No polynomial time algorithm for this problem has appeared in the literature. We present an O(n2) time algorithm for the local testability problem based on two simple properties that characterize locally testable automata.
Partial support for this research was provided by the Directorate of Computer and Information Science and Engineering of the National Science Foundation under Institutional Infrastructure Grant No. CDA-8805910.
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© 1989 Springer-Verlag Berlin Heidelberg
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Kim, S., McNaughton, R., McCloskey, R. (1989). A polynomial time algorithm for the local testability problem of deterministic finite automata. In: Dehne, F., Sack, J.R., Santoro, N. (eds) Algorithms and Data Structures. WADS 1989. Lecture Notes in Computer Science, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51542-9_35
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DOI: https://doi.org/10.1007/3-540-51542-9_35
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