State Complexity of Basic Operations on Finite Languages
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The state complexity of basic operations on regular languages has been studied in ,,. Here we focus on finite languages. We show that the catenation of two finite languages accepted by an mstate and an n-state DFA, respectively, with m > n is accepted by a DFA of (m − n + 3)2 n−2 − 1 states in the two-letter alphabet case, and this bound is shown to be reachable. We also show that the tight upperbounds for the number of states of a DFA that accepts the star of an n-state finite language is 2 n−3 + 2 n−4 in the two-letter alphabet case. The same bound for reversal is 3 · 2 p−1 − 1 when n is even and 2 p − 1 when n is odd. Results for alphabets of an arbitrary size are also obtained. These upper-bounds for finite languages are strictly lower than the corresponding ones for general regular languages.
Supplementary Material (0)
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About this Chapter
- State Complexity of Basic Operations on Finite Languages
- Book Title
- Automata Implementation
- Book Subtitle
- 4th International Workshop on Implementing Automata, WIA’99 Potsdam, Germany, July 17–19, 1999 Revised Papers
- pp 60-70
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Springer-Verlag Berlin Heidelberg
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- 4. Universität Potsdam, Institut für Informatik
- 5. Institut für Informatik, Universität Potsdam
- 6. Department of Computer Science, The University of Western Ontario
- Author Affiliations
- 7. Fundamentals of Computer Science Department, Faculty of Mathematics University of Bucharest, Romania
- 8. Department of Computer Science, University of South Carolina, Columbia, SC, 29208, USA
- 9. Department of Computer Science, The University of Western Ontario, London, Ontario, Canada, N6A 5B7
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