Volume 2214 of the series Lecture Notes in Computer Science pp 6070
State Complexity of Basic Operations on Finite Languages
 C. CâmpeanuAffiliated withFundamentals of Computer Science Department, Faculty of Mathematics University of Bucharest
 , K. CulikIIAffiliated withDepartment of Computer Science, University of South Carolina
 , Kai SalomaaAffiliated withDepartment of Computer Science, The University of Western Ontario
 , Sheng YuAffiliated withDepartment of Computer Science, The University of Western Ontario
Abstract
The state complexity of basic operations on regular languages has been studied in [9],[10],[11]. Here we focus on finite languages. We show that the catenation of two finite languages accepted by an mstate and an nstate DFA, respectively, with m > n is accepted by a DFA of (m − n + 3)2^{n−2} − 1 states in the twoletter 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 nstate finite language is 2^{n−3} + 2^{n−4} in the twoletter 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 upperbounds for finite languages are strictly lower than the corresponding ones for general regular languages.
 Title
 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
 Pages
 pp 6070
 Copyright
 2001
 DOI
 10.1007/3540455264_6
 Print ISBN
 9783540428121
 Online ISBN
 9783540455264
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2214
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Oliver Boldt ^{(4)}
 Helmut Jürgensen ^{(5)} ^{(6)}
 Editor Affiliations

 4. Universität Potsdam, Institut für Informatik
 5. Institut für Informatik, Universität Potsdam
 6. Department of Computer Science, The University of Western Ontario
 Authors

 C. Câmpeanu ^{(7)}
 K. Culik II ^{(8)}
 Kai Salomaa ^{(9)}
 Sheng Yu ^{(9)}
 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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