Affiliations: Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia. jiraskov@saske.sk | Department of Mathematics, University of Turku, Turku FIN–20014, Finland, and Academy of Finland. alexander.okhotin@utu.fi
Note: [] Supported by VEGA grant 2/6089/26 and by the Slovak Research and Development Agency under contract APVV-0035-10 “Algorithms, Automata, and Discrete Data Structures”.
Note: [] Supported by the Academy of Finland under grants 118540 and 134860. Address for correspondence: Department of Mathematics, University of Turku, Turku FIN–20014, Finland
Abstract: The state complexity of the star of union of an m-state DFA language and an n-state DFA language is proved to be 2m+n−1−2m−1−2n−1+1 for every alphabet of at least two letters. The state complexity of the star of intersection is established as 3/4 2mn for every alphabet of six or more letters. This improves the recent results of A. Salomaa, K. Salomaa and Yu (“State complexity of combined operations”, Theoret. Comput. Sci., 383 (2007) 140–152).
Keywords: Descriptional complexity, finite automata, state complexity, combined operations
