On the State Complexity of Star of Union and Star of Intersection

Authors:
Galina Jirásková;Alexander Okhotin
Affiliations:
(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”.) Mathematical Ins ...;(Correspd.) (Supported by the Academy of Finland under grants 118540 and 134860.) Department of Mathematics, University of Turku, Turku FIN-20014, Finland, and Academy of Finland. alexander.okhoti ...
Venue:
Fundamenta Informaticae
Year:
2011

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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 2 m+n−1−2 m−1−2 n−1+1 for every alphabet of at least two letters. The state complexity of the star of intersection is established as 3/4 2 mn 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).