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

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−1−2ⁿ⁻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).