State Complexity of Catenation Combined with Star and Reversal

This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.Comment: In Proceedings DCFS 2010, arXiv:1008.127

State complexity of union and intersection of star on k regular languages

AbstractIn this paper, we continue our study on state complexity of combined operations. We study the state complexities of L1∗∪L2∗, ⋃i=1kLi∗, L1∗∩L2∗, and ⋂i=1kLi∗ for regular languages Li, 1≤i≤k. We obtain the exact bounds for these combined operations and show that the bounds are different from the mathematical compositions of the state complexities of their component individual operations