State complexity of union and intersection of square and reversal on k regular languages

In the paper, we continue our study on the state complexity of combined operations on regular languages. We study the state complexities of k ∪ i=1 Li , k ∩ i=1 Li , k ∪ i=1 Li , and k ∩ i=1 Li , for regular languages Li, 1 ≤ i ≤ k. We obtain the exact bounds for these combined operations and show that the state complexities of k ∪ i=1 Li and k ∩ i=1 Li are the same as the mathematical compositions of the state complexities of their component individual operations, while, on the other hand, the state complexities of k ∪ i=1 Li and k ∩ i=1 Li are lower than the corresponding mathematical compositions.