Abstract. We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. We compute the upper bounds based on the structural properties of minimal deterministic finite-state automata (DFAs) for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input DFAs. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet. 1

We investigate the state complexity of basic operations for suffix-free regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst-case for the minimal deterministic finite-state automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, Kleene star, reversal and the Boolean operations for suffix-free regular languages.

Regular languages are closed under union, intersection, complementation, Kleene-closure and reversal operations. Regular languages can be classified into infix-free, prefixfree and suffix-free. In this paper various closure properties of prefix-free regular languages are investigated and result shows that prefix-free regular languages are closed under union and concatenation. Under complementation, reverse, Kleene-closure and intersection operations prefix-free regular languages are not closed.