On Iterated Scattered Deletion

In this note, we solve an open problem of Ito et al. 2] on iterated scattered deletion. Note: Since this note has appeared in Bull. EATCS, I have been informed that this problem has been previously solved; see Ito and Silva 1], where the authors show that there exists a regular language R such that (;) + (R) is not a CFL. I am grateful to Masami Ito for pointing me to this reference. is the set of words which result from deleting y as a scattered subword from x. We extend this operation to languages L 1 ; L 2 as follows: L 1 ; L 2 = x2L 1 y2L 2 x ; y: For unexplained notions in formal language and automata theory, please see Yu 6]. For languages L 1 ; ; L k , we use the notation Q k i=1 L i = L 1 L 2 L k. We now deene an iterated scattered deletion operation 2]. Let i 1, L .