Deletion operations: closure properties.dvi

The paper studies some variants of deletion operations which generalize the left/right quotient of languages. The main emphasis is put on how these deletions can be expressed as a combination of other operations, and on closure properties of various language families under deletion. Some results are the expected ones: the sequential (iterated sequential, dipolar) deletion from a regular language produces a regular set regardless of the complexity of the deleted language. On the other hand, it still remains a challenging open problem whether or not the family of regular languages is closed under iterated parallel deletion with singletons.