5' → 3' Watson-Crick Automata with Several Runs

5′ → 3′ WK-automata are Watson-Crick automata whose two heads start on opposite ends of the input word and always run in opposite directions. One full reading in both directions is called a run. We prove that the automatas’ power increases with every run more they can make. This defines an infinite hierarchy of language classes between the regular and the context-sensitive languages. This hierarchy is complemented with classes defined by several restricted variants of 5′ → 3′ WK-automata like stateless automata. Finally we show that the emptiness and the finiteness problems are undecidable for languages accepted by 5′ → 3′ WK-automata in only one run.