5′ → 3′ Watson-Crick AutomataWith Several Runs

Abstract

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 expressive power of these automata increases with every additional run that they can make, both for deterministic and non-deterministic machines. This defines two incomparable infinite hierarchies of language classes between the regular and the context-sensitive languages. These hierarchies are complemented with classes defined by several restricted variants of 5′ → 3′ WK-automata like stateless automata. Finally we show that several standard problems are undecidable for languages accepted by 5′ → 3′ WK-automata in only one run, for example the emptiness and the finiteness problems.