5′ → 3′ Watson-Crick Automata With Several Runs

Authors:
Peter Leupold;Benedek Nagy
Affiliations:
(Correspd.) (This work was done in part by Jap. Soc. for the Promotion of Science under grant number P07810 and in part, by the Alexander von Humboldt-Stiftung) Fachbereich Elektrotechnik/Informat ...;(This work was done in part during a visit of Benedek Nagy in Kyoto under a project funded by the (TéT) and during a visit in Kassel funded by a bilateral project by the (Balassi Institute) a ...
Venue:
Fundamenta Informaticae - Non-Classical Models of Automata and Applications
Year:
2010

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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.