On deterministic sensing $$5'\rightarrow 3'$$ Watson–Crick finite automata: a full hierarchy in 2detLIN

Abstract

Watson–Crick (abbreviated as WK) finite automata are working on double stranded DNA molecule that is also called Watson–Crick tape. Subsequently, these automata have two reading heads, one for each strand. While in traditional WK automata both heads read the whole input in the same physical direction, in $$5'\rightarrow 3'$$ WK automata the heads start from the two extremes (say $$5'$$ end of the strands) and read the input in opposite direction. In sensing $$5'\rightarrow 3'$$ WK automata the process on the input is finished when the heads meet. Since the heads of a WK automaton may read longer strings in a transition, in previous models a so-called sensing parameter took care for the proper meeting of the heads (not allowing to read the same positions of the input in the last step). Recently a new model is investigated, which works without the sensing parameter. In this paper, the deterministic counterpart is studied and is proven to accept the language class 2detLIN defined by the deterministic variant of the earlier version. However, using some of the restricted variants, e.g, all-final automata, the classes of the accepted languages are changed showing a finer hierarchy inside the class of linear context-free languages.