Quasi-deterministic 5' -> 3' Watson-Crick Automata (2208.14730v1)

Abstract: Watson-Crick (WK) finite automata are working on a Watson-Crick tape, that is, on a DNA molecule. A double stranded DNA molecule contains two strands, each having a 5' and a 3' end, and these two strands together form the molecule with the following properties. The strands have the same length, their 5' to 3' directions are opposite, and in each position, the two strands have nucleotides that are complement of each other (by the Watson-Crick complementary relation). Consequently, WK automata have two reading heads, one for each strand. In traditional WK automata both heads read the whole input in the same physical direction, but in 5'->3' WK automata the heads start from the two extremes and read the input in opposite direction. In sensing 5'->3' WK automata, the process on the input is finished when the heads meet, and the model is capable to accept the class of linear context-free languages. Deterministic variants are weaker, the class named 2detLIN, a proper subclass of linear languages is accepted by them. Recently, another specific variants, the state-deterministic sensing 5'->3' WK automata are investigated in which the graph of the automaton has the special property that for each node of the graph, all out edges (if any) go to a sole node, i.e., for each state there is (at most) one state that can be reached by a direct transition. It was shown that this concept is somewhat orthogonal to the usual concept of determinism in case of sensing 5'->3' WK automata. In this paper a new concept, the quasi-determinism is investigated, that is in each configuration of a computation (if it is not finished yet), the next state is uniquely determined although the next configuration may not be, in case various transitions are enabled at the same time. We show that this new concept is a common generalisation of the usual determinism and the state-determinism, i.e., the class of quasi-deterministic sensing 5'->3' WK automata is a superclass of both of the mentioned other classes. There are various usual restrictions on WK automata, e.g., stateless or 1-limited variants. We also prove some hierarchy results among language classes accepted by various subclasses of quasi-deterministic sensing 5'->3' WK automata and also some other already known language classes.