Two-Party Watson-Crick Computations

We investigate synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input. The automata communicate by sending messages. The communication is quantitatively measured by the number of messages sent during a computation. It is shown that even the weakest non-trivial devices in question, that is, systems that are allowed to communicate constantly often only, accept non-context-free languages. We investigate the computational capacity of the devices in question and prove a strict four-level hierarchy depending on the number of messages sent. The strictness of the hierarchy is shown by means of Kolmogorov complexity. For systems with unlimited communication several properties are known to be undecidable. A question is to what extent communication has to be reduced in order to regain decidability. Here, we derive that the problems remain non-semidecidable even if the communication is reduced to a limit close to the logarithm of the length of the input. Furthermore, we show that the border between decidability and undecidability is crossed when the communication is reduced to be constant. In this case only semilinear languages can be accepted.