On the descriptional complexity of Watson–Crick automata

Watson–Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper, we continue the investigation of descriptional complexity of Watson–Crick automata initiated by Păun et al. [A. Păun, M. Păun, State and transition complexity of Watson–Crick finite automata, in: G. Ciobanu, G. Paun (Eds.), Fundamentals of Computation Theory, FCT’99, in: LNCS, vol. 1684, 1999, pp. 409–420]. In particular, we show that any finite language, as well as any unary regular language, can be recognized by a Watson–Crick automaton with only two, and respectively three, states. Also, we formally define the notion of determinism for these systems. Contrary to the case of non-deterministic Watson–Crick automata, we show that, for deterministic ones, the complementarity relation plays a major role in the acceptance power of these systems.