5′→ 3′ Sensing Watson-Crick Finite Automata

DNA computers provide new paradigms of computing (Păun et al., 1998). They appeared at the end of the last century. In contrast, the theory of finite automata is well developed and intensively used in both theory and practice. The Watson-Crick automata, introduced in (Freund et al., 1997), relate to both fields. They are important in the field of (DNA) computing and have important relation to formal language and automata theory as well. Watson-Crick automata are (theoretical) devices that have two reading heads to scan the two strands of a DNA molecule and decide if the molecule is acceptable (i.e., belongs to a desired class of languages). Enzymes slide across the backbones of DNA, usually from the 5′ to 3′ ends of the strand, therefore 5′→ 3′ automata are of particular interest. We investigate several variations of Watson-Crick automata in which both heads of the automata read the doubled DNA strand from the 5′ to 3′ direction. In sensing variation, the heads sense if they meet (i.e., their distance is less than a fixed small distance). The accepted language classes of these automata are analyzed and compared to well-known language classes, such as languages of the Chomsky hierarchy. Variations such as deterministic, all-final, simple, 1-limited, and stateless 5′ → 3′ Watson-Crick automata are also detailed. From a practical point of view, the stateless variant is likely the most realistic, however all models are of theoretical interest.