Generating DNA Code Words Using Forbidding and Enforcing Systems

Research in DNA computing was initiated by Leonard Adleman in 1994 when he solved an instance of an NP-complete problem solely by molecules. DNA code words arose in the attempt to avoid unwanted hybridizations of DNA strands for DNA based computations. Given a set of constraints, generating a large set of DNA strands that satisfy the constraints is an important problem in DNA computing. On the other hand, motivated by the non-determinism of molecular reactions, A. Ehrenfeucht and G. Rozenberg introduced forbidding and enforcing systems (fe-systems) as a model of computation that defines classes of languages based on two sets of constraints. We attempt to establish a connection between these two areas of research in natural computing by characterizing a variety of DNA codes that avoid certain types of cross hybridizations by fe-systems. We show that one fe-system can generate the entire class of DNA codes of a certain property, for example θ-kcodes, and confirm some properties of DNA codes through fe-systems. We generalize by fe-systems some known methods of generating good DNA code words which have been tested experimentally.