Horn Clause Computation with DNA Molecules

In this paper, we will propose Horn clause computation as an underlying computational framework of DNA computer. Horn clause program is a subclass of the formulas of first order logic and has close relation to PROLOG language. The computational power of Horn clauses was discussed in (Tärnland, 1977) and it was shown that a finite set of Horn clauses is computationally equivalent to Turing Machine. Furthermore, it should be noted that Horn programs are adequate for representing nondeterministic computation. Thus, its parallel implementation with huge number of molecules might have possibility to overcome the computational power of conventional computers. It should also be noted that the clear logical semantics of Horn programs might enable us to accept it as a higher-level programming language of DNA computer. The aim of this paper is to propose an experimental method for implementing deduction with a subclass of Horn programs, called simple Horn programs. The computational power of this model is theoretically investigated and demonstrated with some applications to NP-complete problems.