Horn Clause Computation by Self-assembly of DNA Molecules

Abstract

Kobayashi proposed Horn clause computation by DNA molecules, which is more suitable for expressing complex algorithms than other models for DNA computing. This paper describes a new implementation of Horn clause computation by DNA. It employs branching DNA molecules for representing Horn clauses. As derivations are realized by self-assembly of such molecules, the implementation requires only a constant number of laboratory operations. Furthermore, it deals with first-order Horn clauses with some restrictions. In order to realize first-order logic, we implement variable substitutions by string tiling proposed by Winfree, et al. As we show the computational power of a Horn clause program in our model, we give another proof that a polynomial number of operations using self-assembly of DNA molecules can compute any problem in NP.