Space and Energy Efficient Computation with DNA Strand Displacement Systems

Abstract

Chemical reaction networks (CRN’s) are important models of molecular programming that can be realized by logically reversible, and thus energy efficient, DNA strand displacement systems (DSD’s). Qian et al. [12] showed that energy efficient DSD’s are Turing-universal; however their simulation of a computation requires space (or volume) proportional to the number of steps of the computation. Here we show that polynomially space bounded computations can be simulated in both a space and energy efficient manner using logically reversible CRN’s and DSD’s. A consequence of our proofs is that determining whether a particular molecular species can be produced from an initial pool of molecules of a CRN or DSD is PSPACE-hard, and thus also verifying the correctness of CRN’s and DSD’s is PSPACE-hard.