A Study Of Logic And Application Based On DNA Computing

Recently,with the progressive development of silicon computing,people are seeking for more Moore and more than Moore.However,with the ever-increasing demand of informa-tion storage and processing,a novel computing mode has become one of the hot research top-ics.Among all the candidates,including quantum and optic computing,molecular computing,namely DNA computing,has interested both academia and industry for its large-scale parallel computation,massive data storage and genetic information property.From silicon to DNA,molecular computing makes computation to be conducted at the molecular level.As a novel computing mode,biomolecules are become data to be manipulated.After encoding those biomolecules,a myriad of operations,including arithmatic calculation and logic computing,could be realized.The significance of molecular computing is not only the hardware transfer from silicon to DNA,but also lies in helping us to understand the self-assembly abounded in the nature.More importantly,due to its powerful data storage capacity,DNA substrate was envisioned to implement an energy-efficient Turing machine back to 1982.This means,DNA computing is promising to build the abstract Turing machine in the real world.However,the significance of DNA computing is not limited to build the abstract Turing machine in the real world,but also lies in its powerful capacity of implementing any computable valid algorithm,as well as its extensive application scenes,which are not applied to silicon-based counterpart.The research on logic and application based on DNA computing is hence profound.In short,using formal chemical reaction networks?CRNs?as an efficient Turing-complete programming language,harnessing DNA strand displacement reactions as the physical imple-mentation,this paper devotes itself in designing formal CRNs to realize both the logic func-tion and the computing power,employing ordinary differential equations?ODEs?endowed by mass-action law to demonstrate the dynamic evolution of chemical systems.In terms of logic research,combinational logic is undoubted to be the first research point of this paper.The study of sequential logic calls for a clock signal,which thus turns out to be the second research con-tent.Existing work has been done to successfully synthesize sequential logic with CRNs,which makes the rudiment of FSM to be real.On a chassis of this fact,Turing-complete CRNs can real-ize nearly any valid algorithm.Thus,this paper employs CRNs to programme message-passing algorithm?MPA?.Molecular LDPC decoder is exacting the third one to be studied in this pa-per.Considering the situation that silicon-based LDPC decoders require too many hardware resources,thus this topic could be viewed as an application study for DNA computing.Borrowing ideas from traditional electronics,especially the utilization of a Karnaugh map to construct combinational logic,this paper also employs such a Karnaugh map to aid CRN design.Totally five approaches are proposed.Considering the complete logic expression hidden in a Karnaugh map,we map it into CRNs with the assumption of such map is a configuration component.This mapping actually skips the redundant step to construct a circuit using this map.Different mappings result in totally five approaches.1).One-to-one mapping:map all independent squares into chemical reactions.2).?Karnaugh map?-aided simplified approach:a maxterm/minterm responses to a chemical.Simplified rules are different from silicon ones.Karnaugh circles here must cover a whole row or column.3).Partial mapping:only map those independent squares with logic value“1”,this method is called Approach 1.Noted that,partial mapping has three approaches,and all of them need a rate constant adjustment scheme.4).Approach 2:Based on Approach 1,this approach employs a symmetric refinement reaction.5).Approach 3:On a chassis of Approach 2,this method removes the dual-rail representation reactions for the output.Additionally,we conduct both stability and feasibility analysis for all five approaches.Based on chemical kinetics,all proposed five approaches have been proved their validness and feasibility via analyzing their ODEs.It is worth noting that,our proposal is applied to the combinational logic with N input signals.Inspired from well-studied gear systems,there exist a lot of resemblances between a clock signal and a gear.After offering the concepts that could be mapped between a gear system and a clock tree,we measure the time period and phase signal's existing time of the clock signal synthesized by CRNs.We also standardly prescribe the gear size,especially the gear teeth and diameter.This paper focuses on the CRN implementation of clock signals'duty cycle and frequency alteration,which includes frequency division and multiplication.In terms of sequential logic,this paper devotes itself in designing CRNs for synchronous sequential.According to the given sequential logic function,we can easily draw its state digram,which can be mapped into CRNs.The proposed method is based on Key-Keysmith mechanism,which is robust.In this paper,we propose a method to construct a molecular LDPC decoder based on MPA.This method is not limited to the degree of variable nodes and check nodes.It could theoret-ically implement a molecular LDPC decoder with any code length,code rate,and even any degree.Note that,the updated rule of check node messages r_jiin classic MPA is not liable to be constructed by CRN.To address this issue,we successfully derive a theoretically easy-implementation equation.Giving probability values to chemical species concentrations,the transference among species essentially realize the messages update between check nodes and variable nodes in the factor graph for an LDPC decoder.The iteration is realized by introducing a clock signal into the decoding schedule.