Design of Four-bit Subtracter Using Excess-3 Code Rules Based on DNA Domain Coding
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摘要: DNA分子逻辑电路的设计是DNA计算领域的重要研究方向。该文针对当前双轨分子逻辑电路复杂度高、响应时间慢的问题，提出一种基于域编码策略的DNA逻辑电路设计的新方法。该文设计了“多输入1输出”逻辑运算模块，构建了扇出门和放大器，并利用所构建的电路模块搭建了4位平方根分子逻辑电路，与经典的双轨策略下的4位平方根电路相比，反应物的数量由双轨的130种降低为61种，系统响应时间缩减为双轨的1/24，大大简化了电路的复杂度，提高了系统的响应速度，进一步验证了域编码策略在分子逻辑电路设计中的有效性。为了深度解析基于域编码策略的大规模复杂分子逻辑电路的设计思想，该文构造了“余三码四位减法器”，为设计大规模功能性DNA逻辑电路提供了更多的解决方案。Abstract: The design of DNA molecular logic circuits is an important direction in the field of DNA computing. Considering the problems of high complexity and slow response time for dual rail molecular logic circuits, a new strategy based on DNA domain coding is proposed in this study, which is used to construct molecular logic circuits. In this paper, the operation modules of “multiple-inputs-one-output” are introduced, and the fan-out gates and amplification gates are also constructed. Then, the molecular logic circuit to solve four-bits-square-rooting is formed with these logic computing modules designed in this paper. Compared with the four-bit square root circuit under the classical dual-track strategy, the number of reactants is reduced from 130 to 61, and the system response time is reduced to 1 / 24 of the dual-track strategy, which simplifies greatly the complexity of the circuit and improves the response speed of the system. It verifies further the effectiveness of the domain coding strategy in the design of molecular logic circuits. In order to analyze further the design concept for large-scale complicated molecular logic circuits based on domain coding, a four-bit excess-3 code subtracter is constructed, which provides more solutions for designing large-scale functional DNA logic circuits.
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Key words:
- Domain coding /
- DNA strand displacement /
- Dual rail /
- Excess-3 code /
- Subtracter
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表 1 DNA信号链及逻辑值
DNA信号链 输入/输出 逻辑值 <j1L^ b j1R^ T^ u1L^ a u1R^> A0 0 <j3L^ b j3R^ T^ u3L^ a u3R^> A1 0 <j5L^ b j5R^ T^ u5L^ a u5R^> A2 0 <j7L^ b j7R^ T^ u7L^ b u7R^> A3 1 <j2L^ b j2R^ T^ u2L^ b u2R^> B0 1 <j4L^ b j4R^ T^ u4L^ a u4R^> B1 0 <j6L^ b j6R^ T^ u6L^ b u6R^> B2 1 <j8L^ b j8R^ T^ u8L^ a u8R^> B3 0 <j0L^ b j0R^ T^ u0L^ a u0R^> H0 0 <j9L^ b j9R^ T^ u9L^ a u9R^> I0 0 <j10L^ b j10R^ T^ u10L^ b u10R^> D0 1 <j11L^ b j11R^ T^ u11L^ b u11R^> D1 1 <j12L^ b j12R^ T^ u12L^ a u12R^> D2 0 <j13L^ b j13R^ T^ u13L^ a u13R^> D3 0 <wL^ a wR^ fluor01> Y00 0 <pL^ b pR^ fluor12> Y11 1 <qL^ b qR^ fluor22> Y21 1 <mL^ a mR^ fluor31> Y30 0 <nL^ a nR^ fluor33> I40 0 
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